Three Card Poker odds
The exact numbers behind the game: how often each hand appears, how often the dealer qualifies, and how hands resolve under optimal play.
The short answer
A pair or better shows up about 25.6% of hands. The dealer qualifies about 69.6% of the time. Playing optimally, you make the Play bet on about 67.4% of hands and fold the rest.
Hand frequencies
Out of 22,100 distinct three-card hands, here is how the categories divide up.
| Hand | Combinations | Probability |
|---|---|---|
| Straight flush | 48 | 0.2172% |
| Three of a kind | 52 | 0.2353% |
| Straight | 720 | 3.2579% |
| Flush | 1096 | 4.9593% |
| Pair | 3744 | 16.9412% |
| High card | 16440 | 74.3891% |
Dealer qualification
The dealer qualifies with Queen-high or better. Enumerated over all hands, the dealer qualifies about 69.6% of the time and fails to qualify about 30.4%. A non-qualifying dealer pays your Ante at 1 to 1 and pushes your Play bet, which is a good outcome for you.
Win, lose, and push under optimal play
Playing Q-6-4, you make the Play bet on about 67.4% of hands and fold about 32.6%. On the hands you play, here is how they resolve.
| Outcome | Share of played hands |
|---|---|
| Dealer does not qualify (Ante wins, Play pushes) | 31.1% |
| You win the showdown | 35.5% |
| You lose the showdown | 33.3% |
| Tie (push) | 0.1% |
Common questions
How often will I be dealt a pair or better?
About 25.6% of hands are a pair or better. High-card hands make up the other 74.3891%. A pair or better is always a Play.
How often does the dealer qualify?
About 69.6% of the time. The dealer needs Queen-high or better, so roughly 30.4% of hands the dealer fails to qualify, which pays your Ante and pushes your Play bet.
What are my chances of winning a hand?
When you play, about 31.1% of the time the dealer does not qualify and you collect the Ante, about 35.5% you win the showdown, about 33.3% you lose it, and about 0.1% ties. Folded hands lose the Ante.