Three Card Poker odds: hand probabilities, house edge and pay tables
Three Card Poker looks simple: three cards for you, three for the dealer, and a choice to play or fold. The odds behind it are less obvious, because a three-card hand does not rank like a five-card hand, and the two main bets carry very different house edges. This guide gives the exact odds of every hand, what each bet returns, the simple playing rule that keeps the edge as low as it goes, and what changes when a crypto casino deals the game from an online deck.
Every figure below was computed by us in code, by going through all 22,100 possible three-card hands and, for the Ante bet, every possible dealer hand against each of them.
How Three Card Poker works
The rules here follow New Jersey's regulation for the game (N.J.A.C. 13:69F-20), the rules published by Singapore's Gambling Regulatory Authority for Marina Bay Sands, and the Evolution live version described on theScore Bet's help pages.
- The game uses one standard 52-card deck, shuffled before each round.
- You can place an Ante bet, a Pair Plus bet, or both.
- After seeing your three cards you either Play, by adding a bet equal to your Ante, or fold and lose the Ante. In New Jersey, folding also forfeits a Pair Plus bet placed with the Ante.
- The dealer needs queen high or better to qualify. If the dealer does not qualify, the Ante pays 1 to 1 and the Play bet is returned.
- If the dealer qualifies, the higher hand wins. Ante and Play both pay 1 to 1. A tie is a push.
- The Ante Bonus pays on a straight or better whatever the dealer holds, as long as you played the hand.
- Pair Plus is a separate bet on your own hand only. It pays on a pair or better and ignores the dealer completely.
Three Card Poker hand odds
With three cards, a straight is harder to make than a flush, so the ranking differs from standard poker. New Jersey's rules rank the hands as straight flush, three of a kind, straight, flush, pair, then high card. A-2-3 counts as a straight and A-K-Q is the highest one.
| Hand | Combinations | Probability | About 1 in |
|---|---|---|---|
| Straight flush | 48 | 0.22% | 460 |
| Three of a kind | 52 | 0.24% | 425 |
| Straight | 720 | 3.26% | 31 |
| Flush | 1,096 | 4.96% | 20 |
| Pair | 3,744 | 16.94% | 5.9 |
| High card | 16,440 | 74.39% | 1.3 |
| Total | 22,100 | 100% |
Three of a kind is slightly more common than a straight flush, which is why some pay tables pay the straight flush more. Of the 48 straight flushes, 4 are A-K-Q suited, the "mini royal" that some tables pay separately.
The headline number: you get a pair or better on 25.61% of deals, roughly one hand in four. Three hands in four have nothing but a high card.
The Ante and Play bet: odds and house edge
Most of the decisions in the game happen here. We compared each of the 22,100 player hands against all 18,424 dealer hands that can be made from the remaining 49 cards, using the base Ante Bonus from New Jersey's rules (straight 1 to 1, three of a kind 4 to 1, straight flush 5 to 1).
The best strategy turned out to be the one players call Q-6-4:
- Play any hand of Q-6-4 or better. That means any pair or better, any hand with a king or an ace, or a queen high hand whose second card is above a 6, or is a 6 with a third card of 4 or higher.
- Fold anything lower, for example Q-6-3, Q-5-4 or J-10-8.
| Result with Q-6-4 strategy | Figure |
|---|---|
| Hands you play | 67.42% |
| Hands you fold | 32.58% |
| House edge, per unit of Ante | 3.37% |
| Return to player | 96.63% |
| Average amount bet per round | 1.67 units |
| Loss per unit actually bet | 2.01% |
Our 96.63% matches the RTP theScore Bet publishes for Evolution's live Three Card Poker, which is a useful check on both. The edge is per unit of Ante. Because you add a Play bet on two hands in three, the loss per dollar actually put on the table is lower, about 2.01%.
Two things the strategy cannot do. It cannot turn the bet positive: 3.37% is the lowest edge available on the Ante with these payouts. And the dealer's qualifying rule is part of the edge. When the dealer fails to qualify you win only the Ante, even with a strong hand, which is why the Play bet does not simply pay whenever you win.
