Three Card Poker Odds

Published: 16/06/2012

Because only three cards are used to form a Three Card Poker hand, and there are no cards to draw, it should be quite easy to calculate the odds for the game. However, the process is complicated to some degree by the varying payout rates employed by different casinos for Ante Bonuses and Pair Plus wins

On average, the House Edge anticipated for Three Card Poker wagers comes to approximately 3.37% for both the Ante and Play bets. On the other hand, the advantage for the House on Pair Plus bets can fluctuate between 2.32% and 7.28%, depending on what payout schedule is offered. As with most other table games, having higher payouts for side bets results in a greater margin for the House overall.

Taken all together, 22,100 unique hand combinations can be formed when a standard 52-card deck is used to deal three cards at random. Among these, only 48 will result in the highest possible combination—a Straight Flush. What’s more, there are just 52 ways to obtain Three-of-a-Kind, so the odds obtaining the top two ranked hands are 0.22% and 0.24%, respectively. Only one other premium hand is eligible for an Ante Bonus—a Straight, which can be formed in 720 ways for a 3.36% probability of occurrence.

Taking a look at the two additional hands eligible for a Pair Plus payout, a Flush can be formed in 1,096 ways, which should occur in 4.96% of all deals. Any Pair has a likelihood of being dealt 16.94% of the time, with exactly 3,744 such hands that can be formed. It become obvious, then, that High Card hands predominate. Players should expect to see an Ace high hand or lower on 74.39% of all deals.

Another way to look at these odds is to see that more than half of all deals are potential losers, which can be rescued only if the Dealer’s hand fails to qualify. In that case, however, only the Ante bet returns even money, while the Play bet produces a push, as if never wagered.

Because the Pair Plus wager pays only even money paid for a pair, far from true odds of about 6-to-1, the payouts for the other premium hands must be quite large to compensate. A Pair Plus option that pays at least 4-to-1 for a Flush should be accompanied by payments of 6-to-1 for a Straight, 30-to-1 for Three-of-a-Kind and 40-to-1 for a Straight Flush. Those rates bring the House Edge to 2.32%, which is competitive with games like Roulette and Blackjack.

When the Play Both Bets” option is offered, allowing the Ante/Play and Pair Plus wagers to be made in combination, the House advantage increases. The Player’s hand will be favoured to win 32.06% of the time and can be expected to push on 13.23% of all deals. That means the House should win the other 54.71%.

Of course, players should look for the most advantageous payout schedule, but they should also be on guard for any other modifications that casinos have made to the game. Some offer a “Mini Royal,” for example, with a payout of 50-to-1 on the Pair Plus bet when a suited A-K-Q is obtained. If that’s the only change, the House Edge drops to 2.12%, but the Flush payout is simultaneously decreased to 3-to-1, it lifts the House margin to 7.1% and greatly reduces the player’s odds of winning.

Having an Ante Bonus is of benefit to the player, but inasmuch as the payout rates are favourable. The benchmarks to look for are 5-to-1 for a Straight Flush, 4-to-1 for Three-of-a-Kind and 1-to-1 for a Straight. These are the rates that yield 3.37% as the overall House Edge for Ante and Play wagering. Should the payouts be reduced even slightly, the scales tip further in the House’s favour, as high as 4.28% if the payouts fall to 3-to-1, 2-to-1, and 1-to-1, respectively.

When Mini Royals appear on the Ante Bonus schedule, payouts for the other premium hands are likely to be affected. A casino offering 10-to-1 for a Mini Royal, and 50-to-1 for one in spades, offset these payouts by eliminating the payout for a Straight. What’s more, payouts for Straight Flushes dropped to 4-to-1 and for Three-of-a-Kind to 3-to-1. As a result, the overall House Hedge leapt to 6.79%. So remember, any supposed “improvements” to the basic game are almost always to the House’s advantage.

Published on: 16/06/2012

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