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Pineapple
Introduction
The purpose of this page will be to show how to play the initial hand decision in the poker game Pineapple. For those who don't know, Pineapple is played like Texas Hold 'Em, except the player is dealt three hole cards and must discard one after an initial round of betting and before the flop. This is not to be confused with Crazy Pineapple, where the discard decision is made just before the Turn, or Lazy Pineapple, where the player holds onto all three throughout the game.
This page only endeavors to cover the decision on which card to discard and the power of each starting hand. Through the page you will find expected value statistics. This is how much the player can expect to get back based on a one unit ante. For example, an expected return of 1.000 would be breaking even.
A term you will see a lot on this page is "penalty," which I get from video poker. It means discarding a card which could be potentially helpful. To be specific, a rank penalty is the card you discard after being dealt a three of a kind. This is a heartbreaking hand to get in Pineapple, because you must throw one of the cards away. Not only does this lower the value of your hand, but there is one less card in the deck to improve your pair. Suit penalties are much more common. If your discard is suited to one of the cards you're keeping, it lowers the chances of making a flush. The ideal situation is no penalty of either kind.
Assumptions
This page assumes a six-player game where nobody ever folds or raises. Each player antes one unit and the best hand at the end wins.
Three of a Kind
The strategy for being dealt a three of a kind is simple — hold any two cards.
The following table shows the expected return of holding any two cards when dealt a three of a kind.
Dealt Three of Kind
Rank | Expected Return |
---|---|
A | 2.425 |
K | 1.925 |
Q | 1.563 |
J | 1.297 |
10 | 1.084 |
9 | 0.899 |
8 | 0.777 |
7 | 0.687 |
6 | 0.624 |
5 | 0.571 |
4 | 0.521 |
3 | 0.483 |
2 | 0.448 |
Pair without Suit Penalty
The strategy with any pair is simple — hold the pair.
The following table shows the expected return for both viable ways to play when dealt a pair and a singleton, when the singleton is not suited to either of the cards in the pair. Either you keep the pair or the singleton and either card in the pair. As you can see, the table shows holding the pair is always has the greater expected value, by far.
Dealt Three of Kind
Rank | Singleton | Pair | Two Singletons |
---|---|---|---|
A | K | 2.708 | 1.289 |
A | Q | 2.719 | 1.159 |
A | J | 2.729 | 1.059 |
A | 10 | 2.740 | 0.985 |
A | 9 | 2.739 | 0.827 |
A | 8 | 2.734 | 0.785 |
A | 7 | 2.736 | 0.753 |
A | 6 | 2.737 | 0.722 |
A | 5 | 2.734 | 0.777 |
A | 4 | 2.719 | 0.753 |
A | 3 | 2.701 | 0.728 |
A | 2 | 2.674 | 0.694 |
K | A | 2.392 | 1.276 |
K | Q | 2.224 | 1.082 |
K | J | 2.237 | 0.999 |
K | 10 | 2.245 | 0.936 |
K | 9 | 2.246 | 0.784 |
K | 8 | 2.243 | 0.683 |
K | 7 | 2.245 | 0.661 |
K | 6 | 2.247 | 0.641 |
K | 5 | 2.245 | 0.622 |
K | 4 | 2.234 | 0.603 |
K | 3 | 2.219 | 0.582 |
K | 2 | 2.201 | 0.562 |
Q | A | 1.999 | 1.147 |
Q | K | 1.994 | 1.080 |
Q | J | 1.865 | 0.975 |
Q | 10 | 1.880 | 0.920 |
Q | 9 | 1.876 | 0.773 |
Q | 8 | 1.877 | 0.676 |
Q | 7 | 1.879 | 0.592 |
Q | 6 | 1.881 | 0.580 |
Q | 5 | 1.880 | 0.564 |
Q | 4 | 1.873 | 0.543 |
Q | 3 | 1.859 | 0.525 |
Q | 2 | 1.847 | 0.509 |
J | A | 1.702 | 1.052 |
J | K | 1.696 | 0.998 |
J | Q | 1.696 | 0.971 |
J | 10 | 1.601 | 0.931 |
J | 9 | 1.600 | 0.792 |
J | 8 | 1.599 | 0.696 |
J | 7 | 1.601 | 0.610 |
J | 6 | 1.603 | 0.537 |
J | 5 | 1.606 | 0.523 |
J | 4 | 1.597 | 0.506 |
J | 3 | 1.591 | 0.488 |
J | 2 | 1.582 | 0.474 |
10 | A | 1.466 | 0.980 |
10 | K | 1.465 | 0.934 |
10 | Q | 1.464 | 0.918 |
10 | J | 1.465 | 0.926 |
10 | 9 | 1.388 | 0.823 |
10 | 8 | 1.388 | 0.734 |
10 | 7 | 1.388 | 0.650 |
10 | 6 | 1.394 | 0.569 |
10 | 5 | 1.394 | 0.497 |
10 | 4 | 1.388 | 0.481 |
10 | 3 | 1.383 | 0.465 |
10 | 2 | 1.377 | 0.453 |
9 | A | 1.284 | 0.815 |
9 | K | 1.288 | 0.767 |
9 | Q | 1.286 | 0.755 |
9 | J | 1.287 | 0.769 |
9 | 10 | 1.288 | 0.803 |
9 | 8 | 1.223 | 0.720 |
9 | 7 | 1.224 | 0.663 |
9 | 6 | 1.226 | 0.591 |
9 | 5 | 1.226 | 0.513 |
9 | 4 | 1.225 | 0.438 |
9 | 3 | 1.221 | 0.426 |
9 | 2 | 1.216 | 0.414 |
8 | A | 1.159 | 0.774 |
8 | K | 1.159 | 0.669 |
8 | Q | 1.160 | 0.655 |
8 | J | 1.163 | 0.672 |
8 | 10 | 1.162 | 0.708 |
8 | 9 | 1.159 | 0.708 |
8 | 7 | 1.110 | 0.688 |
8 | 6 | 1.110 | 0.635 |
8 | 5 | 1.112 | 0.560 |
8 | 4 | 1.109 | 0.479 |
8 | 3 | 1.108 | 0.407 |
8 | 2 | 1.103 | 0.398 |
7 | A | 1.059 | 0.739 |
7 | K | 1.063 | 0.649 |
7 | Q | 1.066 | 0.577 |
7 | J | 1.068 | 0.584 |
7 | 10 | 1.069 | 0.620 |
7 | 9 | 1.062 | 0.643 |
7 | 8 | 1.065 | 0.673 |
7 | 6 | 1.021 | 0.661 |
7 | 5 | 1.027 | 0.609 |
7 | 4 | 1.024 | 0.532 |
7 | 3 | 1.024 | 0.451 |
7 | 2 | 1.022 | 0.383 |
6 | A | 0.989 | 0.713 |
6 | K | 0.994 | 0.629 |
6 | Q | 0.994 | 0.564 |
6 | J | 1.000 | 0.515 |
6 | 10 | 1.000 | 0.541 |
6 | 9 | 0.997 | 0.568 |
6 | 8 | 0.996 | 0.617 |
6 | 7 | 0.995 | 0.650 |
6 | 5 | 0.962 | 0.643 |
6 | 4 | 0.961 | 0.584 |
6 | 3 | 0.959 | 0.508 |
6 | 2 | 0.960 | 0.429 |
5 | A | 0.931 | 0.775 |
5 | K | 0.935 | 0.613 |
5 | Q | 0.937 | 0.552 |
5 | J | 0.939 | 0.507 |
5 | 10 | 0.943 | 0.476 |
5 | 9 | 0.940 | 0.494 |
5 | 8 | 0.940 | 0.543 |
5 | 7 | 0.940 | 0.597 |
5 | 6 | 0.937 | 0.635 |
5 | 4 | 0.911 | 0.633 |
5 | 3 | 0.906 | 0.571 |
5 | 2 | 0.909 | 0.500 |
4 | A | 0.882 | 0.749 |
4 | K | 0.887 | 0.590 |
4 | Q | 0.891 | 0.530 |
4 | J | 0.891 | 0.487 |
4 | 10 | 0.893 | 0.458 |
4 | 9 | 0.894 | 0.420 |
4 | 8 | 0.891 | 0.460 |
4 | 7 | 0.895 | 0.514 |
4 | 6 | 0.891 | 0.570 |
4 | 5 | 0.891 | 0.623 |
4 | 3 | 0.866 | 0.534 |
4 | 2 | 0.864 | 0.478 |
3 | A | 0.843 | 0.723 |
3 | K | 0.848 | 0.568 |
3 | Q | 0.850 | 0.509 |
3 | J | 0.852 | 0.467 |
3 | 10 | 0.853 | 0.440 |
3 | 9 | 0.851 | 0.404 |
3 | 8 | 0.854 | 0.386 |
3 | 7 | 0.853 | 0.429 |
3 | 6 | 0.853 | 0.488 |
3 | 5 | 0.851 | 0.556 |
3 | 4 | 0.851 | 0.525 |
3 | 2 | 0.829 | 0.440 |
2 | A | 0.816 | 0.683 |
2 | K | 0.818 | 0.544 |
2 | Q | 0.823 | 0.489 |
2 | J | 0.823 | 0.445 |
2 | 10 | 0.826 | 0.421 |
2 | 9 | 0.824 | 0.386 |
2 | 8 | 0.823 | 0.374 |
2 | 7 | 0.826 | 0.360 |
2 | 6 | 0.824 | 0.403 |
2 | 5 | 0.824 | 0.478 |
2 | 4 | 0.823 | 0.459 |
2 | 3 | 0.821 | 0.431 |
Pair with Suit Penalty
The strategy with any pair is simple — hold the pair.
The following table shows the expected return for all three possible plays when dealt a pair and a singleton, when the singleton is suited to one of the cards in the pair. Being suited is bad, because it lowers the chance of forming a flush when holding the pair. As you can see, the table shows holding the pair is always has the greatest expected value, by far.
Dealt Three of Kind
Rank | Singleton | Pair | Suited Singletons |
Unsuited Singletons |
---|---|---|---|---|
A | K | 2.678 | 1.496 | 1.272 |
A | Q | 2.690 | 1.379 | 1.143 |
A | J | 2.704 | 1.287 | 1.045 |
A | 10 | 2.714 | 1.224 | 0.975 |
A | 9 | 2.712 | 1.080 | 0.820 |
A | 8 | 2.707 | 1.042 | 0.777 |
A | 7 | 2.708 | 1.013 | 0.745 |
A | 6 | 2.710 | 0.986 | 0.713 |
A | 5 | 2.708 | 1.037 | 0.768 |
A | 4 | 2.691 | 1.014 | 0.744 |
A | 3 | 2.672 | 0.995 | 0.722 |
A | 2 | 2.650 | 0.962 | 0.687 |
K | A | 2.378 | 1.485 | 1.250 |
K | Q | 2.205 | 1.300 | 1.072 |
K | J | 2.214 | 1.221 | 0.986 |
K | 10 | 2.222 | 1.168 | 0.926 |
K | 9 | 2.223 | 1.026 | 0.773 |
K | 8 | 2.224 | 0.936 | 0.675 |
K | 7 | 2.224 | 0.915 | 0.652 |
K | 6 | 2.226 | 0.899 | 0.635 |
K | 5 | 2.226 | 0.884 | 0.618 |
K | 4 | 2.210 | 0.863 | 0.594 |
K | 3 | 2.198 | 0.846 | 0.576 |
K | 2 | 2.181 | 0.828 | 0.557 |
Q | A | 1.984 | 1.367 | 1.119 |
Q | K | 1.980 | 1.295 | 1.057 |
Q | J | 1.849 | 1.192 | 0.961 |
Q | 10 | 1.858 | 1.145 | 0.911 |
Q | 9 | 1.856 | 1.007 | 0.762 |
Q | 8 | 1.858 | 0.921 | 0.668 |
Q | 7 | 1.865 | 0.848 | 0.587 |
Q | 6 | 1.858 | 0.834 | 0.573 |
Q | 5 | 1.860 | 0.822 | 0.558 |
Q | 4 | 1.854 | 0.803 | 0.539 |
Q | 3 | 1.841 | 0.787 | 0.521 |
Q | 2 | 1.828 | 0.769 | 0.503 |
J | A | 1.686 | 1.280 | 1.024 |
J | K | 1.687 | 1.221 | 0.975 |
J | Q | 1.684 | 1.189 | 0.953 |
J | 10 | 1.587 | 1.150 | 0.922 |
J | 9 | 1.582 | 1.019 | 0.781 |
J | 8 | 1.584 | 0.936 | 0.689 |
J | 7 | 1.585 | 0.856 | 0.603 |
J | 6 | 1.592 | 0.784 | 0.529 |
J | 5 | 1.589 | 0.777 | 0.518 |
J | 4 | 1.584 | 0.758 | 0.500 |
J | 3 | 1.576 | 0.744 | 0.483 |
J | 2 | 1.566 | 0.730 | 0.468 |
10 | A | 1.459 | 1.220 | 0.957 |
10 | K | 1.454 | 1.169 | 0.917 |
10 | Q | 1.456 | 1.144 | 0.901 |
10 | J | 1.456 | 1.145 | 0.912 |
10 | 9 | 1.371 | 1.048 | 0.816 |
10 | 8 | 1.372 | 0.962 | 0.724 |
10 | 7 | 1.374 | 0.885 | 0.641 |
10 | 6 | 1.378 | 0.813 | 0.562 |
10 | 5 | 1.383 | 0.744 | 0.490 |
10 | 4 | 1.374 | 0.733 | 0.476 |
10 | 3 | 1.369 | 0.717 | 0.460 |
10 | 2 | 1.364 | 0.703 | 0.447 |
9 | A | 1.276 | 1.068 | 0.792 |
9 | K | 1.275 | 1.011 | 0.746 |
9 | Q | 1.278 | 0.992 | 0.737 |
9 | J | 1.280 | 0.999 | 0.754 |
9 | 10 | 1.280 | 1.027 | 0.789 |
9 | 8 | 1.212 | 0.949 | 0.713 |
9 | 7 | 1.212 | 0.896 | 0.656 |
9 | 6 | 1.213 | 0.827 | 0.583 |
9 | 5 | 1.214 | 0.757 | 0.507 |
9 | 4 | 1.215 | 0.688 | 0.433 |
9 | 3 | 1.210 | 0.676 | 0.422 |
9 | 2 | 1.205 | 0.661 | 0.407 |
8 | A | 1.148 | 1.029 | 0.748 |
8 | K | 1.149 | 0.923 | 0.652 |
8 | Q | 1.154 | 0.902 | 0.639 |
8 | J | 1.155 | 0.911 | 0.658 |
8 | 10 | 1.153 | 0.939 | 0.695 |
8 | 9 | 1.150 | 0.934 | 0.694 |
8 | 7 | 1.099 | 0.915 | 0.678 |
8 | 6 | 1.101 | 0.866 | 0.627 |
8 | 5 | 1.102 | 0.799 | 0.556 |
8 | 4 | 1.100 | 0.722 | 0.474 |
8 | 3 | 1.097 | 0.653 | 0.401 |
8 | 2 | 1.094 | 0.644 | 0.394 |
7 | A | 1.053 | 1.000 | 0.715 |
7 | K | 1.054 | 0.904 | 0.627 |
7 | Q | 1.058 | 0.829 | 0.560 |
7 | J | 1.059 | 0.831 | 0.570 |
7 | 10 | 1.062 | 0.862 | 0.612 |
7 | 9 | 1.057 | 0.878 | 0.633 |
7 | 8 | 1.054 | 0.902 | 0.663 |
7 | 6 | 1.016 | 0.889 | 0.655 |
7 | 5 | 1.016 | 0.841 | 0.605 |
7 | 4 | 1.014 | 0.763 | 0.524 |
7 | 3 | 1.014 | 0.689 | 0.445 |
7 | 2 | 1.013 | 0.625 | 0.379 |
6 | A | 0.984 | 0.975 | 0.688 |
6 | K | 0.985 | 0.888 | 0.610 |
6 | Q | 0.988 | 0.820 | 0.549 |
6 | J | 0.991 | 0.768 | 0.503 |
6 | 10 | 0.992 | 0.785 | 0.529 |
6 | 9 | 0.988 | 0.808 | 0.558 |
6 | 8 | 0.988 | 0.848 | 0.606 |
6 | 7 | 0.986 | 0.877 | 0.641 |
6 | 5 | 0.953 | 0.868 | 0.637 |
6 | 4 | 0.952 | 0.811 | 0.577 |
6 | 3 | 0.950 | 0.737 | 0.500 |
6 | 2 | 0.949 | 0.663 | 0.424 |
5 | A | 0.924 | 1.037 | 0.752 |
5 | K | 0.930 | 0.876 | 0.596 |
5 | Q | 0.931 | 0.811 | 0.538 |
5 | J | 0.933 | 0.760 | 0.494 |
5 | 10 | 0.939 | 0.725 | 0.464 |
5 | 9 | 0.936 | 0.740 | 0.484 |
5 | 8 | 0.931 | 0.783 | 0.535 |
5 | 7 | 0.933 | 0.827 | 0.587 |
5 | 6 | 0.930 | 0.859 | 0.626 |
5 | 4 | 0.900 | 0.855 | 0.627 |
5 | 3 | 0.900 | 0.798 | 0.568 |
5 | 2 | 0.902 | 0.727 | 0.496 |
4 | A | 0.876 | 1.011 | 0.726 |
4 | K | 0.880 | 0.856 | 0.573 |
4 | Q | 0.884 | 0.792 | 0.516 |
4 | J | 0.885 | 0.742 | 0.473 |
4 | 10 | 0.886 | 0.712 | 0.449 |
4 | 9 | 0.888 | 0.670 | 0.410 |
4 | 8 | 0.887 | 0.704 | 0.452 |
4 | 7 | 0.886 | 0.749 | 0.505 |
4 | 6 | 0.884 | 0.796 | 0.561 |
4 | 5 | 0.883 | 0.848 | 0.618 |
4 | 3 | 0.859 | 0.759 | 0.530 |
4 | 2 | 0.858 | 0.704 | 0.474 |
3 | A | 0.839 | 0.989 | 0.699 |
3 | K | 0.840 | 0.834 | 0.549 |
3 | Q | 0.846 | 0.771 | 0.494 |
3 | J | 0.847 | 0.724 | 0.453 |
3 | 10 | 0.849 | 0.694 | 0.429 |
3 | 9 | 0.846 | 0.656 | 0.394 |
3 | 8 | 0.848 | 0.634 | 0.378 |
3 | 7 | 0.846 | 0.669 | 0.421 |
3 | 6 | 0.846 | 0.721 | 0.481 |
3 | 5 | 0.845 | 0.781 | 0.549 |
3 | 4 | 0.843 | 0.749 | 0.518 |
3 | 2 | 0.822 | 0.667 | 0.436 |
2 | A | 0.811 | 0.954 | 0.660 |
2 | K | 0.813 | 0.813 | 0.526 |
2 | Q | 0.816 | 0.751 | 0.472 |
2 | J | 0.817 | 0.707 | 0.434 |
2 | 10 | 0.819 | 0.675 | 0.410 |
2 | 9 | 0.816 | 0.640 | 0.377 |
2 | 8 | 0.819 | 0.623 | 0.366 |
2 | 7 | 0.818 | 0.603 | 0.352 |
2 | 6 | 0.816 | 0.641 | 0.397 |
2 | 5 | 0.819 | 0.704 | 0.470 |
2 | 4 | 0.817 | 0.687 | 0.454 |
2 | 3 | 0.815 | 0.660 | 0.427 |
Three Suited Singletons
The following table shows the expected return for all three possible plays when dealt three suited singletons. Most of the time, the best play is to discard the lowest one. However, if all the cards are low, and the lowest two are close together and the highest not, then sometimes you go for the straight by playing the two lowest.
