Three Card Poker is a casino table game based on poker. The basic game is very straight forward; played with a standard 52 card deck the player places an Ante wager then the player and the dealer are each dealt 3 cards face down (online variants normally deal the player’s cards face up).

Three Card Poker Game Layout 

Three card poker is played with a single deck of cards, which are shuffled on every hand. In a brick and mortar casino, the cards are usually shuffled by an automatic machine and the game is played on a standard, seven-player table.

A three card poker table layout includes:

• Three card shaped spaced for the dealer to place his cards
• A diamond shaped space market ‘Ante’
• A card shaped pace marked ‘Play’
• A circular spot marked ‘Pair Plus’
• Pay tables for the Pair Plus bet and for ante bonus payouts
• A notice which states the minimum and maximum bet

Rules For 3 Card Poker 

In three card poker there are two basic ways to play; Ante-play and Pair Plus play. Some table may also offer additional side bets, but in this guide we’re going to focus on the standard, basic gameplay. Here is a step-by-step walk through of how the game will unfold:

1. The player must make an ante bet (by placing their wager in the diamond shape marked ‘ante’), or a pair plus bet (by placing their wager on the circular spot marked ‘pair plus).
2. The dealer then gives each player and themselves three cards. The dealer’s cards are placed face down, but players can examine their own cards.
3. If you are playing with a ‘Pair Plus’ bet, there is nothing more to do now. However, if you are playing an ante-bet, you must now decide whether to fold or raise. Folding forfeits your wager, whilst raising means you must make an additional play bet which is equal to your original wager.
4. The dealer then shows his cards and must reveal a queen-high hand to qualify.
5. If the dealer doesn’t qualify, you win even money on the original ante wager and the play bet is pushed.
6. If the dealer does qualify, your hands are then compared and the best hand wins.
7. If you have the better hand, you win even money on the original ante wager and the play bet.
8. If the dealer has the better hand, you lose both bets.
9. In the case of a tie, both bets are pushed.
10. If you have a straight or better, you receive the ante bonus (regardless of the value of the dealer’s hand).

3 Card Poker – Ante and Play Strategy

Calculating Strategy

To determine the correct strategy for any hand of Three Card Poker it is necessary to calculate the expected value (E.V.) for each possible decision, in this case either to:

• Fold
• Make the Play bet

The correct strategy is to make which ever decision has the highest expected value.

For the purpose of these calculations the conditions are:

• Use the Standard Rules of Three Card Poker.
• The player has no information other than the three cards dealt to their hand.
• Expected value is calculated on the basis of an Ante bet of 1 unit as opposed to the total amount bet (i.e. Ante + Play bet).
• The Ante Bonus is ignored as it is awarded independently of the result of the hand.

The expected value of the player folding is simply equal to losing the ante bet which is -1.

The expected value of the player making the Play bet is calculated by cycling through all possible dealer hands (⁴⁹C₃ = 18424 possible dealer hands) and determining the frequency of each possible result. The table below illustrates the calculations involved in determining the expected value for making the Play bet given the frequency of each result. While it might be possible to do this calculation by hand, computers can easily and quickly calculate the frequencies and expected value.

Result	Frequency	Probability	Win/Loss	Expected Value
Dealer does not qualify	f1	p1 = f1/18424	1	EV1 = 1 x p1
Dealer qualifies, player’s hand wins	f2	p2 = f2/18424	2	EV2 = 2 x p2
Dealer qualifies, player’s hand ties	f3	p3 = f3/18424	0	0
Dealer qualifies, player’s hand lose	f4	p4 = f4/18424	-2	EV4 = -2 x p4
Total	18424	1.00000000		EV = EV1+EV2+EV4

Optimal Strategy 

By calculating the expected value of each possible player hand it is determined that the optimal strategy is for the player to make the Play bet on all hands ranked Q-6-4 High or better. Any other hand should be folded. Below are the expected values for making the Play bet for Q-6-3 High, Q-6-4 High, and Q-6-5 High. Note that there are only 4 distinct suit combinations with other suit combinations being equivalent to the ones listed (e.g. Q 6 4 is equivalent to Q 6 4).

Hand	No Qualify	Win	Tie	Lose	Play E.V.
Q  6  3	5747	271	26	12380	-1.002551
Q  6  3	5747	270	25	12382	-1.002877
Q  6  3	5747	268	25	12384	-1.003311
Q  6  3	5739	271	25	12389	-1.003962

Hand	No Qualify	Win	Tie	Lose	Play E.V.
Q  6  4	5758	305	26	12335	-0.993378
Q  6  4	5758	303	25	12338	-0.993921
Q  6  4	5758	302	25	12339	-0.994138
Q  6  4	5751	305	25	12343	-0.994627

Hand	No Qualify	Win	Tie	Lose	Play E.V.
Q  6  5	5754	339	26	12305	-0.986648
Q  6  5	5754	336	25	12309	-0.987408
Q  6  5	5754	336	25	12309	-0.987408
Q  6  5	5748	339	25	12312	-0.987733