Three Card Poker Ante and Play Strategy

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.

Dealer does not qualifyf1p1 = f1/184241EV1 = 1 x p1
Dealer qualifies, player's hand winsf2p2 = f2/184242EV2 = 2 x p2
Dealer qualifies, player's hand tiesf3p3 = f3/1842400
Dealer qualifies, player's hand losef4p4 = f4/18424-2EV4 = -2 x p4
Total184241.00000000 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. QDiamond 6Diamond 4Club is equivalent to QSpade 6Spade 4Heart).

HandNo QualifyWinTieLosePlay E.V.
QSpade 6Heart 3Club57472712612380-1.002551
QSpade 6Spade 3Heart57472702512382-1.002877
QSpade 6Heart 3Spade57472682512384-1.003311
QHeart 6Spade 3Spade57392712512389-1.003962

HandNo QualifyWinTieLosePlay E.V.
QSpade 6Heart 4Club57583052612335-0.993378
QSpade 6Spade 4Heart57583032512338-0.993921
QSpade 6Heart 4Spade57583022512339-0.994138
QHeart 6Spade 4Spade57513052512343-0.994627

HandNo QualifyWinTieLosePlay E.V.
QSpade 6Heart 5Club57543392612305-0.986648
QSpade 6Spade 5Heart57543362512309-0.987408
QSpade 6Heart 5Spade57543362512309-0.987408
QHeart 6Spade 5Spade57483392512312-0.987733

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