Three Suited Singletons
Hand | Discard | Expected Return Middle and High |
Expected Return Low and High |
Expected Return Low and Middle |
---|---|---|---|---|
A-K-Q | Q | 1.541 | 1.443 | 1.405 |
A-K-J | J | 1.550 | 1.325 | 1.305 |
A-K-10 | 10 | 1.550 | 1.240 | 1.230 |
A-K-9 | 9 | 1.559 | 1.102 | 1.093 |
A-K-8 | 8 | 1.548 | 1.053 | 0.988 |
A-K-7 | 7 | 1.557 | 1.016 | 0.967 |
A-K-6 | 6 | 1.551 | 0.986 | 0.942 |
A-K-5 | 5 | 1.559 | 1.031 | 0.924 |
A-K-4 | 4 | 1.554 | 1.012 | 0.903 |
A-K-3 | 3 | 1.543 | 0.987 | 0.885 |
A-K-2 | 2 | 1.536 | 0.955 | 0.865 |
A-Q-J | J | 1.402 | 1.325 | 1.245 |
A-Q-10 | 10 | 1.399 | 1.238 | 1.185 |
A-Q-9 | 9 | 1.415 | 1.099 | 1.055 |
A-Q-8 | 8 | 1.414 | 1.054 | 0.957 |
A-Q-7 | 7 | 1.412 | 1.018 | 0.885 |
A-Q-6 | 6 | 1.417 | 0.987 | 0.870 |
A-Q-5 | 5 | 1.418 | 1.032 | 0.852 |
A-Q-4 | 4 | 1.411 | 1.009 | 0.831 |
A-Q-3 | 3 | 1.405 | 0.987 | 0.814 |
A-Q-2 | 2 | 1.398 | 0.954 | 0.800 |
A-J-10 | 10 | 1.298 | 1.238 | 1.174 |
A-J-9 | 9 | 1.307 | 1.099 | 1.048 |
A-J-8 | 8 | 1.306 | 1.052 | 0.952 |
A-J-7 | 7 | 1.305 | 1.021 | 0.877 |
A-J-6 | 6 | 1.307 | 0.990 | 0.813 |
A-J-5 | 5 | 1.310 | 1.028 | 0.798 |
A-J-4 | 4 | 1.306 | 1.013 | 0.780 |
A-J-3 | 3 | 1.305 | 0.989 | 0.767 |
A-J-2 | 2 | 1.295 | 0.956 | 0.752 |
A-10-9 | 9 | 1.228 | 1.099 | 1.068 |
A-10-8 | 8 | 1.229 | 1.054 | 0.979 |
A-10-7 | 7 | 1.227 | 1.015 | 0.895 |
A-10-6 | 6 | 1.233 | 0.992 | 0.828 |
A-10-5 | 5 | 1.234 | 1.037 | 0.764 |
A-10-4 | 4 | 1.229 | 1.010 | 0.747 |
A-10-3 | 3 | 1.225 | 0.990 | 0.735 |
A-10-2 | 2 | 1.223 | 0.959 | 0.722 |
A-9-8 | 8 | 1.078 | 1.046 | 0.969 |
A-9-7 | 7 | 1.079 | 1.015 | 0.915 |
A-9-6 | 6 | 1.079 | 0.985 | 0.845 |
A-9-5 | 5 | 1.083 | 1.031 | 0.779 |
A-9-4 | 4 | 1.077 | 1.010 | 0.709 |
A-9-3 | 3 | 1.079 | 0.989 | 0.704 |
A-9-2 | 2 | 1.070 | 0.951 | 0.686 |
A-8-7 | 7 | 1.032 | 1.010 | 0.926 |
A-8-6 | 6 | 1.031 | 0.982 | 0.880 |
A-8-5 | 5 | 1.034 | 1.026 | 0.814 |
A-8-4 | 4 | 1.037 | 1.011 | 0.739 |
A-8-3 | 3 | 1.034 | 0.990 | 0.679 |
A-8-2 | 2 | 1.025 | 0.953 | 0.670 |
A-7-6 | 6 | 0.997 | 0.978 | 0.904 |
A-7-5 | 7 | 1.000 | 1.028 | 0.854 |
A-7-4 | 7 | 1.003 | 1.009 | 0.783 |
A-7-3 | 3 | 0.998 | 0.988 | 0.710 |
A-7-2 | 2 | 0.996 | 0.962 | 0.650 |
A-6-5 | 6 | 0.971 | 1.025 | 0.883 |
A-6-4 | 6 | 0.973 | 1.005 | 0.829 |
A-6-3 | 6 | 0.970 | 0.986 | 0.762 |
A-6-2 | 2 | 0.969 | 0.961 | 0.688 |
A-5-4 | 4 | 1.003 | 0.990 | 0.855 |
A-5-3 | 3 | 1.003 | 0.971 | 0.800 |
A-5-2 | 2 | 1.001 | 0.944 | 0.731 |
A-4-3 | 3 | 0.981 | 0.967 | 0.766 |
A-4-2 | 2 | 0.982 | 0.941 | 0.713 |
A-3-2 | 2 | 0.959 | 0.937 | 0.686 |
K-Q-J | J | 1.300 | 1.239 | 1.234 |
K-Q-10 | 10 | 1.303 | 1.166 | 1.170 |
K-Q-9 | 9 | 1.316 | 1.030 | 1.045 |
K-Q-8 | 8 | 1.324 | 0.950 | 0.961 |
K-Q-7 | 7 | 1.321 | 0.923 | 0.878 |
K-Q-6 | 6 | 1.324 | 0.904 | 0.867 |
K-Q-5 | 5 | 1.326 | 0.886 | 0.852 |
K-Q-4 | 4 | 1.321 | 0.868 | 0.836 |
K-Q-3 | 3 | 1.316 | 0.844 | 0.816 |
K-Q-2 | 2 | 1.309 | 0.829 | 0.801 |
K-J-10 | 10 | 1.216 | 1.170 | 1.159 |
K-J-9 | 9 | 1.227 | 1.033 | 1.038 |
K-J-8 | 8 | 1.239 | 0.953 | 0.964 |
K-J-7 | 7 | 1.239 | 0.930 | 0.880 |
K-J-6 | 6 | 1.235 | 0.906 | 0.813 |
K-J-5 | 5 | 1.239 | 0.891 | 0.804 |
K-J-4 | 4 | 1.232 | 0.864 | 0.780 |
K-J-3 | 3 | 1.227 | 0.849 | 0.769 |
K-J-2 | 2 | 1.223 | 0.830 | 0.752 |
K-10-9 | 9 | 1.156 | 1.027 | 1.046 |
K-10-8 | 8 | 1.172 | 0.952 | 0.981 |
K-10-7 | 7 | 1.170 | 0.927 | 0.899 |
K-10-6 | 6 | 1.174 | 0.907 | 0.825 |
K-10-5 | 5 | 1.173 | 0.888 | 0.763 |
K-10-4 | 4 | 1.169 | 0.867 | 0.747 |
K-10-3 | 3 | 1.167 | 0.851 | 0.736 |
K-10-2 | 2 | 1.164 | 0.831 | 0.721 |
K-9-8 | 8 | 1.017 | 0.946 | 0.976 |
K-9-7 | 7 | 1.023 | 0.925 | 0.914 |
K-9-6 | 6 | 1.018 | 0.901 | 0.845 |
K-9-5 | 5 | 1.023 | 0.888 | 0.779 |
K-9-4 | 4 | 1.023 | 0.869 | 0.714 |
K-9-3 | 3 | 1.016 | 0.849 | 0.701 |
K-9-2 | 2 | 1.014 | 0.832 | 0.689 |
K-8-7 | K | 0.931 | 0.917 | 0.933 |
K-8-6 | 6 | 0.931 | 0.897 | 0.882 |
K-8-5 | 5 | 0.935 | 0.884 | 0.816 |
K-8-4 | 4 | 0.934 | 0.866 | 0.745 |
K-8-3 | 3 | 0.930 | 0.848 | 0.682 |
K-8-2 | 2 | 0.927 | 0.826 | 0.675 |
K-7-6 | 6 | 0.906 | 0.894 | 0.901 |
K-7-5 | 5 | 0.908 | 0.880 | 0.857 |
K-7-4 | 4 | 0.908 | 0.866 | 0.785 |
K-7-3 | 3 | 0.907 | 0.848 | 0.714 |
K-7-2 | 2 | 0.905 | 0.833 | 0.655 |
K-6-5 | 5 | 0.883 | 0.874 | 0.880 |
K-6-4 | 4 | 0.883 | 0.859 | 0.824 |
K-6-3 | 3 | 0.888 | 0.846 | 0.760 |
K-6-2 | 2 | 0.886 | 0.831 | 0.689 |
K-5-4 | K | 0.868 | 0.856 | 0.871 |
K-5-3 | 3 | 0.870 | 0.843 | 0.817 |
K-5-2 | 2 | 0.868 | 0.827 | 0.750 |
K-4-3 | 3 | 0.850 | 0.840 | 0.784 |
K-4-2 | 2 | 0.847 | 0.822 | 0.728 |
K-3-2 | 2 | 0.828 | 0.818 | 0.699 |
Q-J-10 | 10 | 1.156 | 1.119 | 1.142 |
Q-J-9 | 9 | 1.174 | 0.995 | 1.022 |
Q-J-8 | 8 | 1.181 | 0.914 | 0.948 |
Q-J-7 | 7 | 1.199 | 0.859 | 0.881 |
Q-J-6 | 6 | 1.191 | 0.842 | 0.810 |
Q-J-5 | 5 | 1.198 | 0.826 | 0.801 |
Q-J-4 | 4 | 1.190 | 0.806 | 0.781 |
Q-J-3 | 3 | 1.186 | 0.786 | 0.763 |
Q-J-2 | 2 | 1.182 | 0.775 | 0.755 |
Q-10-9 | 9 | 1.114 | 0.993 | 1.034 |
Q-10-8 | 8 | 1.126 | 0.912 | 0.963 |
Q-10-7 | 7 | 1.141 | 0.854 | 0.900 |
Q-10-6 | 6 | 1.143 | 0.841 | 0.824 |
Q-10-5 | 5 | 1.139 | 0.825 | 0.763 |
Q-10-4 | 4 | 1.140 | 0.808 | 0.746 |
Q-10-3 | 3 | 1.140 | 0.793 | 0.734 |
Q-10-2 | 2 | 1.134 | 0.779 | 0.725 |
Q-9-8 | 8 | 0.981 | 0.911 | 0.960 |
Q-9-7 | 7 | 0.998 | 0.846 | 0.915 |
Q-9-6 | 6 | 0.997 | 0.840 | 0.841 |
Q-9-5 | 5 | 0.997 | 0.826 | 0.777 |
Q-9-4 | 4 | 0.999 | 0.810 | 0.712 |
Q-9-3 | 3 | 0.997 | 0.793 | 0.704 |
Q-9-2 | 2 | 0.993 | 0.775 | 0.692 |
Q-8-7 | Q | 0.906 | 0.843 | 0.938 |
Q-8-6 | 6 | 0.910 | 0.833 | 0.883 |
Q-8-5 | 5 | 0.909 | 0.821 | 0.818 |
Q-8-4 | 4 | 0.909 | 0.805 | 0.742 |
Q-8-3 | 3 | 0.908 | 0.792 | 0.682 |
Q-8-2 | 2 | 0.906 | 0.773 | 0.672 |
Q-7-6 | Q | 0.837 | 0.833 | 0.913 |
Q-7-5 | Q | 0.836 | 0.816 | 0.860 |
Q-7-4 | 4 | 0.839 | 0.806 | 0.788 |
Q-7-3 | 3 | 0.840 | 0.788 | 0.715 |
Q-7-2 | 2 | 0.832 | 0.773 | 0.655 |
Q-6-5 | Q | 0.821 | 0.813 | 0.883 |
Q-6-4 | Q | 0.826 | 0.801 | 0.830 |
Q-6-3 | 3 | 0.823 | 0.786 | 0.761 |
Q-6-2 | 2 | 0.824 | 0.774 | 0.690 |
Q-5-4 | Q | 0.808 | 0.794 | 0.873 |
Q-5-3 | Q | 0.806 | 0.781 | 0.817 |
Q-5-2 | 2 | 0.808 | 0.770 | 0.750 |
Q-4-3 | 3 | 0.789 | 0.782 | 0.785 |
Q-4-2 | 2 | 0.789 | 0.768 | 0.732 |
Q-3-2 | 2 | 0.777 | 0.767 | 0.703 |
J-10-9 | 9 | 1.094 | 0.979 | 1.021 |
J-10-8 | 8 | 1.112 | 0.911 | 0.955 |
J-10-7 | 7 | 1.122 | 0.839 | 0.886 |
J-10-6 | 6 | 1.140 | 0.792 | 0.829 |
J-10-5 | 5 | 1.136 | 0.781 | 0.762 |
J-10-4 | 4 | 1.132 | 0.763 | 0.745 |
J-10-3 | 3 | 1.132 | 0.749 | 0.730 |
J-10-2 | 2 | 1.129 | 0.734 | 0.721 |
J-9-8 | 8 | 0.974 | 0.903 | 0.946 |
J-9-7 | 7 | 0.991 | 0.841 | 0.907 |
J-9-6 | 6 | 1.006 | 0.791 | 0.853 |
J-9-5 | 5 | 1.000 | 0.778 | 0.777 |
J-9-4 | 4 | 1.000 | 0.764 | 0.711 |
J-9-3 | 3 | 0.997 | 0.744 | 0.700 |
J-9-2 | 2 | 0.998 | 0.731 | 0.689 |
J-8-7 | J | 0.902 | 0.836 | 0.928 |
J-8-6 | 6 | 0.917 | 0.785 | 0.888 |
J-8-5 | 5 | 0.920 | 0.776 | 0.817 |
J-8-4 | 4 | 0.918 | 0.758 | 0.741 |
J-8-3 | 3 | 0.913 | 0.743 | 0.679 |
J-8-2 | 2 | 0.916 | 0.730 | 0.672 |
J-7-6 | J | 0.836 | 0.781 | 0.913 |
J-7-5 | J | 0.838 | 0.771 | 0.858 |
J-7-4 | 4 | 0.839 | 0.756 | 0.786 |
J-7-3 | 3 | 0.837 | 0.739 | 0.710 |
J-7-2 | 2 | 0.839 | 0.734 | 0.655 |
J-6-5 | J | 0.778 | 0.773 | 0.890 |
J-6-4 | J | 0.775 | 0.756 | 0.833 |
J-6-3 | 3 | 0.775 | 0.740 | 0.766 |
J-6-2 | 2 | 0.776 | 0.732 | 0.691 |
J-5-4 | J | 0.765 | 0.756 | 0.875 |
