# Three Card Whist

## Introduction

For the readers under a certain age, the game of whist is an old English card game, from which the game of bridge is derived. I think it could be said to be a simplified version of bridge, without the bidding and randomized partners.

In this casino version of the game, each Player competes against the Dealer and not against other Players. The object of the game is to win more tricks than the Dealer. The game appeared in some UK casinos during 2017 and spread to others in 2018. The House Edge = 1.872% with an Element of Risk = 1.177%.

## Rules

For those unfamiliar with the game of whist or other trick-taking card games, the object is to win tricks. After the trump suit is chosen, the Dealer plays their cards, one at a time. The Player can win a trick either by playing a higher card in the suit led, or trumping; note you always have to follow suit if possible. If you cannot follow suit then you should play a trump, otherwise you just discard one of your remaining cards. Following are the rules of Three-Card Whist:

• One pack of standard cards is used with Ace always being high.
• Each Player should make an “Ante” bet and may also make any of the side bet wagers.
• The Player and Dealer then each receive three cards; the Dealer’s cards are face down.
• An additional card is dealt face up and its suit becomes the trump suit.
• Players look at their hands and decide whether to make a “Play” bet equal to the “Ante” or fold. If you fold then your “Ante” is lost, but any side-bets remain active until they are resolved.
• One by one the Dealer reveals each of their three cards. Players play a card to each trick subject to the rules on following suit, trumping or discarding.
• If the Player wins all three tricks then the “Ante” is paid 1 to 1 and the “Play” is paid 3 to 1.
• If the Player wins two of the three tricks then the “Ante” is paid 1 to 1 and the “Raise” is paid 2 to 1.
• If the Player wins none or one trick, then both “Ante” and “Play” lose.

## Strategy

There are two phases where Players have to make a decision:

• Whether to “Play” or “Fold” — some decisions are easy, but sometimes more thought is required.
• Which card to play to each trick – usually easy to work out, but there are a few discarding quirks.

## “Play” or “Fold” Strategy

In these examples Spades are shown as trumps. When playing please ensure you know which suit is trumps.

Count how many trump cards you hold and then count how other suits you hold. This helps classify the types of hands you may encounter. With some of them the decision whether to play or fold is fairly clear. However for others the decision can depend on the exact ranks and suits of the cards.

## Simple Strategy

The House Edge when using the simple strategy and playing tricks optimally is 2.236% (cost = 0.364%).

## Intermediate Strategy

Use the simple strategy except if you have one trump card only, play as follows (otherwise fold):

## Perfect Strategy

1. 3 or 2 trumps — Always PLAY

2. 1 trump — it is usually correct to play even with medium non-trump cards; however fold with low cards.

Note: when playing optimally the decision is sometimes based on the exact rank of your trump. Rather than saying nth highest trump, the table assumes the trump card being shown face-up is a 2. Thus in the table below the 3 is the 12th highest (or lowest) trump left and A is the highest (or 12th lowest). Therefore adjust your decision depending on the actual rank of the face-up trump card.

With a trump and two other suits:
Fold 3 4 with 64-, 72, 73, 82
Fold 5 with 64-, 72
Fold 6 7 8 with 63-, 72
Fold 9 with 54-, 62, 63
Fold T with 54-, 62
Fold JQKA with 53-, 62

With a trump with the other two cards are in same suit:
Fold 3 4 5 6 7 with 76-
Fold 8 with 74-
Fold 9TJQKA with 65-

3. 0 trumps

• Three different suits - you need 21 outs (i.e. there are 21 cards left in the pack lower than your cards, so you play 999 but fold 998; exceptions are to play QJ3, QQ2, KJ2 and to fold A76). Note: If it is easier to work out, use a total of 27 counting A=14, K=13, Q=12, J=11, 10…2.
• Two different suits
- fold if your two card suit is 10-high or lower.
- fold if your one card suit (singleton) is 7 or lower.
- play if your singleton is
8 with AT+
9 with A7+
T with K7+ (but not A3 A2)
J with Q8+ (but not K3 K2)
Q with Q4+
K with J5+
A with J2+
• 3 cards in same suit — Always FOLD

## Strategy when playing tricks

This part is added for beginners who might be unfamiliar with trick-playing games.

• When a suit is led and you have a card in that suit, ensure you follow suit: —
(a) if you can win the trick — play the lowest card that wins (e.g. 6♥ led: from K♥ 8♥ J♦ play 8♥),
(b) if you can win the trick — play the lowest card that wins (e.g. J♥ led: from K♥ 8♥ J♦ play K♥),
(c) you must follow suit — you cannot trump if you can follow (e.g. A♥ led: from 3♠ K♥ 8♥ play 8♥).

• When a suit is led and you do not have a card in that suit:—
(a) if you can win by trumping play the lowest trump that wins (e.g. J♦ led: from 9♠ 3♠ K♥ play 3♠),
(b) if you cannot win the trick usually discard your lowest card (e.g. 3♠ led: from K♥ 8♥ J♦ play 8♥).
Most the time, subject to the above, you will either have to follow suit or trump; so you only have one sensible play. Sometimes on the first or second tricks you may have to find a discard, normally you just discard your lowest card. One exception of note is if you have a hand such as A♥ K♥ 10♦ (0 trumps, 2 suits) and have to discard on the first trick then discard the lower card of your two-card suit.

## First Round

If playing as per normal strategy above you should always discard the lower card from your two-card suit. The exception to the above is if you somehow find yourself playing a low singleton. In which case you should keep both cards in the doubleton as follows:

K with low 7-2 A♥ K♥ 7♦
Q or J with 6-2 A♥ Q♥ 6♦
10 or 9 with 5-2 A♥ 9♥ 5♦
8 or 7 with 4-2 A♥ 7♥ 4♦
6 or 5 with 3-2 A♥ 5♥ 3♦

The logic is that you have more chances of winning the second trick by holding two different suits and this outweighs the disadvantage of possibly having a lower card left for the third trick. e.g. A♥K♥8♦ discard K♥.

## Second Round

There's also a small chance of discarding the wrong card on the second round. A hand such as A♥6♥K♦: you won the first trick with 6♥, but now have to discard on dealer's A♠. K♦ now has a better chance to win than A♥ (11 to 10 outs), so you discard A♥. In essence this only happens where the singleton is only one rank lower than the higher doubleton, so this is fairly rare and has a very minor effect on the House Edge.

## Seeing other players hands

With a hand such as 10♥ 10♦ 10♣ it’s a pure guess what to throw when the dealer plays a Spade trump. There can also be a similar dilemma if you won the first trick and now have to discard on the second. In theory if you can see cards that other players have played, or hold, then if you saw a lower card in one suit that could help sway your decision. Essentially you are trying to counts “outs” (i.e. cards left that would enable you to win) and discard the card with fewest “outs” remaining. In this example, without any other knowledge, each card would have eight outs (9 8 7 6 5 4 3 2 in their suit) and seeing 6♥ and 9♣ would help.

## Three-card Whist Analysis

The following table shows the analysis of the Three-card Whist bet. The lower right cell shows a house edge of 1.872%.

### Three Card Whist Return Table

Event Pays Combinations Probability Return
Player plays — wins 3 tricks 4 138,860,430 0.064253 0.257014
Player plays — wins 2 tricks 3 512,876,361 0.237318 0.711954
Player plays — wins 0 or 1 tricks -2 625,123,113 0.289257 -0.578514
Player folds -1 884,275,296 0.409172 -0.409172
Total   2,161,135,200 1.000000 -0.018717