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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.

pineapple -- pair

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.

suited singletons - suit penalty

The following table shows the power ratings of holding any combination of two suited cards, where the discard is of a different suit.

Suited Singletons without Suit Penalty

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.

Unuited Singletons with Suit Penalty

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.

Unsuited Singletons without Suit Penalty

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.

Written by: Michael Shackleford