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:
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 (^{49}C_{3} = 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  f_{1}  p_{1} = f_{1}/18424  1  EV_{1} = 1 x p_{1} 
Dealer qualifies, player's hand wins  f_{2}  p_{2} = f_{2}/18424  2  EV_{2} = 2 x p_{2} 
Dealer qualifies, player's hand ties  f_{3}  p_{3} = f_{3}/18424  0  0 
Dealer qualifies, player's hand lose  f_{4}  p_{4} = f_{4}/18424  2  EV_{4} = 2 x p_{4} 
Total  18424  1.00000000   EV = EV_{1}+EV_{2}+EV_{4} 
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 Q64 High or better. Any other hand should be folded. Below are the expected values for making the Play bet for Q63 High, Q64 High, and Q65 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 
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