Pair Plus: the pay table is the whole story
Pair Plus has no decisions. Its return depends only on the hand frequencies above and the pay table on the felt. That makes it easy to compute, and it shows how much a small change in the table costs you.
| Pay table (straight flush, trips, straight, flush, pair) | Return | House edge |
|---|---|---|
| 40, 30, 6, 4, 1 | 97.68% | 2.32% |
| 40, 30, 5, 4, 1 (Marina Bay Sands rule sheet) | 94.43% | 5.57% |
| 40, 25, 6, 3, 1 | 91.55% | 8.45% |
| 35, 25, 5, 3, 1 (New Jersey minimum odds) | 87.20% | 12.80% |
The first row is the version most rule books describe as the original. Dropping the straight from 6 to 5 to 1 more than doubles the edge, and the minimum odds allowed by New Jersey's rule cost more than five times as much. Online tables and live studios show their Pair Plus table in the game's information panel. Read it before betting, because the same game name can hide any of these returns.
On a 40, 30, 6, 4, 1 table Pair Plus has a lower edge per bet than the Ante. It is also more volatile, because three bets in four lose outright.
Side bets such as the 6 Card Bonus
Many tables add a 6 Card Bonus that combines your three cards with the dealer's three and pays on the best five-card hand. New Jersey allows several pay tables for it, from 1,000 to 1 for a royal flush down to 5 to 1 for three of a kind, and the Evolution version pays on three of a kind or better. These bets usually carry a much higher edge than the main game. If you play one, find the table on the information panel and treat it as a separate, higher-cost bet.
When the deck is online: why the deck model matters
On a land-based table, and in live dealer studios, the cards come from a real single deck. Crypto casinos that build their own card games often use a different model. Some draw each card independently from a full 52-card deck, which means the same card can appear twice. This is called an infinite deck, and many provably fair card games use it because each card maps cleanly to one random float.
That choice changes the odds of every hand. We recomputed them for an infinite deck:
| Hand | Single 52-card deck | Infinite deck |
|---|---|---|
| Straight flush | 0.22% | 0.20% |
| Three of a kind | 0.24% | 0.59% |
| Straight | 3.26% | 3.07% |
| Flush | 4.96% | 6.01% |
| Pair | 16.94% | 19.97% |
Pairs, flushes and trips all get more common. If an infinite-deck game kept the 40, 30, 6, 4, 1 Pair Plus table, it would pay back 118.2% of stakes, so any honest version must use a different table. The pay table only makes sense alongside the deck model, and a game that does not say which model it uses gives you no way to check its stated RTP.
For a provably fair card game, the fairness page should say how a float becomes a card and whether cards already dealt can repeat. Our guide to provably fair blackjack shows both methods side by side, and which casino games are provably fair lists the games where results can be checked.
What the odds mean for a session
The edge is a long-run average. Over a short session anything can happen, but the expected cost grows with every hand. At $10 Ante with Q-6-4 play, the expected loss is about $0.34 per hand. At 60 hands an hour that is about $20 an hour, before any side bets. Adding $10 Pair Plus on a 40, 30, 6, 4, 1 table adds about $0.23 per hand, or about $14 an hour.
Our guide to what RTP means explains why the result of one session can sit far from these averages. Set a budget, use a deposit limit if the casino offers one, and see our responsible gambling page if play stops being fun.
Sources
- N.J.A.C. 13:69F-20.3, Three-card poker rankings (via Justia)
- N.J.A.C. 13:69F-20.2, Cards; number of decks
- N.J.A.C. 13:69F-20.10, Procedures for completion of each round of play
- N.J.A.C. 13:69F-20.11, Payout odds
- Gambling Regulatory Authority of Singapore: Marina Bay Sands Three Card Poker rules, version 6 (PDF)
- theScore Bet help: Three Card Poker (Evolution), RTP 96.63%
- All hand counts, strategy and returns computed by us in C (full enumeration of 22,100 player hands against 18,424 dealer hands each) and Python (infinite-deck table)
Key terms
- House edge
- The average percentage of every wager that a game is built to keep for the casino.
- Return to player (RTP)
- The share of all money staked that a game is designed to return to players across a very large number of rounds.
- Volatility
- How sharply a game's results swing: high volatility brings rare big wins, low volatility brings frequent small ones.
- Live dealer games
- Table games broadcast from a studio with a real dealer, where physical cards, wheels or dice decide the outcome.
- Random number generator (RNG)
- The software behind third-party slot and table results, trusted through lab certification instead of player-checkable seeds.
- Provably fair
- A cryptographic method that lets you confirm a game result was set before your bet and left untouched afterwards.
- Random float
- A number between 0 and 1 derived from a provably fair hash, which a game formula turns into a result.
- Deposit limit
- A ceiling you choose on the amount you can deposit to one casino account per day, week or month.