J-5-3 | J | 0.765 | 0.738 | 0.814 |
J-5-2 | 2 | 0.762 | 0.725 | 0.749 |
J-4-3 | J | 0.751 | 0.743 | 0.788 |
J-4-2 | 2 | 0.749 | 0.729 | 0.731 |
J-3-2 | 2 | 0.734 | 0.725 | 0.702 |
10-9-8 | 8 | 0.982 | 0.915 | 0.929 |
10-9-7 | 7 | 0.997 | 0.850 | 0.887 |
10-9-6 | 6 | 1.007 | 0.792 | 0.833 |
10-9-5 | 5 | 1.025 | 0.744 | 0.780 |
10-9-4 | 4 | 1.023 | 0.733 | 0.710 |
10-9-3 | 3 | 1.017 | 0.715 | 0.696 |
10-9-2 | 2 | 1.018 | 0.705 | 0.687 |
10-8-7 | 7 | 0.916 | 0.852 | 0.911 |
10-8-6 | 6 | 0.932 | 0.792 | 0.873 |
10-8-5 | 5 | 0.942 | 0.743 | 0.817 |
10-8-4 | 4 | 0.938 | 0.729 | 0.737 |
10-8-3 | 3 | 0.943 | 0.722 | 0.680 |
10-8-2 | 2 | 0.938 | 0.705 | 0.670 |
10-7-6 | 10 | 0.853 | 0.788 | 0.901 |
10-7-5 | 5 | 0.863 | 0.736 | 0.858 |
10-7-4 | 4 | 0.864 | 0.728 | 0.783 |
10-7-3 | 3 | 0.867 | 0.717 | 0.709 |
10-7-2 | 2 | 0.865 | 0.709 | 0.654 |
10-6-5 | 10 | 0.793 | 0.738 | 0.892 |
10-6-4 | 10 | 0.792 | 0.727 | 0.827 |
10-6-3 | 3 | 0.794 | 0.714 | 0.762 |
10-6-2 | 2 | 0.790 | 0.700 | 0.687 |
10-5-4 | 10 | 0.733 | 0.724 | 0.876 |
10-5-3 | 10 | 0.732 | 0.711 | 0.822 |
10-5-2 | 10 | 0.733 | 0.700 | 0.753 |
10-4-3 | 10 | 0.718 | 0.709 | 0.784 |
10-4-2 | 10 | 0.720 | 0.700 | 0.734 |
10-3-2 | 2 | 0.706 | 0.699 | 0.702 |
9-8-7 | 7 | 0.898 | 0.856 | 0.897 |
9-8-6 | 6 | 0.910 | 0.800 | 0.857 |
9-8-5 | 5 | 0.925 | 0.748 | 0.806 |
9-8-4 | 4 | 0.941 | 0.698 | 0.746 |
9-8-3 | 3 | 0.934 | 0.682 | 0.677 |
9-8-2 | 2 | 0.929 | 0.673 | 0.669 |
9-7-6 | 9 | 0.858 | 0.800 | 0.886 |
9-7-5 | 5 | 0.869 | 0.744 | 0.847 |
9-7-4 | 4 | 0.883 | 0.689 | 0.788 |
9-7-3 | 3 | 0.881 | 0.680 | 0.710 |
9-7-2 | 2 | 0.879 | 0.670 | 0.651 |
9-6-5 | 9 | 0.802 | 0.743 | 0.881 |
9-6-4 | 9 | 0.816 | 0.690 | 0.831 |
9-6-3 | 3 | 0.814 | 0.680 | 0.759 |
9-6-2 | 2 | 0.816 | 0.668 | 0.688 |
9-5-4 | 9 | 0.748 | 0.689 | 0.882 |
9-5-3 | 9 | 0.746 | 0.676 | 0.817 |
9-5-2 | 9 | 0.750 | 0.669 | 0.752 |
9-4-3 | 9 | 0.683 | 0.676 | 0.792 |
9-4-2 | 9 | 0.685 | 0.668 | 0.736 |
9-3-2 | 9 | 0.672 | 0.666 | 0.704 |
8-7-6 | 8 | 0.864 | 0.825 | 0.869 |
8-7-5 | 5 | 0.875 | 0.772 | 0.832 |
8-7-4 | 4 | 0.890 | 0.712 | 0.773 |
8-7-3 | 3 | 0.907 | 0.665 | 0.715 |
8-7-2 | 2 | 0.902 | 0.657 | 0.653 |
8-6-5 | 8 | 0.831 | 0.771 | 0.866 |
8-6-4 | 4 | 0.842 | 0.710 | 0.816 |
8-6-3 | 3 | 0.855 | 0.661 | 0.762 |
8-6-2 | 2 | 0.855 | 0.654 | 0.689 |
8-5-4 | 8 | 0.775 | 0.706 | 0.864 |
8-5-3 | 8 | 0.791 | 0.658 | 0.823 |
8-5-2 | 2 | 0.786 | 0.652 | 0.748 |
8-4-3 | 8 | 0.717 | 0.657 | 0.796 |
8-4-2 | 8 | 0.717 | 0.652 | 0.733 |
8-3-2 | 8 | 0.653 | 0.652 | 0.709 |
7-6-5 | 7 | 0.841 | 0.802 | 0.849 |
7-6-4 | 4 | 0.852 | 0.740 | 0.800 |
7-6-3 | 3 | 0.868 | 0.683 | 0.746 |
7-6-2 | 2 | 0.882 | 0.637 | 0.693 |
7-5-4 | 7 | 0.804 | 0.742 | 0.852 |
7-5-3 | 3 | 0.819 | 0.680 | 0.808 |
7-5-2 | 2 | 0.836 | 0.636 | 0.753 |
7-4-3 | 7 | 0.754 | 0.685 | 0.784 |
7-4-2 | 2 | 0.769 | 0.637 | 0.740 |
7-3-2 | 7 | 0.694 | 0.639 | 0.715 |
6-5-4 | 6 | 0.823 | 0.777 | 0.832 |
6-5-3 | 3 | 0.838 | 0.720 | 0.790 |
6-5-2 | 2 | 0.851 | 0.665 | 0.738 |
6-4-3 | 3 | 0.782 | 0.718 | 0.762 |
6-4-2 | 2 | 0.796 | 0.662 | 0.720 |
6-3-2 | 2 | 0.732 | 0.661 | 0.696 |
5-4-3 | 3 | 0.810 | 0.759 | 0.742 |
5-4-2 | 2 | 0.826 | 0.711 | 0.700 |
5-3-2 | 2 | 0.772 | 0.709 | 0.677 |
4-3-2 | 2 | 0.738 | 0.691 | 0.673 |
Three Unsuited Singletons
The following table shows the expected return for all three possible plays when dealt three unsuited singletons. Most of the time, the best play is to discard the lowest one. However, if all the cards are low, and the lowest two are close together and the highest not, then sometimes you go for the straight by playing the two lowest.
Three Unsuited Singletons
Hand | Discard | Expected Return Middle and High |
Expected Return Low and High |
Expected Return Low and Middle |
---|---|---|---|---|
A-K-Q | Q | 1.423 | 1.309 | 1.263 |
A-K-J | J | 1.429 | 1.186 | 1.155 |
A-K-10 | 10 | 1.431 | 1.092 | 1.074 |
A-K-9 | 9 | 1.443 | 0.943 | 0.924 |
A-K-8 | 8 | 1.438 | 0.888 | 0.814 |
A-K-7 | 7 | 1.441 | 0.846 | 0.781 |
A-K-6 | 6 | 1.440 | 0.814 | 0.756 |
A-K-5 | 5 | 1.443 | 0.856 | 0.733 |
A-K-4 | 4 | 1.440 | 0.835 | 0.712 |
A-K-3 | 3 | 1.431 | 0.809 | 0.690 |
A-K-2 | 2 | 1.420 | 0.773 | 0.669 |
A-Q-J | J | 1.272 | 1.186 | 1.099 |
A-Q-10 | 10 | 1.273 | 1.091 | 1.028 |
A-Q-9 | 9 | 1.288 | 0.940 | 0.890 |
A-Q-8 | 8 | 1.285 | 0.889 | 0.783 |
A-Q-7 | 7 | 1.284 | 0.850 | 0.700 |
A-Q-6 | 6 | 1.286 | 0.813 | 0.682 |
A-Q-5 | 5 | 1.288 | 0.859 | 0.663 |
A-Q-4 | 4 | 1.284 | 0.834 | 0.642 |
A-Q-3 | 3 | 1.279 | 0.811 | 0.622 |
A-Q-2 | 2 | 1.271 | 0.777 | 0.607 |
A-J-10 | 10 | 1.154 | 1.091 | 1.017 |
A-J-9 | 9 | 1.169 | 0.941 | 0.890 |
A-J-8 | 8 | 1.169 | 0.888 | 0.785 |
A-J-7 | 7 | 1.169 | 0.850 | 0.697 |
A-J-6 | 6 | 1.169 | 0.819 | 0.626 |
A-J-5 | 5 | 1.172 | 0.861 | 0.611 |
A-J-4 | 4 | 1.170 | 0.838 | 0.591 |
A-J-3 | 3 | 1.164 | 0.812 | 0.572 |
A-J-2 | 2 | 1.156 | 0.778 | 0.558 |
A-10-9 | 9 | 1.080 | 0.941 | 0.905 |
A-10-8 | 8 | 1.080 | 0.888 | 0.809 |
A-10-7 | 7 | 1.079 | 0.848 | 0.721 |
A-10-6 | 6 | 1.082 | 0.818 | 0.643 |
A-10-5 | 5 | 1.086 | 0.866 | 0.576 |
A-10-4 | 4 | 1.083 | 0.838 | 0.558 |
A-10-3 | 3 | 1.078 | 0.811 | 0.542 |
A-10-2 | 2 | 1.072 | 0.778 | 0.528 |
A-9-8 | 8 | 0.915 | 0.880 | 0.805 |
A-9-7 | 7 | 0.916 | 0.842 | 0.741 |
A-9-6 | 6 | 0.917 | 0.811 | 0.666 |
A-9-5 | 5 | 0.921 | 0.860 | 0.592 |
A-9-4 | 4 | 0.919 | 0.837 | 0.521 |
A-9-3 | 3 | 0.916 | 0.809 | 0.508 |
A-9-2 | 2 | 0.910 | 0.774 | 0.494 |
A-8-7 | 7 | 0.862 | 0.838 | 0.757 |
A-8-6 | 6 | 0.864 | 0.809 | 0.705 |
A-8-5 | 5 | 0.870 | 0.858 | 0.632 |
A-8-4 | 4 | 0.868 | 0.834 | 0.553 |
A-8-3 | 3 | 0.866 | 0.815 | 0.487 |
A-8-2 | 2 | 0.863 | 0.775 | 0.479 |
A-7-6 | 6 | 0.827 | 0.805 | 0.729 |
A-7-5 | 7 | 0.830 | 0.855 | 0.677 |
A-7-4 | 7 | 0.829 | 0.832 | 0.603 |
A-7-3 | 3 | 0.828 | 0.811 | 0.523 |
A-7-2 | 2 | 0.827 | 0.782 | 0.463 |
A-6-5 | 6 | 0.798 | 0.857 | 0.710 |
A-6-4 | 6 | 0.796 | 0.835 | 0.652 |
A-6-3 | 6 | 0.795 | 0.811 | 0.581 |
A-6-2 | 2 | 0.796 | 0.781 | 0.505 |
A-5-4 | 4 | 0.830 | 0.814 | 0.680 |
A-5-3 | 3 | 0.827 | 0.791 | 0.624 |
A-5-2 | 2 | 0.827 | 0.762 | 0.554 |
A-4-3 | 3 | 0.804 | 0.789 | 0.591 |
A-4-2 | 2 | 0.803 | 0.760 | 0.537 |
A-3-2 | 2 | 0.782 | 0.758 | 0.508 |
K-Q-J | J | 1.166 | 1.093 | 1.081 |
K-Q-10 | 10 | 1.165 | 1.013 | 1.011 |
K-Q-9 | 9 | 1.183 | 0.869 | 0.873 |
K-Q-8 | 8 | 1.195 | 0.782 | 0.787 |
K-Q-7 | 7 | 1.195 | 0.753 | 0.700 |
K-Q-6 | 6 | 1.194 | 0.727 | 0.683 |
K-Q-5 | 5 | 1.193 | 0.707 | 0.665 |
K-Q-4 | 4 | 1.190 | 0.685 | 0.644 |
K-Q-3 | 3 | 1.185 | 0.665 | 0.625 |
K-Q-2 | 2 | 1.180 | 0.647 | 0.610 |
K-J-10 | 10 | 1.065 | 1.013 | 1.002 |
K-J-9 | 9 | 1.082 | 0.870 | 0.872 |
K-J-8 | 8 | 1.096 | 0.783 | 0.789 |
K-J-7 | 7 | 1.095 | 0.752 | 0.695 |
K-J-6 | 6 | 1.094 | 0.731 | 0.625 |
K-J-5 | 5 | 1.095 | 0.707 | 0.611 |
K-J-4 | 4 | 1.093 | 0.686 | 0.592 |
K-J-3 | 3 | 1.089 | 0.666 | 0.575 |
K-J-2 | 2 | 1.083 | 0.646 | 0.559 |
K-10-9 | 9 | 1.009 | 0.868 | 0.890 |
K-10-8 | 8 | 1.023 | 0.780 | 0.813 |
K-10-7 | 7 | 1.021 | 0.751 | 0.721 |
K-10-6 | 6 | 1.023 | 0.730 | 0.642 |
K-10-5 | 5 | 1.023 | 0.712 | 0.576 |
K-10-4 | 4 | 1.023 | 0.688 | 0.560 |
K-10-3 | 3 | 1.018 | 0.666 | 0.544 |
K-10-2 | 2 | 1.013 | 0.646 | 0.530 |
K-9-8 | 8 | 0.857 | 0.778 | 0.810 |
K-9-7 | 7 | 0.856 | 0.747 | 0.740 |
K-9-6 | 6 | 0.859 | 0.726 | 0.666 |
K-9-5 | 5 | 0.860 | 0.709 | 0.593 |
