Three Card Poker Odds Calculator
Use this interactive calculator to understand Three Card Poker probabilities, analyze different paytables, and learn the optimal Q-6-4 strategy. Whether you're evaluating Pair Plus payouts or checking if your hand meets the play threshold, this tool provides the mathematical foundation for informed decisions.
Three Card Poker combines poker hand rankings with casino-style play, offering two primary bets: the Ante/Play wager where you compete against the dealer, and the Pair Plus side bet that pays based solely on your hand strength. Understanding the complete rules of Three Card Poker alongside these probability calculations helps you appreciate why certain strategies work.
Three Card Poker Analyzer
| Hand Type | Combinations | Probability | Odds (1 in X) |
|---|---|---|---|
| Straight Flush | 48 | 0.22% | 1 in 460 |
| Three of a Kind | 52 | 0.24% | 1 in 425 |
| Straight | 720 | 3.26% | 1 in 31 |
| Flush | 1,096 | 4.96% | 1 in 20 |
| Pair | 3,744 | 16.94% | 1 in 6 |
| High Card | 16,440 | 74.39% | 3 in 4 |
In three-card hands, the ranking differs from five-card poker. With only three cards, straights (720 combinations) occur less frequently than flushes (1,096 combinations), so straights rank higher. This is the reverse of standard poker where flushes are rarer.
| Outcome | Probability | Meaning |
|---|---|---|
| Dealer Qualifies (Q-high or better) | 69.08% | Your hands will be compared |
| Dealer Does NOT Qualify | 30.92% | You win Ante (1:1), Play pushes |
The flush payout makes a massive difference in house edge. Always check the paytable before playing.
The Ante Bonus pays regardless of whether you beat the dealer or if the dealer qualifies.
| Hand | Standard Payout | Probability | Contribution to Edge |
|---|---|---|---|
| Straight Flush | 5:1 | 0.22% | +1.08% |
| Three of a Kind | 4:1 | 0.24% | +0.94% |
| Straight | 1:1 | 3.26% | +3.26% |
Ante/Play with optimal strategy: ~3.37% house edge
Pair Plus (best paytable): ~2.32% house edge
Combined betting (equal Ante + Pair Plus): ~2.85% house edge
Expected value represents the mathematical average outcome over many hands. While individual sessions vary widely due to variance, the house edge means long-term play will trend toward these expected losses. Use this calculator to understand the "entertainment cost" of play.
| Bet Strategy | Total Wagered/Hand | House Edge | Expected Loss/100 Hands |
|---|---|---|---|
| Ante/Play Only ($10) | $20 (when playing) | 3.37% | $67.40 |
| Pair Plus Only ($10, best table) | $10 | 2.32% | $23.20 |
| Both ($10 each, best table) | $30 (when playing) | ~2.85% | $85.50 |
The Q-6-4 Optimal Strategy
The mathematically optimal strategy for the Ante/Play bet is remarkably simple: Play with Queen-6-4 or better; fold with anything worse. This threshold was calculated by gaming mathematicians at Wizard of Odds through extensive analysis of all possible hand combinations and outcomes.
Here's how to apply it:
- Any pair or better: Always play. Even 2-2-3 beats all high card hands.
- Ace-high or King-high: Always play. These hands have strong equity.
- Queen-high: Check your other two cards. Q-6-4 or better (like Q-7-2, Q-8-5) plays; Q-6-3 or worse folds.
- Jack-high or worse: Always fold. The equity is too low to justify the Play bet.
According to research published by the UNLV International Gaming Institute, following this strategy reduces the Ante/Play house edge to approximately 3.37%. Deviating from Q-6-4 by playing too loose or too tight increases your expected losses.
Understanding Three Card Poker Mathematics
Three Card Poker's appeal lies in its mathematical elegance. With only 22,100 possible three-card combinations from a 52-card deck, the probabilities are precisely calculable. The game was designed by Derek Webb in 1994 specifically to balance speed, excitement, and reasonable house edges—making it one of the most successful proprietary casino games ever created.
The dealer qualification rule (Queen-high or better) is the key mathematical lever. Without it, the game would have a much higher house edge because players would lose both bets whenever the dealer won. By requiring qualification, roughly 31% of hands result in automatic Ante wins with Play pushes—a significant player-friendly mechanic that reduces the edge.
The Ante Bonus serves a similar purpose. By paying straights, trips, and straight flushes regardless of the dealer's hand, the game returns approximately 5.3% back to players on these premium hands. This bonus makes the game feel more rewarding when hitting big hands, even if the dealer happens to beat you.
Pair Plus: The Side Bet Analysis
Unlike the Ante/Play bet which involves strategy, Pair Plus is purely probabilistic—you bet before seeing cards and have no decisions afterward. According to the American Gaming Association's gaming guidelines, the Pair Plus house edge varies dramatically based on the paytable:
- 40-30-6-4-1 (flush pays 4:1): 2.32% house edge—actually better than Ante/Play
- 40-30-6-3-1 (flush pays 3:1): 3.83% house edge—slightly worse than Ante/Play
- 40-25-6-3-1 (trips 25:1, flush 3:1): 7.28% house edge—significantly worse
The single-unit difference between 3:1 and 4:1 on flushes seems small, but flushes occur in approximately 5% of hands. Over hundreds of hands, this difference compounds substantially. Always scan the felt for paytables before sitting down.
Related Tools and Resources
Three Card Poker shares concepts with other casino games. If you enjoy analyzing odds and probabilities, explore these related calculators:
- Blackjack Basic Strategy Calculator – Learn optimal hit/stand/double/split decisions for the lowest-edge casino game
- Baccarat Odds Calculator – Compare house edges and understand why Banker bets are mathematically superior
- Expected Value Calculator – Analyze any betting decision through the lens of expected value
- Poker Probability & Mathematics – Deep dive into probability theory across all poker variants
For a complete understanding of Three Card Poker gameplay, hand rankings, and table etiquette, read our comprehensive Three Card Poker rules guide. Understanding the rules alongside these probability calculations provides the foundation for informed play.
Responsible Gaming Reminder
Three Card Poker, like all casino games, is designed with a mathematical house edge that ensures long-term profitability for the casino. No strategy can overcome this edge. The calculations in this tool help you understand the true cost of play so you can approach the game as entertainment with a predictable price.
If gambling stops being fun or you find yourself exceeding intended limits, resources are available through the National Council on Problem Gambling at 1-800-522-4700.