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Over 40 Years in the Casino Business
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The game of Three-Card Poker is relatively new; the credit for inventing the game goes to Derek Webb, a poker player. Webb came up with this game in the 1990s and it has since found an avid following at online casinos. Three Card Poker is basically a table game that has as its point of origin Three Card Brag, an English poker game.
How to play 3-Card Poker:
First you make an ante bet and your optional Pair Plus bet . In most Casinos you can make either/or with the Ante and Pair Plus, but in a few Casinos you must make an Ante in order to also make a Pair Plus bet.
Then the dealer gives each player three cards and himself three cards. You get to look at your own cards, but in most Casinos you aren't allowed to look at any other player's hands. (It's still a poker game.) The dealer's cards are dealt face down.
If you made the Ante bet, at this time you must either fold or raise. If you fold, you lose your Ante wager. Your hand is over. If you opt to play, or "raise", then you have to make an additional Play bet, equal exactly to your Ante bet. If you have a hand of Queen/6/4 or better, you should bet on it, if you don't, you should fold; really it's as simple as that.
The dealer will turn over his cards. The dealer needs a queen high or better to qualify.
If the dealer does not qualify by having a queen or better in has hand then you will win even money on the Ante bet and the Play bet will push.
If the dealer qualifies, then your hand will be compared to the dealer's hand, the higher hand wins.
If you have the higher poker hand the Ante and Play will both win even money. If the dealer has the higher poker hand the Ante and Play will both lose. If you tie then the Ante and Play bets will push.
If you made the Ante bet and have a straight or higher then you will receive an Ante Bonus regardless of the value of the dealer's hand. If his flush is higher than your flush, he wins the ante bet and you win the bonus bet.
The Pair Plus bet will pay entirely based on the poker value of your hand. You are not betting against the dealer with the Pair Plus. You are simply betting that you will get a pair of some kind, or a 3 card straight or flush, or trips or a straight flush. You can have three of a kind and lose your Ante and Play bets to the dealers three of a kind if his is higher, but you will still win 30 to one on your Pair Plus bet.
Strategy
Optimal strategy in ante and play is to raise if you have a Q/6/4 (that is a Queen, 6, and 4 all in the same hand) or greater. Overall you stand to lose 8.66% of the Ante but win 5.29% on the "raise".
In any poker based game hands are scored first according to the highest card, then the second, and then the third, and so on if there are more. So a queen/7/3 would beat queen/6/4. The queens tie so the second highest cards are used to break the tie, and a 7 beats a 6. The third card does not matter in this case because the hand was resolved by the second card.
If you want to know why Q/6/4 is the borderline hand it is because if you raise on queen/6/3 you can expect to lose 1.00255 units, which is more than the 1 unit you lose by folding. However if you raise on queen/6/4 the expected loss is .993378, less than the 1 you lose unit by folding.
Raising on any queen or better is not a bad strategy but you will lose more with it than the strategy above. The house edge playing this strategy is 3.45%. Playing blind results in a house edge of 7.65%.
Player Wins Ties
What about the probability of tieing the dealer in Three Card Poker? This is a valid question because some casinos let ties go to the player. The effect of this rule lowers the house edge from 3.37% to 3.24%.
There is a small strategy change to make if the ties go to the player. Under this rule the player should still raise on Q/6/4 or better, plus raise on Q/6/3, only when all three suits are different, which lowers the probability of a dealer flush.
If you follow the proper raising strategy under the ties win rules then the probability of a tie is 1 in 1517.75 hands. If the player always raises then the probability of a tie is 1 in 903.76.