K-9-4 | 4 | 0.857 | 0.687 | 0.523 |
K-9-3 | 3 | 0.856 | 0.664 | 0.511 |
K-9-2 | 2 | 0.851 | 0.645 | 0.499 |
K-8-7 | K | 0.761 | 0.743 | 0.767 |
K-8-6 | 6 | 0.761 | 0.723 | 0.710 |
K-8-5 | 5 | 0.764 | 0.704 | 0.637 |
K-8-4 | 4 | 0.762 | 0.683 | 0.558 |
K-8-3 | 3 | 0.761 | 0.665 | 0.493 |
K-8-2 | 2 | 0.759 | 0.643 | 0.483 |
K-7-6 | 6 | 0.732 | 0.721 | 0.731 |
K-7-5 | 5 | 0.732 | 0.703 | 0.680 |
K-7-4 | 4 | 0.734 | 0.682 | 0.605 |
K-7-3 | 3 | 0.733 | 0.664 | 0.528 |
K-7-2 | 2 | 0.731 | 0.647 | 0.465 |
K-6-5 | K | 0.708 | 0.698 | 0.712 |
K-6-4 | 4 | 0.708 | 0.679 | 0.653 |
K-6-3 | 3 | 0.709 | 0.663 | 0.581 |
K-6-2 | 2 | 0.711 | 0.646 | 0.506 |
K-5-4 | K | 0.690 | 0.676 | 0.701 |
K-5-3 | 3 | 0.689 | 0.657 | 0.643 |
K-5-2 | 2 | 0.689 | 0.641 | 0.572 |
K-4-3 | 3 | 0.668 | 0.656 | 0.610 |
K-4-2 | 2 | 0.667 | 0.639 | 0.555 |
K-3-2 | 2 | 0.649 | 0.637 | 0.526 |
Q-J-10 | 10 | 1.005 | 0.964 | 0.984 |
Q-J-9 | 9 | 1.024 | 0.829 | 0.855 |
Q-J-8 | 8 | 1.038 | 0.745 | 0.773 |
Q-J-7 | 7 | 1.054 | 0.678 | 0.701 |
Q-J-6 | 6 | 1.051 | 0.662 | 0.624 |
Q-J-5 | 5 | 1.054 | 0.643 | 0.610 |
Q-J-4 | 4 | 1.051 | 0.624 | 0.592 |
Q-J-3 | 3 | 1.046 | 0.605 | 0.574 |
Q-J-2 | 2 | 1.043 | 0.589 | 0.559 |
Q-10-9 | 9 | 0.961 | 0.827 | 0.872 |
Q-10-8 | 8 | 0.978 | 0.744 | 0.796 |
Q-10-7 | 7 | 0.993 | 0.677 | 0.726 |
Q-10-6 | 6 | 0.992 | 0.662 | 0.640 |
Q-10-5 | 5 | 0.993 | 0.647 | 0.574 |
Q-10-4 | 4 | 0.992 | 0.624 | 0.558 |
Q-10-3 | 3 | 0.989 | 0.607 | 0.544 |
Q-10-2 | 2 | 0.985 | 0.589 | 0.529 |
Q-9-8 | 8 | 0.819 | 0.740 | 0.795 |
Q-9-7 | 7 | 0.835 | 0.675 | 0.746 |
Q-9-6 | 6 | 0.836 | 0.660 | 0.667 |
Q-9-5 | 5 | 0.836 | 0.644 | 0.591 |
Q-9-4 | 4 | 0.835 | 0.626 | 0.522 |
Q-9-3 | 3 | 0.835 | 0.605 | 0.511 |
Q-9-2 | 2 | 0.831 | 0.590 | 0.497 |
Q-8-7 | Q | 0.740 | 0.671 | 0.770 |
Q-8-6 | 6 | 0.739 | 0.655 | 0.708 |
Q-8-5 | 5 | 0.739 | 0.640 | 0.636 |
Q-8-4 | 4 | 0.741 | 0.624 | 0.558 |
Q-8-3 | 3 | 0.740 | 0.607 | 0.492 |
Q-8-2 | 2 | 0.737 | 0.586 | 0.482 |
Q-7-6 | Q | 0.660 | 0.654 | 0.741 |
Q-7-5 | Q | 0.662 | 0.640 | 0.685 |
Q-7-4 | 4 | 0.662 | 0.620 | 0.608 |
Q-7-3 | 3 | 0.663 | 0.606 | 0.531 |
Q-7-2 | 2 | 0.662 | 0.590 | 0.469 |
Q-6-5 | Q | 0.644 | 0.636 | 0.712 |
Q-6-4 | Q | 0.646 | 0.618 | 0.654 |
Q-6-3 | 3 | 0.646 | 0.603 | 0.582 |
Q-6-2 | 2 | 0.647 | 0.588 | 0.507 |
Q-5-4 | Q | 0.628 | 0.616 | 0.700 |
Q-5-3 | Q | 0.628 | 0.598 | 0.645 |
Q-5-2 | 2 | 0.629 | 0.584 | 0.573 |
Q-4-3 | Q | 0.608 | 0.597 | 0.612 |
Q-4-2 | 2 | 0.608 | 0.582 | 0.556 |
Q-3-2 | 2 | 0.593 | 0.583 | 0.526 |
J-10-9 | 9 | 0.943 | 0.815 | 0.857 |
J-10-8 | 8 | 0.958 | 0.734 | 0.778 |
J-10-7 | 7 | 0.975 | 0.667 | 0.710 |
J-10-6 | 6 | 0.992 | 0.610 | 0.648 |
J-10-5 | 5 | 0.992 | 0.597 | 0.574 |
J-10-4 | 4 | 0.988 | 0.575 | 0.557 |
J-10-3 | 3 | 0.987 | 0.559 | 0.541 |
J-10-2 | 2 | 0.984 | 0.545 | 0.528 |
J-9-8 | 8 | 0.812 | 0.734 | 0.778 |
J-9-7 | 7 | 0.828 | 0.665 | 0.730 |
J-9-6 | 6 | 0.843 | 0.607 | 0.671 |
J-9-5 | 5 | 0.842 | 0.596 | 0.591 |
J-9-4 | 4 | 0.844 | 0.579 | 0.521 |
J-9-3 | 3 | 0.841 | 0.559 | 0.508 |
J-9-2 | 2 | 0.839 | 0.544 | 0.496 |
J-8-7 | J | 0.734 | 0.663 | 0.756 |
J-8-6 | 6 | 0.750 | 0.605 | 0.715 |
J-8-5 | 5 | 0.750 | 0.594 | 0.635 |
J-8-4 | 4 | 0.749 | 0.577 | 0.556 |
J-8-3 | 3 | 0.750 | 0.562 | 0.492 |
J-8-2 | 2 | 0.749 | 0.545 | 0.482 |
J-7-6 | J | 0.664 | 0.602 | 0.746 |
J-7-5 | J | 0.662 | 0.590 | 0.684 |
J-7-4 | 4 | 0.667 | 0.575 | 0.607 |
J-7-3 | 3 | 0.667 | 0.560 | 0.530 |
J-7-2 | 2 | 0.666 | 0.548 | 0.468 |
J-6-5 | J | 0.595 | 0.590 | 0.721 |
J-6-4 | J | 0.596 | 0.574 | 0.658 |
J-6-3 | 3 | 0.597 | 0.559 | 0.586 |
J-6-2 | 2 | 0.598 | 0.545 | 0.510 |
J-5-4 | J | 0.581 | 0.569 | 0.701 |
J-5-3 | J | 0.584 | 0.556 | 0.646 |
J-5-2 | 2 | 0.585 | 0.543 | 0.574 |
J-4-3 | J | 0.565 | 0.555 | 0.613 |
J-4-2 | 2 | 0.565 | 0.542 | 0.556 |
J-3-2 | 2 | 0.549 | 0.540 | 0.526 |
10-9-8 | 8 | 0.821 | 0.746 | 0.762 |
10-9-7 | 7 | 0.836 | 0.678 | 0.712 |
10-9-6 | 6 | 0.854 | 0.615 | 0.655 |
10-9-5 | 5 | 0.868 | 0.563 | 0.594 |
10-9-4 | 4 | 0.866 | 0.548 | 0.520 |
10-9-3 | 3 | 0.867 | 0.529 | 0.507 |
10-9-2 | 2 | 0.865 | 0.517 | 0.494 |
10-8-7 | 7 | 0.749 | 0.677 | 0.739 |
10-8-6 | 6 | 0.763 | 0.614 | 0.698 |
10-8-5 | 5 | 0.780 | 0.561 | 0.642 |
10-8-4 | 4 | 0.779 | 0.547 | 0.555 |
10-8-3 | 3 | 0.780 | 0.534 | 0.489 |
10-8-2 | 2 | 0.779 | 0.518 | 0.481 |
10-7-6 | 10 | 0.681 | 0.612 | 0.730 |
10-7-5 | 5 | 0.696 | 0.559 | 0.688 |
10-7-4 | 4 | 0.696 | 0.546 | 0.606 |
10-7-3 | 3 | 0.697 | 0.533 | 0.527 |
10-7-2 | 2 | 0.697 | 0.522 | 0.466 |
10-6-5 | 10 | 0.619 | 0.558 | 0.725 |
10-6-4 | 10 | 0.616 | 0.543 | 0.657 |
10-6-3 | 3 | 0.619 | 0.531 | 0.585 |
10-6-2 | 2 | 0.619 | 0.520 | 0.508 |
10-5-4 | 10 | 0.552 | 0.541 | 0.708 |
10-5-3 | 10 | 0.553 | 0.527 | 0.649 |
10-5-2 | 10 | 0.553 | 0.516 | 0.576 |
10-4-3 | 10 | 0.538 | 0.528 | 0.612 |
10-4-2 | 10 | 0.537 | 0.516 | 0.557 |
10-3-2 | 10 | 0.525 | 0.516 | 0.528 |
9-8-7 | 7 | 0.725 | 0.680 | 0.721 |
9-8-6 | 6 | 0.741 | 0.622 | 0.679 |
9-8-5 | 5 | 0.756 | 0.564 | 0.623 |
9-8-4 | 4 | 0.773 | 0.508 | 0.559 |
9-8-3 | 3 | 0.774 | 0.498 | 0.487 |
9-8-2 | 2 | 0.772 | 0.483 | 0.477 |
9-7-6 | 9 | 0.682 | 0.620 | 0.710 |
9-7-5 | 5 | 0.698 | 0.562 | 0.670 |
9-7-4 | 4 | 0.715 | 0.506 | 0.611 |
9-7-3 | 3 | 0.716 | 0.497 | 0.526 |
9-7-2 | 2 | 0.716 | 0.486 | 0.464 |
9-6-5 | 9 | 0.626 | 0.560 | 0.709 |
9-6-4 | 9 | 0.644 | 0.505 | 0.662 |
9-6-3 | 3 | 0.643 | 0.495 | 0.583 |
9-6-2 | 2 | 0.645 | 0.482 | 0.506 |
9-5-4 | 9 | 0.568 | 0.502 | 0.711 |
9-5-3 | 9 | 0.569 | 0.492 | 0.647 |
9-5-2 | 9 | 0.572 | 0.483 | 0.575 |
9-4-3 | 9 | 0.501 | 0.493 | 0.618 |
9-4-2 | 9 | 0.501 | 0.483 | 0.561 |
9-3-2 | 9 | 0.490 | 0.481 | 0.526 |
8-7-6 | 8 | 0.692 | 0.650 | 0.694 |
8-7-5 | 5 | 0.705 | 0.594 | 0.652 |
8-7-4 | 4 | 0.725 | 0.530 | 0.593 |
8-7-3 | 3 | 0.742 | 0.479 | 0.531 |
8-7-2 | 2 | 0.739 | 0.471 | 0.461 |
8-6-5 | 8 | 0.654 | 0.592 | 0.692 |
8-6-4 | 4 | 0.672 | 0.528 | 0.644 |
8-6-3 | 3 | 0.690 | 0.477 | 0.589 |
8-6-2 | 2 | 0.690 | 0.469 | 0.503 |
8-5-4 | 8 | 0.601 | 0.527 | 0.695 |
8-5-3 | 8 | 0.618 | 0.476 | 0.652 |
8-5-2 | 2 | 0.618 | 0.468 | 0.572 |
8-4-3 | 8 | 0.540 | 0.476 | 0.623 |
8-4-2 | 8 | 0.539 | 0.470 | 0.559 |
8-3-2 | 8 | 0.474 | 0.469 | 0.534 |
7-6-5 | 7 | 0.667 | 0.625 | 0.674 |
7-6-4 | 4 | 0.685 | 0.565 | 0.627 |
7-6-3 | 3 | 0.704 | 0.504 | 0.571 |
7-6-2 | 2 | 0.719 | 0.455 | 0.510 |
7-5-4 | 7 | 0.632 | 0.562 | 0.678 |
7-5-3 | 3 | 0.650 | 0.501 | 0.635 |
7-5-2 | 2 | 0.668 | 0.452 | 0.579 |
7-4-3 | 7 | 0.576 | 0.502 | 0.607 |
7-4-2 | 2 | 0.592 | 0.454 | 0.563 |
7-3-2 | 7 | 0.517 | 0.456 | 0.539 |
6-5-4 | 6 | 0.651 | 0.598 | 0.662 |
6-5-3 | 3 | 0.669 | 0.541 | 0.616 |
6-5-2 | 2 | 0.685 | 0.482 | 0.561 |
6-4-3 | 3 | 0.611 | 0.543 | 0.588 |
6-4-2 | 2 | 0.629 | 0.483 | 0.546 |
6-3-2 | 2 | 0.558 | 0.486 | 0.522 |
5-4-3 | 3 | 0.640 | 0.588 | 0.566 |
5-4-2 | 2 | 0.658 | 0.533 | 0.521 |
5-3-2 | 2 | 0.602 | 0.535 | 0.498 |
4-3-2 | 2 | 0.572 | 0.519 | 0.500 |
Three Singletons — Lowest Two Suited
The following table shows the expected return for all three possible plays when dealt three singletons when the lowest two are suited. 60.5% of the time, the best play is to keep the suited cards and discard the highest. The rest of the time, discard the lowest card. The following table shows the expected return for all three ways ways to choose two of the three cards.
