Three cards against the dealer. Ante, look at your hand, then play or fold — with the exact value of both choices for the hand in front of you, and every house edge counted out rather than simulated.
Three Card Poker is small enough to count completely: there are 22,100 three-card hands, and for each one the dealer can hold any of 18,424 hands from the other 49 cards — 407,170,400 combinations. Every number on this tab comes from playing all of them. Nothing is simulated.
| Hand | Ways | Probability | Pays | Return |
|---|---|---|---|---|
| Straight flush | 48 | 0.2172% | 40:1 | +8.69% |
| Three of a kind | 52 | 0.2353% | 30:1 | +7.06% |
| Straight | 720 | 3.2579% | 6:1 | +19.55% |
| Flush | 1,096 | 4.9593% | 3:1 | +14.88% |
| Pair | 3,744 | 16.9412% | 1:1 | +16.94% |
| High card | 16,440 | 74.3891% | loses | −74.39% |
| Total | 22,100 | 100% | −7.28% |
With three cards a straight (720 ways) is rarer than a flush (1,096 ways), so it ranks higher — the reverse of five-card poker. “Return” is probability × payout: the rows add up to what the side bet gives back per unit, and what is missing is the house edge. Cutting the flush from 4:1 to 3:1 more than triples it.
With the best strategy — play Q-6-4 or better — each of the 407,170,400 combinations ends in one of five ways. The Ante Bonus is paid on top whenever you hold a straight or better.
| Outcome | Net (antes) | Probability | Combinations | Return |
|---|---|---|---|---|
| You fold | −1 | 32.579% | 132,652,800 | −32.579% |
| You play, the dealer doesn’t qualify | +1 | 20.997% | 85,493,652 | +20.997% |
| You play and beat the dealer | +2 | 23.910% | 97,354,684 | +47.820% |
| You play and tie | 0 | 0.066% | 267,648 | 0.000% |
| You play and the dealer wins | −2 | 22.448% | 91,401,616 | −44.896% |
| Ante Bonus (on top) | +1 / +4 / +5 | 3.710% | — | +5.285% |
| Total | 100% | 407,170,400 | −3.373% |
The house edge is quoted against the Ante: you lose 3.37% of it per hand. But two hands in three you put a second, equal bet on the table, so the average wager is 1.674 antes — per unit actually risked (the “element of risk”) the game costs 2.01%.
Folding always costs one ante. Playing puts a second ante at risk: you win one when the dealer fails to qualify, and win or lose two at a showdown. A hand is worth playing as soon as that averages better than −1. The curve shows the value of playing every unsuited high-card hand, weakest to strongest: flat while the hand can’t beat any qualifying dealer, then climbing through the fold line between Q-6-3 and Q-6-4.
| Hand | EV of playing | vs folding | Dealer doesn’t qualify | You win | Best |
|---|---|---|---|---|---|
| J-10-8 | −1.1415 | −0.1415 | 28.62% | 0.00% | Fold |
| Q-3-2 | −1.0672 | −0.0672 | 31.00% | 0.00% | Fold |
| Q-5-4 | −1.0214 | −0.0214 | 31.22% | 0.98% | Fold |
| Q-6-2 | −1.0128 | −0.0128 | 31.10% | 1.28% | Fold |
| Q-6-3 | −1.0031 | −0.0031 | 31.18% | 1.47% | Fold |
| Q-6-4 | −0.9939 | +0.0061 | 31.25% | 1.65% | Play |
| Q-6-5 | −0.9872 | +0.0128 | 31.22% | 1.83% | Play |
| Q-7-2 | −0.9762 | +0.0238 | 31.10% | 2.20% | Play |
| Q-J-9 | −0.6811 | +0.3189 | 31.08% | 9.59% | Play |
| K-3-2 | −0.5518 | +0.4482 | 31.00% | 12.88% | Play |
| A-K-J | +0.6336 | +1.6336 | 33.62% | 40.55% | Play |
Each row averages the 60 suit combinations of those ranks. Which exact cards you hold changes what the dealer can have, but only in the third decimal: the worst Q-6-4 is still worth −0.9946 and the best Q-6-3 only −1.0026.
The bonus is paid on the Ante for a straight or better, win or lose. Those hands are never folded, so its value is simply how often they come up times what they pay.
| Hand | Return | Pays | Probability |
|---|---|---|---|
| Straight flush | +1.086% | 5:1 | 0.2172% |
| Three of a kind | +0.941% | 4:1 | 0.2353% |
| Straight | +3.258% | 1:1 | 3.2579% |
| Total | +5.285% |
Together the bonus returns 5.29% of every Ante. Without it the house edge would be 8.66%.
The same count prices any rule for playing or folding.
| Strategy | House edge | Element of risk | Hands played | Average wager |
|---|---|---|---|---|
| Optimal: play Q-6-4 or better | 3.37% | 2.01% | 67.42% | 1.674 |
| Play like the dealer: Queen-high or better | 3.45% | 2.03% | 69.59% | 1.696 |
| Always play | 7.65% | 3.83% | 100.00% | 2.000 |
Playing like the dealer only goes wrong on the 480 Queen-high hands weaker than Q-6-4, and each of those mistakes is tiny, so it costs less than a tenth of a point. Never folding plays 7,200 hands the best strategy folds — 6,720 of them can’t beat any dealer who qualifies — and more than doubles the edge.
Shuffles a fresh deck for every hand, deals three cards each and lets all three strategies play that same deal through the table’s own rules, one Ante a hand. The dashed lines are the exact edges from the Odds tab.