Enter your three cards to see whether Play or Fold is mathematically correct, with the exact expected value.
Play any hand of Queen-6-4 or better; Fold everything else. Every King-high and Ace-high hand is always a Play, every Jack-high (or lower) hand is always a Fold, and Queen-high hands are a Play only when the second and third cards are 6-4 or better. Any pair, straight, flush, three of a kind or straight flush is always a Play.
Under optimal Q-6-4 strategy, the Ante/Play bet has a house edge of 3.37% based on the Ante wager, or 2.01% expressed as the element of risk (based on the average total amount put at risk, since a Play bet doubles your action about 67% of the time). Verified by exact enumeration of all 22,100 possible player hands against all 18,424 possible dealer hands for each.
Pair Plus is a side bet on your own 3 cards only — it doesn't matter what the dealer has. It pays on a pair or better, using a paytable set by the casino. The example below (a common paytable: straight flush 40:1, three of a kind 30:1, straight 6:1, flush 4:1, pair 1:1) has a house edge of 2.32%. A cheaper paytable, such as one that pays only 3:1 on a flush, raises the house edge to 7.28% — always check the paytable posted at the table.
| Hand | Pays | Probability |
|---|---|---|
| Straight Flush | 40 : 1 | 0.22% |
| Three of a Kind | 30 : 1 | 0.24% |
| Straight | 6 : 1 | 3.26% |
| Flush | 4 : 1 | 4.96% |
| Pair | 1 : 1 | 16.94% |
This tool computes the exact expected value (EV) of the Play decision for your 3-card hand, using exact probability math rather than simulation. It enumerates every one of the 18,424 possible 3-card hands the dealer could hold from the remaining 49 cards, applies the dealer's Queen-high qualifying rule, and compares your hand to the dealer's under the standard win/push/lose payout rules — plus the Ante Bonus if your hand is a straight or better.
The result is the exact Play EV per unit Ante staked; folding is always exactly -1 unit. If Play's EV beats -1, the calculator recommends Play; otherwise it recommends Fold. This matches the well-known Q-6-4 strategy card exactly — this tool exists to let you check any specific hand rather than memorize the chart. It's built for probability education, not gambling advice.
Compare your three cards to the Q-6-4 rule: any King-high or Ace-high hand is always a Play; any Jack-high hand or lower is always a Fold; a Queen-high hand is a Play only if the second and third cards are 6-4 or better (Q-6-4, Q-6-5, Q-7-2, and so on), otherwise Fold. Any pair, straight, flush, three of a kind, or straight flush is always a Play. This threshold was verified by enumerating all 18,424 possible dealer hands against every possible player hand -- Q-6-4 is the exact break-even boundary, not an approximation.
Yes. Q-6-4 is the exact break-even threshold: playing it has an EV of -0.9934 per ante unit, better than folding's guaranteed -1.0000. It's the worst hand that's still correct to play.
No, fold. Q-6-3 has an EV of -1.0026 if played -- worse than the guaranteed -1.0000 from folding -- so Q-6-3, and anything ranked below it, should always fold.
3.37% based on the Ante wager alone, or 2.01% expressed as the 'element of risk' (using the average total amount put at risk, since you sometimes place a second Play bet). Verified by exact enumeration of all 22,100 possible player hands against all 18,424 possible dealer hands for each.
No. Every hand of a pair or better always has an EV that beats folding's guaranteed -1.0000 -- these hands are always played.
Always play. Every King-high and Ace-high hand, no matter how weak the other two cards, has a better EV than folding.
A side payout on the Ante alone -- paid at 1:1 for a straight, 4:1 for three of a kind, and 5:1 for a straight flush -- regardless of what the dealer has. It's already included in this calculator's EV figures.
It depends entirely on the casino's paytable. For a common 40/30/6/4/1 paytable (straight flush/three of a kind/straight/flush/pair), the house edge is 2.32%. A cheaper table paying only 3:1 on a flush raises it to 7.28%.
Yes. If the dealer's hand doesn't reach Queen-high, the Ante wins even money automatically and the Play bet simply pushes back to you untouched, regardless of what you're holding.
| Hand | Type | Decision | EV per ante unit |
|---|---|---|---|
| Q-6-4 (mixed suits) | High card (exact Q-6-4 threshold) | Play | -0.993 |
| Q-6-3 (mixed suits) | High card (one step below threshold) | Fold | -1.000 |
| K-2-3 (mixed suits) | High card, King high | Play | -0.552 |
| J-9-8 (mixed suits) | High card, Jack high (best possible J-high) | Fold | -1.000 |
| 8-8-4 | Pair | Play | +1.010 |
| 5-6-7 (mixed suits) | Straight | Play | +2.609 |
| 7-7-7 | Three of a kind | Play | +5.701 |
| 4-5-6 (same suit) | Straight flush | Play | +6.706 |
Yes. Q-6-4 has an EV of -0.9934 per ante unit if played, which beats folding's guaranteed -1.0000 -- it's the worst hand that's still correct to play, and the exact break-even boundary of the strategy.
No, fold. Q-6-3 has an EV of -1.0026 if played -- worse than folding's guaranteed -1.0000 -- so Q-6-3, and anything ranked below it, should always fold.
No. Every hand that's a pair or better always has an EV better than folding's guaranteed -1.0000, so these hands are always played, including under the Q-6-4 rule's plain-English exceptions.
The Ante Bonus is a side payout on the Ante alone -- 1:1 for a straight, 4:1 for three of a kind, 5:1 for a straight flush -- paid regardless of the dealer's hand. Yes, it's already folded into every EV figure this calculator shows.
The 3.37% figure is the house's expected profit per unit of Ante staked. The 2.01% 'element of risk' figure divides that same expected profit by the average total amount actually put at risk, which is higher because you place a second, equal-sized Play bet roughly 67% of the time under optimal strategy.
This tool is for probability and house-edge education, not gambling advice. It assumes the standard Three Card Poker rules described above -- the dealer qualifies with Queen-high or better, and the Ante Bonus pays 1:1/4:1/5:1 for a straight/three of a kind/straight flush. Some casinos use a different Ante Bonus schedule or omit it entirely, and the optional Pair Plus side bet's paytable and house edge vary significantly by casino -- always check the table posted where you play. Results assume you follow the mathematically optimal Play/Fold strategy exactly; deviating from it increases the house edge.
Sources: Wizard of Odds, Three Card Poker