Three Singletons — Lowest Two Suited
Hand | Discard | Expected Return Middle and High |
Expected Return Low and High |
Expected Return Low and Middle |
---|---|---|---|---|
A-K-Q | A | 1.404 | 1.296 | 1.480 |
A-K-J | J | 1.407 | 1.175 | 1.379 |
A-K-10 | 10 | 1.408 | 1.082 | 1.304 |
A-K-9 | 9 | 1.421 | 0.936 | 1.168 |
A-K-8 | 8 | 1.419 | 0.884 | 1.068 |
A-K-7 | 7 | 1.419 | 0.840 | 1.037 |
A-K-6 | 6 | 1.419 | 0.808 | 1.015 |
A-K-5 | 5 | 1.421 | 0.853 | 0.995 |
A-K-4 | 4 | 1.416 | 0.829 | 0.976 |
A-K-3 | 3 | 1.409 | 0.805 | 0.953 |
A-K-2 | 2 | 1.396 | 0.770 | 0.934 |
A-Q-J | A | 1.255 | 1.175 | 1.317 |
A-Q-10 | 10 | 1.257 | 1.081 | 1.255 |
A-Q-9 | 9 | 1.269 | 0.933 | 1.129 |
A-Q-8 | 8 | 1.268 | 0.884 | 1.030 |
A-Q-7 | 7 | 1.268 | 0.845 | 0.953 |
A-Q-6 | 6 | 1.269 | 0.809 | 0.939 |
A-Q-5 | 5 | 1.271 | 0.856 | 0.923 |
A-Q-4 | 4 | 1.269 | 0.833 | 0.904 |
A-Q-3 | 3 | 1.262 | 0.809 | 0.886 |
A-Q-2 | 2 | 1.252 | 0.773 | 0.868 |
A-J-10 | A | 1.140 | 1.082 | 1.238 |
A-J-9 | 9 | 1.156 | 0.936 | 1.122 |
A-J-8 | 8 | 1.155 | 0.883 | 1.024 |
A-J-7 | 7 | 1.157 | 0.845 | 0.945 |
A-J-6 | 6 | 1.154 | 0.814 | 0.879 |
A-J-5 | 5 | 1.160 | 0.857 | 0.866 |
A-J-4 | 4 | 1.156 | 0.833 | 0.848 |
A-J-3 | 3 | 1.150 | 0.809 | 0.831 |
A-J-2 | 2 | 1.143 | 0.775 | 0.818 |
A-10-9 | A | 1.068 | 0.935 | 1.131 |
A-10-8 | 8 | 1.070 | 0.881 | 1.041 |
A-10-7 | 7 | 1.067 | 0.843 | 0.962 |
A-10-6 | 6 | 1.069 | 0.812 | 0.888 |
A-10-5 | 5 | 1.074 | 0.861 | 0.824 |
A-10-4 | 4 | 1.071 | 0.834 | 0.811 |
A-10-3 | 3 | 1.068 | 0.809 | 0.796 |
A-10-2 | 2 | 1.061 | 0.775 | 0.782 |
A-9-8 | A | 0.904 | 0.875 | 1.034 |
A-9-7 | A | 0.906 | 0.836 | 0.975 |
A-9-6 | 6 | 0.908 | 0.807 | 0.905 |
A-9-5 | 5 | 0.912 | 0.856 | 0.838 |
A-9-4 | 4 | 0.911 | 0.834 | 0.773 |
A-9-3 | 3 | 0.906 | 0.805 | 0.760 |
A-9-2 | 2 | 0.902 | 0.772 | 0.751 |
A-8-7 | A | 0.855 | 0.835 | 0.987 |
A-8-6 | A | 0.856 | 0.805 | 0.939 |
A-8-5 | A | 0.862 | 0.853 | 0.873 |
A-8-4 | 4 | 0.862 | 0.832 | 0.799 |
A-8-3 | 3 | 0.857 | 0.810 | 0.734 |
A-8-2 | 2 | 0.854 | 0.772 | 0.726 |
A-7-6 | A | 0.820 | 0.802 | 0.958 |
A-7-5 | A | 0.821 | 0.849 | 0.908 |
A-7-4 | A | 0.821 | 0.828 | 0.839 |
A-7-3 | 3 | 0.821 | 0.807 | 0.764 |
A-7-2 | 2 | 0.819 | 0.778 | 0.705 |
A-6-5 | A | 0.791 | 0.853 | 0.937 |
A-6-4 | A | 0.789 | 0.827 | 0.880 |
A-6-3 | A | 0.789 | 0.807 | 0.814 |
A-6-2 | 2 | 0.790 | 0.779 | 0.742 |
A-5-4 | A | 0.824 | 0.810 | 0.906 |
A-5-3 | A | 0.822 | 0.787 | 0.849 |
A-5-2 | 2 | 0.823 | 0.760 | 0.784 |
A-4-3 | A | 0.799 | 0.786 | 0.818 |
A-4-2 | 2 | 0.801 | 0.758 | 0.764 |
A-3-2 | 2 | 0.778 | 0.753 | 0.735 |
K-Q-J | K | 1.148 | 1.082 | 1.300 |
K-Q-10 | K | 1.148 | 1.005 | 1.238 |
K-Q-9 | 9 | 1.164 | 0.862 | 1.114 |
K-Q-8 | 8 | 1.177 | 0.776 | 1.032 |
K-Q-7 | 7 | 1.175 | 0.748 | 0.953 |
K-Q-6 | 6 | 1.178 | 0.723 | 0.938 |
K-Q-5 | 5 | 1.177 | 0.705 | 0.923 |
K-Q-4 | 4 | 1.171 | 0.680 | 0.906 |
K-Q-3 | 3 | 1.171 | 0.664 | 0.885 |
K-Q-2 | 2 | 1.161 | 0.642 | 0.870 |
K-J-10 | K | 1.054 | 1.005 | 1.223 |
K-J-9 | K | 1.069 | 0.861 | 1.105 |
K-J-8 | 8 | 1.081 | 0.776 | 1.031 |
K-J-7 | 7 | 1.084 | 0.749 | 0.944 |
K-J-6 | 6 | 1.080 | 0.726 | 0.879 |
K-J-5 | 5 | 1.083 | 0.705 | 0.867 |
K-J-4 | 4 | 1.079 | 0.682 | 0.849 |
K-J-3 | 3 | 1.077 | 0.663 | 0.833 |
K-J-2 | 2 | 1.068 | 0.643 | 0.819 |
K-10-9 | K | 0.996 | 0.861 | 1.116 |
K-10-8 | K | 1.011 | 0.774 | 1.044 |
K-10-7 | 7 | 1.011 | 0.748 | 0.960 |
K-10-6 | 6 | 1.014 | 0.727 | 0.889 |
K-10-5 | 5 | 1.011 | 0.707 | 0.828 |
K-10-4 | 4 | 1.011 | 0.684 | 0.814 |
K-10-3 | 3 | 1.007 | 0.663 | 0.798 |
K-10-2 | 2 | 1.001 | 0.643 | 0.783 |
K-9-8 | K | 0.846 | 0.769 | 1.038 |
K-9-7 | K | 0.849 | 0.744 | 0.976 |
K-9-6 | K | 0.849 | 0.722 | 0.907 |
K-9-5 | 5 | 0.851 | 0.705 | 0.840 |
K-9-4 | 4 | 0.848 | 0.683 | 0.775 |
K-9-3 | 3 | 0.848 | 0.663 | 0.763 |
K-9-2 | 2 | 0.844 | 0.643 | 0.751 |
K-8-7 | K | 0.751 | 0.737 | 0.994 |
K-8-6 | K | 0.752 | 0.716 | 0.943 |
K-8-5 | K | 0.756 | 0.698 | 0.877 |
K-8-4 | K | 0.757 | 0.682 | 0.803 |
K-8-3 | 3 | 0.753 | 0.662 | 0.741 |
K-8-2 | 2 | 0.749 | 0.639 | 0.732 |
K-7-6 | K | 0.725 | 0.717 | 0.961 |
K-7-5 | K | 0.727 | 0.699 | 0.911 |
K-7-4 | K | 0.727 | 0.680 | 0.840 |
K-7-3 | K | 0.728 | 0.662 | 0.768 |
K-7-2 | 2 | 0.727 | 0.645 | 0.709 |
K-6-5 | K | 0.704 | 0.695 | 0.940 |
K-6-4 | K | 0.703 | 0.676 | 0.883 |
K-6-3 | K | 0.703 | 0.659 | 0.815 |
K-6-2 | K | 0.703 | 0.641 | 0.745 |
K-5-4 | K | 0.683 | 0.671 | 0.925 |
K-5-3 | K | 0.684 | 0.653 | 0.868 |
K-5-2 | K | 0.683 | 0.636 | 0.801 |
K-4-3 | K | 0.664 | 0.651 | 0.837 |
K-4-2 | K | 0.663 | 0.635 | 0.782 |
K-3-2 | K | 0.645 | 0.633 | 0.750 |
Q-J-10 | Q | 0.994 | 0.956 | 1.205 |
Q-J-9 | Q | 1.011 | 0.822 | 1.089 |
Q-J-8 | 8 | 1.026 | 0.738 | 1.013 |
Q-J-7 | 7 | 1.041 | 0.674 | 0.948 |
Q-J-6 | 6 | 1.041 | 0.658 | 0.877 |
Q-J-5 | 5 | 1.041 | 0.641 | 0.866 |
Q-J-4 | 4 | 1.039 | 0.621 | 0.850 |
Q-J-3 | 3 | 1.034 | 0.601 | 0.834 |
Q-J-2 | 2 | 1.030 | 0.585 | 0.818 |
Q-10-9 | Q | 0.953 | 0.822 | 1.101 |
Q-10-8 | Q | 0.965 | 0.737 | 1.029 |
Q-10-7 | 7 | 0.982 | 0.672 | 0.964 |
Q-10-6 | 6 | 0.981 | 0.658 | 0.886 |
Q-10-5 | 5 | 0.982 | 0.645 | 0.825 |
Q-10-4 | 4 | 0.980 | 0.619 | 0.813 |
Q-10-3 | 3 | 0.977 | 0.603 | 0.796 |
Q-10-2 | 2 | 0.974 | 0.586 | 0.781 |
Q-9-8 | Q | 0.812 | 0.737 | 1.027 |
Q-9-7 | Q | 0.826 | 0.669 | 0.980 |
Q-9-6 | Q | 0.826 | 0.655 | 0.906 |
Q-9-5 | Q | 0.827 | 0.640 | 0.838 |
Q-9-4 | 4 | 0.828 | 0.622 | 0.774 |
Q-9-3 | 3 | 0.827 | 0.603 | 0.763 |
Q-9-2 | 2 | 0.823 | 0.587 | 0.750 |
Q-8-7 | Q | 0.729 | 0.665 | 0.999 |
Q-8-6 | Q | 0.732 | 0.651 | 0.943 |
Q-8-5 | Q | 0.732 | 0.637 | 0.873 |
Q-8-4 | Q | 0.733 | 0.620 | 0.803 |
Q-8-3 | Q | 0.734 | 0.605 | 0.741 |
Q-8-2 | Q | 0.730 | 0.586 | 0.731 |
Q-7-6 | Q | 0.651 | 0.647 | 0.968 |
Q-7-5 | Q | 0.652 | 0.633 | 0.917 |
Q-7-4 | Q | 0.656 | 0.618 | 0.846 |
Q-7-3 | Q | 0.657 | 0.600 | 0.772 |
Q-7-2 | Q | 0.655 | 0.587 | 0.713 |
Q-6-5 | Q | 0.639 | 0.633 | 0.938 |
Q-6-4 | Q | 0.638 | 0.615 | 0.882 |
Q-6-3 | Q | 0.640 | 0.599 | 0.816 |
Q-6-2 | Q | 0.641 | 0.585 | 0.747 |
Q-5-4 | Q | 0.624 | 0.612 | 0.927 |
Q-5-3 | Q | 0.622 | 0.595 | 0.870 |
Q-5-2 | Q | 0.624 | 0.582 | 0.804 |
Q-4-3 | Q | 0.605 | 0.594 | 0.838 |
Q-4-2 | Q | 0.605 | 0.580 | 0.783 |
Q-3-2 | Q | 0.590 | 0.579 | 0.751 |
J-10-9 | J | 0.930 | 0.808 | 1.084 |
J-10-8 | J | 0.946 | 0.729 | 1.014 |
J-10-7 | 7 | 0.964 | 0.660 | 0.951 |
J-10-6 | 6 | 0.981 | 0.606 | 0.893 |
J-10-5 | 5 | 0.979 | 0.594 | 0.827 |
J-10-4 | 4 | 0.979 | 0.572 | 0.811 |
J-10-3 | 3 | 0.975 | 0.554 | 0.795 |
J-10-2 | 2 | 0.972 | 0.541 | 0.782 |
J-9-8 | J | 0.803 | 0.729 | 1.012 |
J-9-7 | J | 0.818 | 0.658 | 0.966 |
J-9-6 | J | 0.834 | 0.603 | 0.911 |
J-9-5 | J | 0.833 | 0.592 | 0.838 |
J-9-4 | 4 | 0.835 | 0.575 | 0.773 |
J-9-3 | 3 | 0.833 | 0.556 | 0.760 |
J-9-2 | 2 | 0.831 | 0.541 | 0.748 |
J-8-7 | J | 0.727 | 0.657 | 0.986 |
J-8-6 | J | 0.743 | 0.602 | 0.948 |
J-8-5 | J | 0.743 | 0.591 | 0.875 |
J-8-4 | J | 0.743 | 0.575 | 0.803 |
J-8-3 | 3 | 0.742 | 0.558 | 0.738 |
J-8-2 | 2 | 0.743 | 0.544 | 0.731 |
J-7-6 | J | 0.660 | 0.600 | 0.972 |
J-7-5 | J | 0.657 | 0.587 | 0.916 |
J-7-4 | J | 0.659 | 0.571 | 0.843 |
J-7-3 | J | 0.660 | 0.558 | 0.770 |
J-7-2 | J | 0.660 | 0.545 | 0.711 |
J-6-5 | J | 0.588 | 0.584 | 0.946 |
J-6-4 | J | 0.590 | 0.569 | 0.887 |
J-6-3 | J | 0.592 | 0.554 | 0.817 |
J-6-2 | J | 0.594 | 0.542 | 0.747 |
J-5-4 | J | 0.577 | 0.567 | 0.924 |
J-5-3 | J | 0.579 | 0.553 | 0.871 |
J-5-2 | J | 0.579 | 0.540 | 0.803 |
J-4-3 | J | 0.561 | 0.551 | 0.838 |
J-4-2 | J | 0.562 | 0.540 | 0.783 |
J-3-2 | J | 0.545 | 0.538 | 0.752 |
10-9-8 | 10 | 0.812 | 0.739 | 0.994 |
10-9-7 | 10 | 0.826 | 0.671 | 0.948 |
10-9-6 | 10 | 0.843 | 0.611 | 0.894 |
10-9-5 | 5 | 0.861 | 0.559 | 0.842 |
10-9-4 | 4 | 0.859 | 0.544 | 0.770 |
10-9-3 | 3 | 0.859 | 0.528 | 0.757 |
10-9-2 | 2 | 0.857 | 0.513 | 0.748 |
10-8-7 | 10 | 0.740 | 0.671 | 0.969 |
10-8-6 | 10 | 0.756 | 0.610 | 0.934 |
10-8-5 | 10 | 0.772 | 0.557 | 0.879 |
10-8-4 | 10 | 0.772 | 0.543 | 0.798 |
10-8-3 | 3 | 0.773 | 0.531 | 0.737 |
10-8-2 | 2 | 0.772 | 0.515 | 0.729 |
10-7-6 | 10 | 0.675 | 0.608 | 0.959 |
10-7-5 | 10 | 0.689 | 0.555 | 0.920 |
10-7-4 | 10 | 0.690 | 0.543 | 0.844 |
10-7-3 | 10 | 0.692 | 0.529 | 0.767 |
10-7-2 | 10 | 0.690 | 0.517 | 0.709 |
10-6-5 | 10 | 0.612 | 0.554 | 0.952 |
10-6-4 | 10 | 0.611 | 0.540 | 0.884 |
10-6-3 | 10 | 0.615 | 0.528 | 0.818 |
10-6-2 | 10 | 0.616 | 0.517 | 0.747 |
10-5-4 | 10 | 0.546 | 0.538 | 0.932 |
10-5-3 | 10 | 0.548 | 0.525 | 0.873 |
10-5-2 | 10 | 0.549 | 0.515 | 0.804 |
10-4-3 | 10 | 0.533 | 0.524 | 0.837 |
10-4-2 | 10 | 0.533 | 0.513 | 0.785 |
10-3-2 | 10 | 0.521 | 0.513 | 0.753 |
9-8-7 | 9 | 0.719 | 0.674 | 0.952 |
9-8-6 | 9 | 0.731 | 0.617 | 0.914 |
9-8-5 | 9 | 0.751 | 0.559 | 0.863 |
9-8-4 | 9 | 0.768 | 0.504 | 0.805 |
9-8-3 | 3 | 0.765 | 0.495 | 0.734 |
9-8-2 | 2 | 0.763 | 0.480 | 0.726 |
9-7-6 | 9 | 0.674 | 0.614 | 0.941 |
9-7-5 | 9 | 0.691 | 0.558 | 0.904 |
9-7-4 | 9 | 0.711 | 0.503 | 0.847 |
9-7-3 | 9 | 0.711 | 0.493 | 0.765 |
9-7-2 | 2 | 0.709 | 0.484 | 0.708 |
9-6-5 | 9 | 0.620 | 0.557 | 0.935 |
9-6-4 | 9 | 0.636 | 0.501 | 0.891 |
9-6-3 | 9 | 0.639 | 0.491 | 0.814 |
9-6-2 | 9 | 0.639 | 0.480 | 0.743 |
9-5-4 | 9 | 0.563 | 0.497 | 0.934 |
9-5-3 | 9 | 0.563 | 0.489 | 0.872 |
9-5-2 | 9 | 0.566 | 0.480 | 0.802 |
9-4-3 | 9 | 0.494 | 0.488 | 0.843 |
9-4-2 | 9 | 0.497 | 0.479 | 0.788 |
9-3-2 | 9 | 0.487 | 0.480 | 0.753 |
8-7-6 | 8 | 0.685 | 0.645 | 0.924 |
8-7-5 | 8 | 0.699 | 0.590 | 0.888 |
8-7-4 | 8 | 0.717 | 0.526 | 0.829 |
8-7-3 | 8 | 0.735 | 0.476 | 0.771 |
8-7-2 | 2 | 0.733 | 0.468 | 0.708 |
8-6-5 | 8 | 0.648 | 0.585 | 0.919 |
8-6-4 | 8 | 0.667 | 0.526 | 0.874 |
8-6-3 | 8 | 0.684 | 0.473 | 0.820 |
8-6-2 | 8 | 0.684 | 0.467 | 0.741 |
8-5-4 | 8 | 0.594 | 0.523 | 0.922 |
8-5-3 | 8 | 0.615 | 0.471 | 0.877 |
8-5-2 | 8 | 0.613 | 0.466 | 0.800 |
8-4-3 | 8 | 0.535 | 0.471 | 0.846 |
8-4-2 | 8 | 0.535 | 0.467 | 0.783 |
8-3-2 | 8 | 0.470 | 0.467 | 0.761 |
7-6-5 | 7 | 0.662 | 0.622 | 0.903 |
7-6-4 | 7 | 0.679 | 0.560 | 0.856 |
7-6-3 | 7 | 0.696 | 0.500 | 0.804 |
7-6-2 | 7 | 0.713 | 0.452 | 0.745 |
7-5-4 | 7 | 0.627 | 0.559 | 0.905 |
7-5-3 | 7 | 0.646 | 0.498 | 0.860 |
7-5-2 | 7 | 0.663 | 0.450 | 0.807 |
7-4-3 | 7 | 0.570 | 0.498 | 0.833 |
7-4-2 | 7 | 0.591 | 0.453 | 0.790 |
7-3-2 | 7 | 0.512 | 0.452 | 0.765 |
6-5-4 | 6 | 0.646 | 0.594 | 0.884 |
6-5-3 | 6 | 0.664 | 0.538 | 0.844 |
6-5-2 | 6 | 0.681 | 0.480 | 0.787 |
6-4-3 | 6 | 0.605 | 0.538 | 0.814 |
6-4-2 | 6 | 0.625 | 0.481 | 0.771 |
6-3-2 | 6 | 0.556 | 0.483 | 0.747 |
5-4-3 | 5 | 0.638 | 0.584 | 0.793 |
5-4-2 | 5 | 0.654 | 0.529 | 0.752 |
5-3-2 | 5 | 0.599 | 0.532 | 0.728 |
4-3-2 | 4 | 0.566 | 0.517 | 0.726 |
Three Singletons — Outside Two Suited
The following table shows the expected return for all three possible plays when dealt three singletons when the lowest and highest two are suited. 74.1% of the time, the best play is to keep the suited cards and discard the middle. The following table shows the expected return for all three ways ways to choose two of the three cards.
