Three Card Poker Odds

With only three cards in play and no cards to draw, calculating the Three Card Poker odds for various hands should be rather straightforward. Unfortunately, it is complicated somewhat by the varying payout rates used by casinos for Ante Bonuses and Pair Plus wins, but the House edge tends to be around 3.37% for the Ante and Play bets. As with most games of chance, the higher payouts for side bets come at a cost, and the advantage for the House on Pair Plus wagers ranges from 2.32% to 7.28%, depending on the payout schedule offered.

Odds on Various Three Card Poker Hands

In total, there are 22,100 possible hand combinations when three cards are dealt at random from a 52-card deck. Of these, just 48 result in a Straight Flush and exactly 52 are Three of a Kind combinations, resulting in probabilities of just 0.22% and 0.24% for these premium hands, respectively. The only other hand eligible for an Ante Bonus is a Straight, with 720 ways to be made and a likelihood of just 3.36%.
Of the two additional hands that can win a Pair Plus payout, a Flush can be expected to turn up 1,096 times out of 22,100 deals, or 4.96% of the time. Any Pair will occur with a frequency of 16.94%, there being 3,744 such hands possible. That means High Card hands dominate all deals, so players can look for an Ace high or less nearly three-quarters of the time, or 74.39% to be precise.
With even money paid for a pair on the Pair Plus wager, clearly the payouts for the other top hands must be significant to overcome the poor odds associated with such occurrences. Players should look for Pair Plus options that pay at least 4-to-1 for a Flush, 6-to-1 for a Straight, 30-to-1 for Three of a Kind, and 40-to-1 for a Straight Flush. At those rates, the House edge is 2.32%.
When playing both the Ante/Play and Pair Plus bets in combination, the House advantage is actually somewhat greater. Players can expect to win 32.06% of the time, push on 13.23% of all occasions, and lose on the other 54.71% of all deals.

Additional Odds Available

Apart from looking for the best payout schedule players should also be aware of other ways casinos have modified the game. For example, some casinos offer a “Mini Royal” payout of 50-to-1 on the Pair Plus wager for a suited A-K-Q hand. That decreases the House edge to 2.12% if the other payout rates are unchanged. However, many casinos compensate by decreasing the Flush payout to 3-to-1, which greatly reduces the chances of winning for the player by giving the House a 7.1% advantage.
The existence of the Ante Bonus helps the player, too, but only as much as the payout rates are favorable. The standard is 5-to-1 for a Straight Flush, 4-to-1 for Three of a Kind, and even money for a Straight. It was at these rates that the overall 3.37% House edge was calculated for Ante and Play betting. If the payouts are reduced even slightly, the advantage tips even further in the House’s direction, reaching 4.28% when the rates are decreased to 3-to-1, 2-to-1, and even money, respectively.
Similarly, if Mini Royals are added to the Ante Bonus list, as they often are, look for shifts in the payouts for the other premium hands. On Las Vegas casino was offering 10-to-1 for a Mini Royal and 50-to-1 if it was in spades. As an offset, the payout for Straight was eliminated, Straight Flushes paid only 4-to-1, and Three of a Kind was demoted to 3-to-1. The Result: A whopping 6/79% House edge overall. The Moral: Beware of any supposed “improvements” to the basic game.

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