Three Singletons — Outside Two Suited
Hand | Discard | Expected Return Middle and High |
Expected Return Low and High |
Expected Return Low and Middle |
---|---|---|---|---|
A-K-Q | K | 1.400 | 1.533 | 1.256 |
A-K-J | K | 1.405 | 1.417 | 1.146 |
A-K-10 | 10 | 1.404 | 1.332 | 1.065 |
A-K-9 | 9 | 1.419 | 1.196 | 0.918 |
A-K-8 | 8 | 1.415 | 1.147 | 0.810 |
A-K-7 | 7 | 1.418 | 1.109 | 0.778 |
A-K-6 | 6 | 1.416 | 1.080 | 0.749 |
A-K-5 | 5 | 1.417 | 1.119 | 0.729 |
A-K-4 | 4 | 1.413 | 1.098 | 0.706 |
A-K-3 | 3 | 1.405 | 1.078 | 0.686 |
A-K-2 | 2 | 1.397 | 1.045 | 0.666 |
A-Q-J | Q | 1.244 | 1.416 | 1.088 |
A-Q-10 | Q | 1.250 | 1.329 | 1.021 |
A-Q-9 | 9 | 1.263 | 1.194 | 0.885 |
A-Q-8 | 8 | 1.260 | 1.144 | 0.778 |
A-Q-7 | 7 | 1.260 | 1.111 | 0.696 |
A-Q-6 | 6 | 1.260 | 1.078 | 0.678 |
A-Q-5 | 5 | 1.263 | 1.124 | 0.660 |
A-Q-4 | 4 | 1.260 | 1.103 | 0.641 |
A-Q-3 | 3 | 1.253 | 1.081 | 0.620 |
A-Q-2 | 2 | 1.248 | 1.048 | 0.605 |
A-J-10 | J | 1.133 | 1.331 | 1.011 |
A-J-9 | J | 1.147 | 1.195 | 0.884 |
A-J-8 | J | 1.145 | 1.147 | 0.780 |
A-J-7 | 7 | 1.144 | 1.112 | 0.694 |
A-J-6 | 6 | 1.144 | 1.084 | 0.623 |
A-J-5 | 5 | 1.146 | 1.125 | 0.606 |
A-J-4 | 4 | 1.144 | 1.103 | 0.587 |
A-J-3 | 3 | 1.139 | 1.082 | 0.572 |
A-J-2 | 2 | 1.134 | 1.050 | 0.557 |
A-10-9 | 10 | 1.055 | 1.194 | 0.899 |
A-10-8 | 10 | 1.057 | 1.149 | 0.802 |
A-10-7 | 10 | 1.054 | 1.109 | 0.718 |
A-10-6 | 10 | 1.059 | 1.083 | 0.641 |
A-10-5 | 10 | 1.063 | 1.131 | 0.572 |
A-10-4 | 10 | 1.057 | 1.102 | 0.554 |
A-10-3 | 10 | 1.055 | 1.081 | 0.541 |
A-10-2 | 10 | 1.048 | 1.049 | 0.525 |
A-9-8 | 9 | 0.891 | 1.138 | 0.799 |
A-9-7 | 9 | 0.892 | 1.103 | 0.737 |
A-9-6 | 9 | 0.894 | 1.076 | 0.663 |
A-9-5 | 9 | 0.900 | 1.124 | 0.590 |
A-9-4 | 9 | 0.895 | 1.104 | 0.518 |
A-9-3 | 9 | 0.891 | 1.075 | 0.504 |
A-9-2 | 9 | 0.890 | 1.046 | 0.495 |
A-8-7 | 8 | 0.839 | 1.102 | 0.751 |
A-8-6 | 8 | 0.842 | 1.075 | 0.702 |
A-8-5 | 8 | 0.843 | 1.119 | 0.630 |
A-8-4 | 8 | 0.844 | 1.101 | 0.550 |
A-8-3 | 8 | 0.844 | 1.083 | 0.485 |
A-8-2 | 8 | 0.839 | 1.048 | 0.475 |
A-7-6 | 7 | 0.802 | 1.070 | 0.726 |
A-7-5 | 7 | 0.805 | 1.117 | 0.673 |
A-7-4 | 7 | 0.807 | 1.099 | 0.600 |
A-7-3 | 7 | 0.806 | 1.081 | 0.520 |
A-7-2 | 7 | 0.805 | 1.054 | 0.461 |
A-6-5 | 6 | 0.775 | 1.120 | 0.707 |
A-6-4 | 6 | 0.774 | 1.102 | 0.649 |
A-6-3 | 6 | 0.773 | 1.080 | 0.578 |
A-6-2 | 6 | 0.773 | 1.055 | 0.502 |
A-5-4 | 5 | 0.805 | 1.078 | 0.678 |
A-5-3 | 5 | 0.807 | 1.061 | 0.622 |
A-5-2 | 5 | 0.805 | 1.034 | 0.553 |
A-4-3 | 4 | 0.782 | 1.059 | 0.588 |
A-4-2 | 4 | 0.782 | 1.033 | 0.533 |
A-3-2 | 3 | 0.760 | 1.030 | 0.504 |
K-Q-J | Q | 1.144 | 1.318 | 1.073 |
K-Q-10 | Q | 1.147 | 1.249 | 1.006 |
K-Q-9 | 9 | 1.162 | 1.116 | 0.867 |
K-Q-8 | 8 | 1.175 | 1.038 | 0.783 |
K-Q-7 | 7 | 1.171 | 1.009 | 0.694 |
K-Q-6 | 6 | 1.173 | 0.985 | 0.679 |
K-Q-5 | 5 | 1.172 | 0.969 | 0.661 |
K-Q-4 | 4 | 1.172 | 0.951 | 0.643 |
K-Q-3 | 3 | 1.166 | 0.935 | 0.623 |
K-Q-2 | 2 | 1.159 | 0.914 | 0.607 |
K-J-10 | J | 1.047 | 1.246 | 0.994 |
K-J-9 | J | 1.063 | 1.115 | 0.865 |
K-J-8 | 8 | 1.078 | 1.037 | 0.783 |
K-J-7 | 7 | 1.075 | 1.008 | 0.691 |
K-J-6 | 6 | 1.076 | 0.991 | 0.622 |
K-J-5 | 5 | 1.078 | 0.973 | 0.608 |
K-J-4 | 4 | 1.073 | 0.952 | 0.589 |
K-J-3 | 3 | 1.069 | 0.935 | 0.571 |
K-J-2 | 2 | 1.061 | 0.914 | 0.556 |
K-10-9 | 10 | 0.988 | 1.112 | 0.882 |
K-10-8 | 10 | 1.002 | 1.035 | 0.808 |
K-10-7 | 10 | 1.003 | 1.008 | 0.715 |
K-10-6 | 6 | 1.005 | 0.991 | 0.638 |
K-10-5 | 5 | 1.005 | 0.977 | 0.574 |
K-10-4 | 4 | 1.003 | 0.952 | 0.557 |
K-10-3 | 3 | 0.998 | 0.934 | 0.541 |
K-10-2 | 2 | 0.994 | 0.917 | 0.527 |
K-9-8 | 9 | 0.838 | 1.032 | 0.805 |
K-9-7 | 9 | 0.838 | 1.005 | 0.737 |
K-9-6 | 9 | 0.841 | 0.986 | 0.664 |
K-9-5 | 9 | 0.842 | 0.974 | 0.591 |
K-9-4 | 9 | 0.841 | 0.954 | 0.522 |
K-9-3 | 9 | 0.838 | 0.933 | 0.508 |
K-9-2 | 9 | 0.831 | 0.913 | 0.496 |
K-8-7 | 8 | 0.743 | 1.001 | 0.763 |
K-8-6 | 8 | 0.742 | 0.981 | 0.705 |
K-8-5 | 8 | 0.744 | 0.968 | 0.635 |
K-8-4 | 8 | 0.745 | 0.949 | 0.556 |
K-8-3 | 8 | 0.745 | 0.937 | 0.491 |
K-8-2 | 8 | 0.741 | 0.912 | 0.481 |
K-7-6 | 7 | 0.714 | 0.983 | 0.729 |
K-7-5 | 7 | 0.714 | 0.964 | 0.677 |
K-7-4 | 7 | 0.715 | 0.950 | 0.603 |
K-7-3 | 7 | 0.716 | 0.933 | 0.526 |
K-7-2 | 7 | 0.714 | 0.917 | 0.463 |
K-6-5 | 6 | 0.690 | 0.964 | 0.709 |
K-6-4 | 6 | 0.692 | 0.947 | 0.650 |
K-6-3 | 6 | 0.692 | 0.928 | 0.580 |
K-6-2 | 6 | 0.693 | 0.913 | 0.505 |
K-5-4 | 5 | 0.670 | 0.942 | 0.695 |
K-5-3 | 5 | 0.672 | 0.927 | 0.641 |
K-5-2 | 5 | 0.672 | 0.909 | 0.570 |
K-4-3 | 4 | 0.653 | 0.926 | 0.609 |
K-4-2 | 4 | 0.652 | 0.908 | 0.553 |
K-3-2 | 3 | 0.632 | 0.906 | 0.524 |
Q-J-10 | J | 0.991 | 1.193 | 0.974 |
Q-J-9 | J | 1.009 | 1.069 | 0.849 |
Q-J-8 | 8 | 1.023 | 0.993 | 0.766 |
Q-J-7 | 7 | 1.038 | 0.933 | 0.697 |
Q-J-6 | 6 | 1.037 | 0.920 | 0.622 |
Q-J-5 | 5 | 1.037 | 0.902 | 0.607 |
Q-J-4 | 4 | 1.036 | 0.885 | 0.589 |
Q-J-3 | 3 | 1.035 | 0.872 | 0.572 |
Q-J-2 | 2 | 1.026 | 0.851 | 0.555 |
Q-10-9 | 10 | 0.945 | 1.067 | 0.865 |
Q-10-8 | 10 | 0.965 | 0.991 | 0.792 |
Q-10-7 | 7 | 0.978 | 0.933 | 0.721 |
Q-10-6 | 6 | 0.976 | 0.920 | 0.637 |
Q-10-5 | 5 | 0.977 | 0.904 | 0.572 |
Q-10-4 | 4 | 0.976 | 0.884 | 0.554 |
Q-10-3 | 3 | 0.975 | 0.868 | 0.540 |
Q-10-2 | 2 | 0.971 | 0.854 | 0.527 |
Q-9-8 | 9 | 0.807 | 0.989 | 0.790 |
Q-9-7 | 9 | 0.821 | 0.929 | 0.742 |
Q-9-6 | 9 | 0.820 | 0.915 | 0.662 |
Q-9-5 | 9 | 0.820 | 0.903 | 0.587 |
Q-9-4 | 9 | 0.821 | 0.888 | 0.518 |
Q-9-3 | 9 | 0.824 | 0.870 | 0.509 |
Q-9-2 | 9 | 0.817 | 0.852 | 0.494 |
Q-8-7 | 8 | 0.723 | 0.925 | 0.766 |
Q-8-6 | 8 | 0.724 | 0.912 | 0.704 |
Q-8-5 | 8 | 0.724 | 0.901 | 0.633 |
Q-8-4 | 8 | 0.726 | 0.884 | 0.555 |
Q-8-3 | 8 | 0.726 | 0.869 | 0.490 |
Q-8-2 | 8 | 0.725 | 0.853 | 0.482 |
Q-7-6 | 7 | 0.645 | 0.910 | 0.736 |
Q-7-5 | 7 | 0.646 | 0.897 | 0.681 |
Q-7-4 | 7 | 0.647 | 0.884 | 0.604 |
Q-7-3 | 7 | 0.649 | 0.868 | 0.528 |
Q-7-2 | 7 | 0.647 | 0.854 | 0.465 |
Q-6-5 | 6 | 0.630 | 0.898 | 0.710 |
Q-6-4 | 6 | 0.629 | 0.880 | 0.650 |
Q-6-3 | 6 | 0.631 | 0.865 | 0.581 |
Q-6-2 | 6 | 0.634 | 0.853 | 0.505 |
Q-5-4 | 5 | 0.613 | 0.877 | 0.697 |
Q-5-3 | 5 | 0.613 | 0.863 | 0.642 |
Q-5-2 | 5 | 0.614 | 0.850 | 0.571 |
Q-4-3 | 4 | 0.596 | 0.863 | 0.610 |
Q-4-2 | 4 | 0.595 | 0.848 | 0.554 |
Q-3-2 | 3 | 0.580 | 0.847 | 0.525 |
J-10-9 | 10 | 0.930 | 1.051 | 0.850 |
J-10-8 | 10 | 0.946 | 0.977 | 0.774 |
J-10-7 | 7 | 0.964 | 0.915 | 0.707 |
J-10-6 | 6 | 0.979 | 0.863 | 0.643 |
J-10-5 | 5 | 0.980 | 0.853 | 0.571 |
J-10-4 | 4 | 0.978 | 0.834 | 0.555 |
J-10-3 | 3 | 0.975 | 0.817 | 0.539 |
J-10-2 | 2 | 0.972 | 0.804 | 0.526 |
J-9-8 | 9 | 0.797 | 0.976 | 0.772 |
J-9-7 | 9 | 0.814 | 0.913 | 0.725 |
J-9-6 | 9 | 0.831 | 0.863 | 0.669 |
J-9-5 | 9 | 0.831 | 0.851 | 0.587 |
J-9-4 | 9 | 0.832 | 0.835 | 0.518 |
J-9-3 | 3 | 0.828 | 0.819 | 0.505 |
J-9-2 | 2 | 0.827 | 0.804 | 0.493 |
J-8-7 | 8 | 0.721 | 0.910 | 0.750 |
J-8-6 | 8 | 0.738 | 0.860 | 0.713 |
J-8-5 | 8 | 0.737 | 0.847 | 0.633 |
J-8-4 | 8 | 0.739 | 0.836 | 0.554 |
J-8-3 | 8 | 0.740 | 0.819 | 0.488 |
J-8-2 | 8 | 0.739 | 0.808 | 0.479 |
J-7-6 | 7 | 0.653 | 0.858 | 0.742 |
J-7-5 | 7 | 0.652 | 0.847 | 0.680 |
J-7-4 | 7 | 0.653 | 0.833 | 0.604 |
J-7-3 | 7 | 0.655 | 0.819 | 0.528 |
J-7-2 | 7 | 0.654 | 0.808 | 0.466 |
J-6-5 | 6 | 0.583 | 0.845 | 0.716 |
J-6-4 | 6 | 0.585 | 0.830 | 0.656 |
J-6-3 | 6 | 0.587 | 0.819 | 0.584 |
J-6-2 | 6 | 0.586 | 0.807 | 0.507 |
J-5-4 | 5 | 0.571 | 0.829 | 0.698 |
J-5-3 | 5 | 0.572 | 0.816 | 0.641 |
J-5-2 | 5 | 0.573 | 0.803 | 0.571 |
J-4-3 | 4 | 0.553 | 0.815 | 0.609 |
J-4-2 | 4 | 0.554 | 0.803 | 0.554 |
J-3-2 | 3 | 0.538 | 0.801 | 0.524 |
10-9-8 | 9 | 0.810 | 0.981 | 0.756 |
10-9-7 | 9 | 0.824 | 0.916 | 0.706 |
10-9-6 | 9 | 0.842 | 0.861 | 0.649 |
10-9-5 | 5 | 0.859 | 0.815 | 0.592 |
10-9-4 | 4 | 0.856 | 0.802 | 0.515 |
10-9-3 | 3 | 0.858 | 0.785 | 0.504 |
10-9-2 | 2 | 0.854 | 0.773 | 0.491 |
10-8-7 | 8 | 0.737 | 0.918 | 0.732 |
10-8-6 | 8 | 0.752 | 0.860 | 0.694 |
10-8-5 | 8 | 0.770 | 0.815 | 0.639 |
10-8-4 | 8 | 0.769 | 0.801 | 0.553 |
10-8-3 | 8 | 0.770 | 0.788 | 0.485 |
10-8-2 | 8 | 0.769 | 0.773 | 0.477 |
10-7-6 | 7 | 0.670 | 0.859 | 0.727 |
10-7-5 | 7 | 0.686 | 0.811 | 0.683 |
10-7-4 | 7 | 0.687 | 0.800 | 0.602 |
10-7-3 | 7 | 0.688 | 0.790 | 0.525 |
10-7-2 | 7 | 0.688 | 0.777 | 0.465 |
10-6-5 | 6 | 0.609 | 0.813 | 0.722 |
10-6-4 | 6 | 0.608 | 0.801 | 0.653 |
10-6-3 | 6 | 0.609 | 0.787 | 0.581 |
10-6-2 | 6 | 0.611 | 0.776 | 0.508 |
10-5-4 | 5 | 0.541 | 0.795 | 0.705 |
10-5-3 | 5 | 0.543 | 0.783 | 0.645 |
10-5-2 | 5 | 0.545 | 0.773 | 0.575 |
10-4-3 | 4 | 0.528 | 0.783 | 0.609 |
10-4-2 | 4 | 0.530 | 0.773 | 0.555 |
10-3-2 | 3 | 0.516 | 0.774 | 0.525 |
9-8-7 | 8 | 0.717 | 0.918 | 0.715 |
9-8-6 | 8 | 0.732 | 0.864 | 0.674 |
9-8-5 | 8 | 0.748 | 0.810 | 0.619 |
9-8-4 | 4 | 0.765 | 0.759 | 0.556 |
9-8-3 | 3 | 0.763 | 0.751 | 0.484 |
9-8-2 | 2 | 0.764 | 0.736 | 0.476 |
9-7-6 | 7 | 0.674 | 0.862 | 0.707 |
9-7-5 | 7 | 0.690 | 0.808 | 0.666 |
9-7-4 | 7 | 0.707 | 0.759 | 0.607 |
9-7-3 | 7 | 0.708 | 0.749 | 0.523 |
9-7-2 | 7 | 0.706 | 0.737 | 0.462 |
9-6-5 | 6 | 0.618 | 0.808 | 0.706 |
9-6-4 | 6 | 0.635 | 0.756 | 0.657 |
9-6-3 | 6 | 0.636 | 0.748 | 0.578 |
9-6-2 | 6 | 0.637 | 0.738 | 0.504 |
9-5-4 | 5 | 0.562 | 0.756 | 0.710 |
9-5-3 | 5 | 0.560 | 0.749 | 0.642 |
9-5-2 | 5 | 0.562 | 0.735 | 0.572 |
9-4-3 | 4 | 0.491 | 0.746 | 0.616 |
9-4-2 | 4 | 0.494 | 0.738 | 0.557 |
9-3-2 | 3 | 0.482 | 0.738 | 0.524 |
8-7-6 | 7 | 0.685 | 0.886 | 0.688 |
8-7-5 | 7 | 0.700 | 0.835 | 0.648 |
8-7-4 | 7 | 0.717 | 0.777 | 0.588 |
8-7-3 | 3 | 0.736 | 0.728 | 0.530 |
8-7-2 | 2 | 0.735 | 0.722 | 0.463 |
8-6-5 | 6 | 0.649 | 0.834 | 0.687 |
8-6-4 | 6 | 0.666 | 0.775 | 0.640 |
8-6-3 | 6 | 0.682 | 0.725 | 0.584 |
8-6-2 | 6 | 0.682 | 0.719 | 0.501 |
8-5-4 | 5 | 0.593 | 0.772 | 0.692 |
8-5-3 | 5 | 0.611 | 0.724 | 0.648 |
8-5-2 | 5 | 0.612 | 0.717 | 0.570 |
8-4-3 | 4 | 0.534 | 0.727 | 0.619 |
8-4-2 | 4 | 0.532 | 0.719 | 0.557 |
8-3-2 | 3 | 0.468 | 0.719 | 0.531 |
7-6-5 | 6 | 0.662 | 0.860 | 0.669 |
7-6-4 | 6 | 0.679 | 0.803 | 0.621 |
7-6-3 | 6 | 0.698 | 0.745 | 0.567 |
7-6-2 | 2 | 0.712 | 0.700 | 0.505 |
7-5-4 | 5 | 0.626 | 0.800 | 0.675 |
7-5-3 | 5 | 0.646 | 0.742 | 0.631 |
7-5-2 | 5 | 0.663 | 0.697 | 0.576 |
7-4-3 | 4 | 0.571 | 0.746 | 0.603 |
7-4-2 | 4 | 0.589 | 0.699 | 0.561 |
7-3-2 | 3 | 0.510 | 0.701 | 0.536 |
6-5-4 | 5 | 0.645 | 0.829 | 0.656 |
6-5-3 | 5 | 0.662 | 0.776 | 0.612 |
6-5-2 | 5 | 0.681 | 0.721 | 0.557 |
6-4-3 | 4 | 0.605 | 0.778 | 0.587 |
6-4-2 | 4 | 0.623 | 0.722 | 0.543 |
6-3-2 | 3 | 0.553 | 0.723 | 0.518 |
5-4-3 | 4 | 0.635 | 0.816 | 0.562 |
5-4-2 | 4 | 0.654 | 0.762 | 0.519 |
5-3-2 | 3 | 0.597 | 0.764 | 0.495 |
4-3-2 | 3 | 0.567 | 0.748 | 0.494 |
Three Singletons — Highest Two Suited
The following table shows the expected return for all three possible plays when dealt three singletons when the lowest two are suited. 100% of the time, the best play is to keep the suited cards and discard the lowest. The rest of the time, discard the lowest card. The following table shows the expected return for all three ways ways to choose two of the three cards.
Three Singletons — Highest Two Suited
Hand | Discard | Expected Return Middle and High |
Expected Return Low and High |
Expected Return Low and Middle |
---|---|---|---|---|
A-K-Q | Q | 1.632 | 1.286 | 1.252 |
A-K-J | J | 1.638 | 1.162 | 1.143 |
A-K-10 | 10 | 1.638 | 1.066 | 1.060 |
A-K-9 | 9 | 1.651 | 0.920 | 0.912 |
A-K-8 | 8 | 1.646 | 0.865 | 0.803 |
A-K-7 | 7 | 1.651 | 0.823 | 0.769 |
A-K-6 | 6 | 1.645 | 0.789 | 0.743 |
A-K-5 | 5 | 1.652 | 0.837 | 0.720 |
A-K-4 | 4 | 1.646 | 0.810 | 0.699 |
A-K-3 | 3 | 1.636 | 0.784 | 0.678 |
A-K-2 | 2 | 1.629 | 0.752 | 0.657 |
A-Q-J | J | 1.493 | 1.160 | 1.088 |
A-Q-10 | 10 | 1.498 | 1.067 | 1.019 |
A-Q-9 | 9 | 1.512 | 0.921 | 0.881 |
A-Q-8 | 8 | 1.506 | 0.865 | 0.773 |
A-Q-7 | 7 | 1.506 | 0.827 | 0.691 |
A-Q-6 | 6 | 1.506 | 0.791 | 0.674 |
A-Q-5 | 5 | 1.510 | 0.837 | 0.654 |
A-Q-4 | 4 | 1.507 | 0.812 | 0.633 |
A-Q-3 | 3 | 1.499 | 0.786 | 0.613 |
A-Q-2 | 2 | 1.491 | 0.753 | 0.597 |
A-J-10 | 10 | 1.387 | 1.066 | 1.009 |
A-J-9 | 9 | 1.402 | 0.919 | 0.882 |
A-J-8 | 8 | 1.400 | 0.864 | 0.777 |
A-J-7 | 7 | 1.401 | 0.827 | 0.689 |
A-J-6 | 6 | 1.399 | 0.796 | 0.617 |
A-J-5 | 5 | 1.404 | 0.839 | 0.603 |
A-J-4 | 4 | 1.401 | 0.813 | 0.585 |
A-J-3 | 3 | 1.395 | 0.790 | 0.567 |
A-J-2 | 2 | 1.388 | 0.754 | 0.550 |
A-10-9 | 9 | 1.321 | 0.920 | 0.900 |
A-10-8 | 8 | 1.321 | 0.865 | 0.799 |
A-10-7 | 7 | 1.320 | 0.826 | 0.716 |
A-10-6 | 6 | 1.322 | 0.795 | 0.635 |
A-10-5 | 5 | 1.326 | 0.842 | 0.570 |
A-10-4 | 4 | 1.324 | 0.816 | 0.552 |
A-10-3 | 3 | 1.318 | 0.791 | 0.536 |
A-10-2 | 2 | 1.315 | 0.757 | 0.523 |
A-9-8 | 8 | 1.168 | 0.856 | 0.799 |
A-9-7 | 7 | 1.171 | 0.819 | 0.736 |
A-9-6 | 6 | 1.170 | 0.787 | 0.660 |
A-9-5 | 5 | 1.174 | 0.835 | 0.584 |
A-9-4 | 4 | 1.174 | 0.815 | 0.517 |
A-9-3 | 3 | 1.170 | 0.786 | 0.505 |
A-9-2 | 2 | 1.164 | 0.752 | 0.489 |
A-8-7 | 7 | 1.123 | 0.816 | 0.753 |
A-8-6 | 6 | 1.122 | 0.786 | 0.700 |
A-8-5 | 5 | 1.126 | 0.835 | 0.628 |
A-8-4 | 4 | 1.127 | 0.812 | 0.549 |
A-8-3 | 3 | 1.123 | 0.791 | 0.483 |
A-8-2 | 2 | 1.118 | 0.752 | 0.474 |
A-7-6 | 6 | 1.087 | 0.783 | 0.726 |
A-7-5 | 5 | 1.091 | 0.831 | 0.672 |
A-7-4 | 4 | 1.091 | 0.809 | 0.599 |
A-7-3 | 3 | 1.090 | 0.788 | 0.520 |
A-7-2 | 2 | 1.088 | 0.758 | 0.458 |
A-6-5 | 5 | 1.063 | 0.834 | 0.707 |
A-6-4 | 4 | 1.064 | 0.812 | 0.649 |
A-6-3 | 3 | 1.063 | 0.789 | 0.576 |
A-6-2 | 2 | 1.062 | 0.761 | 0.502 |
A-5-4 | 4 | 1.090 | 0.789 | 0.677 |
A-5-3 | 3 | 1.094 | 0.771 | 0.622 |
A-5-2 | 2 | 1.091 | 0.738 | 0.552 |
A-4-3 | 3 | 1.072 | 0.768 | 0.589 |
A-4-2 | 2 | 1.069 | 0.735 | 0.532 |
A-3-2 | 2 | 1.050 | 0.736 | 0.504 |
K-Q-J | J | 1.384 | 1.072 | 1.071 |
K-Q-10 | 10 | 1.387 | 0.995 | 1.002 |
K-Q-9 | 9 | 1.398 | 0.849 | 0.862 |
K-Q-8 | 8 | 1.414 | 0.764 | 0.779 |
K-Q-7 | 7 | 1.412 | 0.733 | 0.689 |
K-Q-6 | 6 | 1.414 | 0.709 | 0.672 |
K-Q-5 | 5 | 1.411 | 0.689 | 0.655 |
K-Q-4 | 4 | 1.408 | 0.668 | 0.635 |
K-Q-3 | 3 | 1.402 | 0.647 | 0.617 |
K-Q-2 | 2 | 1.393 | 0.625 | 0.599 |
K-J-10 | 10 | 1.291 | 0.992 | 0.991 |
K-J-9 | 9 | 1.311 | 0.849 | 0.864 |
K-J-8 | 8 | 1.323 | 0.765 | 0.783 |
K-J-7 | 7 | 1.323 | 0.735 | 0.688 |
K-J-6 | 6 | 1.321 | 0.712 | 0.619 |
K-J-5 | 5 | 1.322 | 0.689 | 0.604 |
K-J-4 | 4 | 1.322 | 0.669 | 0.587 |
K-J-3 | 3 | 1.316 | 0.649 | 0.569 |
K-J-2 | 2 | 1.309 | 0.629 | 0.552 |
K-10-9 | 9 | 1.242 | 0.850 | 0.885 |
K-10-8 | 8 | 1.258 | 0.762 | 0.806 |
K-10-7 | 7 | 1.258 | 0.734 | 0.714 |
K-10-6 | 6 | 1.258 | 0.713 | 0.637 |
K-10-5 | 5 | 1.254 | 0.691 | 0.570 |
K-10-4 | 4 | 1.254 | 0.670 | 0.553 |
K-10-3 | 3 | 1.252 | 0.649 | 0.538 |
K-10-2 | 2 | 1.246 | 0.629 | 0.522 |
K-9-8 | 8 | 1.104 | 0.758 | 0.805 |
K-9-7 | 7 | 1.104 | 0.730 | 0.736 |
K-9-6 | 6 | 1.106 | 0.707 | 0.662 |
K-9-5 | 5 | 1.107 | 0.688 | 0.586 |
K-9-4 | 4 | 1.105 | 0.670 | 0.519 |
K-9-3 | 3 | 1.103 | 0.647 | 0.504 |
K-9-2 | 2 | 1.097 | 0.627 | 0.494 |
K-8-7 | 7 | 1.016 | 0.726 | 0.762 |
K-8-6 | 6 | 1.016 | 0.701 | 0.706 |
K-8-5 | 5 | 1.019 | 0.686 | 0.633 |
K-8-4 | 4 | 1.019 | 0.666 | 0.555 |
K-8-3 | 3 | 1.017 | 0.647 | 0.488 |
K-8-2 | 2 | 1.013 | 0.624 | 0.478 |
K-7-6 | 6 | 0.992 | 0.702 | 0.727 |
K-7-5 | 5 | 0.993 | 0.685 | 0.679 |
K-7-4 | 4 | 0.992 | 0.664 | 0.601 |
K-7-3 | 3 | 0.993 | 0.647 | 0.524 |
K-7-2 | 2 | 0.992 | 0.631 | 0.464 |
K-6-5 | 5 | 0.970 | 0.681 | 0.710 |
K-6-4 | 4 | 0.970 | 0.662 | 0.649 |
K-6-3 | 3 | 0.970 | 0.643 | 0.577 |
K-6-2 | 2 | 0.972 | 0.627 | 0.503 |
K-5-4 | 4 | 0.954 | 0.658 | 0.697 |
K-5-3 | 3 | 0.951 | 0.641 | 0.642 |
K-5-2 | 2 | 0.953 | 0.623 | 0.571 |
K-4-3 | 3 | 0.935 | 0.638 | 0.610 |
K-4-2 | 2 | 0.934 | 0.621 | 0.553 |
K-3-2 | 2 | 0.916 | 0.620 | 0.523 |
Q-J-10 | 10 | 1.228 | 0.948 | 0.974 |
Q-J-9 | 9 | 1.245 | 0.814 | 0.846 |
Q-J-8 | 8 | 1.262 | 0.732 | 0.765 |
Q-J-7 | 7 | 1.273 | 0.662 | 0.692 |
Q-J-6 | 6 | 1.274 | 0.648 | 0.618 |
Q-J-5 | 5 | 1.275 | 0.628 | 0.602 |
Q-J-4 | 4 | 1.274 | 0.608 | 0.584 |
Q-J-3 | 3 | 1.269 | 0.591 | 0.567 |
Q-J-2 | 2 | 1.265 | 0.573 | 0.550 |
Q-10-9 | 9 | 1.192 | 0.814 | 0.867 |
Q-10-8 | 8 | 1.204 | 0.730 | 0.788 |
Q-10-7 | 7 | 1.224 | 0.665 | 0.720 |
Q-10-6 | 6 | 1.219 | 0.648 | 0.633 |
Q-10-5 | 5 | 1.221 | 0.631 | 0.568 |
Q-10-4 | 4 | 1.219 | 0.608 | 0.551 |
Q-10-3 | 3 | 1.216 | 0.590 | 0.537 |
Q-10-2 | 2 | 1.213 | 0.576 | 0.523 |
Q-9-8 | 8 | 1.062 | 0.724 | 0.789 |
Q-9-7 | 7 | 1.076 | 0.658 | 0.739 |
Q-9-6 | 6 | 1.078 | 0.645 | 0.661 |
Q-9-5 | 5 | 1.077 | 0.630 | 0.587 |
Q-9-4 | 4 | 1.078 | 0.611 | 0.517 |
Q-9-3 | 3 | 1.074 | 0.590 | 0.504 |
Q-9-2 | 2 | 1.072 | 0.573 | 0.491 |
Q-8-7 | 7 | 0.986 | 0.655 | 0.766 |
Q-8-6 | 6 | 0.988 | 0.641 | 0.705 |
Q-8-5 | 5 | 0.987 | 0.626 | 0.632 |
Q-8-4 | 4 | 0.991 | 0.610 | 0.555 |
Q-8-3 | 3 | 0.990 | 0.593 | 0.488 |
Q-8-2 | 2 | 0.986 | 0.574 | 0.478 |
Q-7-6 | 6 | 0.916 | 0.639 | 0.736 |
Q-7-5 | 5 | 0.916 | 0.625 | 0.681 |
Q-7-4 | 4 | 0.917 | 0.605 | 0.604 |
Q-7-3 | 3 | 0.916 | 0.589 | 0.526 |
Q-7-2 | 2 | 0.916 | 0.574 | 0.465 |
Q-6-5 | 5 | 0.902 | 0.625 | 0.710 |
Q-6-4 | 4 | 0.902 | 0.604 | 0.651 |
Q-6-3 | 3 | 0.903 | 0.589 | 0.579 |
Q-6-2 | 2 | 0.904 | 0.573 | 0.504 |
Q-5-4 | 4 | 0.887 | 0.599 | 0.698 |
Q-5-3 | 3 | 0.885 | 0.583 | 0.643 |
Q-5-2 | 2 | 0.889 | 0.571 | 0.573 |
Q-4-3 | 3 | 0.872 | 0.584 | 0.608 |
Q-4-2 | 2 | 0.870 | 0.568 | 0.555 |
Q-3-2 | 2 | 0.855 | 0.568 | 0.525 |
J-10-9 | 9 | 1.165 | 0.803 | 0.850 |
J-10-8 | 8 | 1.183 | 0.723 | 0.773 |
J-10-7 | 7 | 1.197 | 0.654 | 0.704 |
J-10-6 | 6 | 1.214 | 0.599 | 0.641 |
J-10-5 | 5 | 1.213 | 0.585 | 0.566 |
J-10-4 | 4 | 1.210 | 0.564 | 0.551 |
J-10-3 | 3 | 1.209 | 0.547 | 0.535 |
J-10-2 | 2 | 1.206 | 0.533 | 0.521 |
J-9-8 | 8 | 1.046 | 0.721 | 0.772 |
J-9-7 | 7 | 1.062 | 0.650 | 0.725 |
J-9-6 | 6 | 1.077 | 0.596 | 0.666 |
J-9-5 | 5 | 1.078 | 0.585 | 0.586 |
J-9-4 | 4 | 1.075 | 0.566 | 0.516 |
J-9-3 | 3 | 1.077 | 0.548 | 0.504 |
J-9-2 | 2 | 1.075 | 0.534 | 0.491 |
J-8-7 | 7 | 0.976 | 0.650 | 0.753 |
J-8-6 | 6 | 0.992 | 0.593 | 0.710 |
J-8-5 | 5 | 0.990 | 0.581 | 0.632 |
J-8-4 | 4 | 0.994 | 0.566 | 0.553 |
J-8-3 | 3 | 0.990 | 0.549 | 0.485 |
J-8-2 | 2 | 0.989 | 0.533 | 0.476 |
J-7-6 | 6 | 0.914 | 0.591 | 0.740 |
J-7-5 | 5 | 0.914 | 0.581 | 0.681 |
J-7-4 | 4 | 0.916 | 0.563 | 0.603 |
J-7-3 | 3 | 0.915 | 0.548 | 0.526 |
J-7-2 | 2 | 0.915 | 0.536 | 0.465 |
J-6-5 | 5 | 0.848 | 0.577 | 0.716 |
J-6-4 | 4 | 0.851 | 0.562 | 0.655 |
J-6-3 | 3 | 0.850 | 0.546 | 0.582 |
J-6-2 | 2 | 0.853 | 0.534 | 0.507 |
J-5-4 | 4 | 0.839 | 0.559 | 0.698 |
J-5-3 | 3 | 0.839 | 0.541 | 0.641 |
J-5-2 | 2 | 0.840 | 0.531 | 0.572 |
J-4-3 | 3 | 0.822 | 0.542 | 0.609 |
J-4-2 | 2 | 0.823 | 0.530 | 0.555 |
J-3-2 | 2 | 0.810 | 0.530 | 0.524 |
10-9-8 | 8 | 1.050 | 0.735 | 0.756 |
10-9-7 | 7 | 1.066 | 0.667 | 0.706 |
10-9-6 | 6 | 1.083 | 0.604 | 0.649 |
10-9-5 | 5 | 1.099 | 0.553 | 0.592 |
10-9-4 | 4 | 1.096 | 0.538 | 0.513 |
10-9-3 | 3 | 1.097 | 0.521 | 0.501 |
10-9-2 | 2 | 1.093 | 0.508 | 0.488 |
10-8-7 | 7 | 0.983 | 0.665 | 0.733 |
10-8-6 | 6 | 0.999 | 0.604 | 0.693 |
10-8-5 | 5 | 1.016 | 0.553 | 0.638 |
10-8-4 | 4 | 1.014 | 0.538 | 0.549 |
10-8-3 | 3 | 1.016 | 0.524 | 0.486 |
10-8-2 | 2 | 1.014 | 0.507 | 0.474 |
10-7-6 | 6 | 0.922 | 0.602 | 0.724 |
10-7-5 | 5 | 0.937 | 0.551 | 0.685 |
10-7-4 | 4 | 0.937 | 0.536 | 0.599 |
10-7-3 | 3 | 0.937 | 0.523 | 0.523 |
10-7-2 | 2 | 0.939 | 0.511 | 0.462 |
10-6-5 | 5 | 0.866 | 0.549 | 0.721 |
10-6-4 | 4 | 0.864 | 0.533 | 0.653 |
10-6-3 | 3 | 0.866 | 0.520 | 0.581 |
10-6-2 | 2 | 0.868 | 0.510 | 0.505 |
10-5-4 | 4 | 0.803 | 0.531 | 0.705 |
10-5-3 | 3 | 0.804 | 0.519 | 0.645 |
10-5-2 | 2 | 0.807 | 0.508 | 0.575 |
10-4-3 | 3 | 0.792 | 0.518 | 0.609 |
10-4-2 | 2 | 0.794 | 0.506 | 0.555 |
10-3-2 | 2 | 0.779 | 0.506 | 0.525 |
9-8-7 | 7 | 0.959 | 0.671 | 0.715 |
9-8-6 | 6 | 0.975 | 0.614 | 0.673 |
9-8-5 | 5 | 0.990 | 0.556 | 0.619 |
9-8-4 | 4 | 1.006 | 0.500 | 0.554 |
9-8-3 | 3 | 1.006 | 0.488 | 0.481 |
9-8-2 | 2 | 1.003 | 0.474 | 0.471 |
9-7-6 | 6 | 0.918 | 0.611 | 0.707 |
9-7-5 | 5 | 0.937 | 0.554 | 0.668 |
9-7-4 | 4 | 0.951 | 0.497 | 0.605 |
9-7-3 | 3 | 0.953 | 0.486 | 0.520 |
9-7-2 | 2 | 0.952 | 0.478 | 0.458 |
9-6-5 | 5 | 0.869 | 0.553 | 0.704 |
9-6-4 | 4 | 0.883 | 0.497 | 0.656 |
9-6-3 | 3 | 0.886 | 0.486 | 0.578 |
9-6-2 | 2 | 0.887 | 0.475 | 0.503 |
9-5-4 | 4 | 0.817 | 0.495 | 0.707 |
9-5-3 | 3 | 0.817 | 0.485 | 0.645 |
9-5-2 | 2 | 0.818 | 0.472 | 0.571 |
9-4-3 | 3 | 0.754 | 0.485 | 0.616 |
9-4-2 | 2 | 0.755 | 0.476 | 0.556 |
9-3-2 | 2 | 0.744 | 0.476 | 0.524 |
8-7-6 | 6 | 0.927 | 0.643 | 0.690 |
8-7-5 | 5 | 0.941 | 0.587 | 0.649 |
8-7-4 | 4 | 0.957 | 0.525 | 0.589 |
8-7-3 | 3 | 0.973 | 0.472 | 0.525 |
8-7-2 | 2 | 0.973 | 0.464 | 0.456 |
8-6-5 | 5 | 0.892 | 0.587 | 0.688 |
8-6-4 | 4 | 0.907 | 0.522 | 0.639 |
8-6-3 | 3 | 0.923 | 0.468 | 0.582 |
8-6-2 | 2 | 0.925 | 0.463 | 0.502 |
8-5-4 | 4 | 0.841 | 0.520 | 0.692 |
8-5-3 | 3 | 0.859 | 0.467 | 0.647 |
8-5-2 | 2 | 0.860 | 0.462 | 0.569 |
8-4-3 | 3 | 0.786 | 0.468 | 0.621 |
8-4-2 | 2 | 0.787 | 0.463 | 0.556 |
8-3-2 | 2 | 0.724 | 0.463 | 0.531 |
7-6-5 | 5 | 0.899 | 0.618 | 0.668 |
7-6-4 | 4 | 0.915 | 0.559 | 0.622 |
7-6-3 | 3 | 0.933 | 0.498 | 0.565 |
7-6-2 | 2 | 0.947 | 0.449 | 0.505 |
7-5-4 | 4 | 0.868 | 0.557 | 0.675 |
7-5-3 | 3 | 0.885 | 0.493 | 0.630 |
7-5-2 | 2 | 0.902 | 0.447 | 0.574 |
7-4-3 | 3 | 0.814 | 0.495 | 0.603 |
7-4-2 | 2 | 0.831 | 0.449 | 0.561 |
7-3-2 | 2 | 0.758 | 0.448 | 0.533 |
6-5-4 | 4 | 0.881 | 0.591 | 0.658 |
6-5-3 | 3 | 0.897 | 0.536 | 0.611 |
6-5-2 | 2 | 0.916 | 0.477 | 0.557 |
6-4-3 | 3 | 0.841 | 0.537 | 0.585 |
6-4-2 | 2 | 0.860 | 0.479 | 0.543 |
6-3-2 | 2 | 0.793 | 0.480 | 0.518 |
5-4-3 | 3 | 0.866 | 0.582 | 0.562 |
5-4-2 | 2 | 0.884 | 0.528 | 0.519 |
5-3-2 | 2 | 0.829 | 0.530 | 0.497 |
Power Ratings
The following tables show my power ratings for all hands the player might play, assuming he always plays the two cards with the greatest expected value, as shown in the tables above. Assuming that, some situations will never be played, like unsuited K-6, where the discard is suited to the K or 6. I inflated the expected values by 36.9, so that the best possible hand, A-A discarding a non-ace, had a value of 100. Of course, the actual power ratings will depend slightly on the rank of the discard, so the values seen here are a weighted average.
The following table shows the power rating of holding a pair. The columns are divided according to whether there is a rank penalty (being dealt a three of a kind), a suit penalty (a singleton is suited to a card in the pair, lowering the chance of making a flush, and no penalty card at all.
The following table shows the power ratings of holding any combination of two suited cards, where the discard is of the same suit. In other words, being dealt a three-card flush.
The following table shows the power ratings of holding any combination of two suited cards, where the discard is of a different suit.
The following table shows the power ratings of holding any combination of two off-suit cards, where the discard is suited to one of them, lowering the chances of making a flush.
The following table shows the power ratings of holding any combination of two off-suit cards, where the discard is of a different suit to both of them. In other words, being dealt a "rainbow," which is three different suits.
Methodology
The expected values and strategy in this page were the result of a random simulation. To determine the strategy, I first developed a basic strategy for playing against five psychic opponents, who always held the two cards that would maximize the value of the final hand. I then had all five opponents play this anti-psychic strategy and developed a new optimal strategy to defeat that. I then repeated this process four more times, until the strategy found a Nash equilibrium that couldn't be improved upon. The final numbers are based on a simulation of 6,610,500,000 rounds.