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# Win More at Three Card Poker

28 August 2001

Ever since Three Card Poker started to make its way into casinos in the mid-1990s, there has been universal agreement on the best strategy to attack play against the dealer.

The late Lenny Frome, who did the initial mathematical work on the game, said that the best play was to stay in the hand with a Queen or better, and to fold lower-ranking hands.

That had never been challenged until earlier this year, when Chicago analyst Howard Stern saw a note in this column that the dealer makes a qualifying hand of a Queen or better 69.6 percent of the time. That qualifying rate set him to thinking that there might be some Queen-high hands where it's better for the player to fold. He ran an analysis and found that the player was spotting the house an extra edge by staying in any hand of Queen-5-4 or lower. The lowest-ranking hand with which the player should stay is Queen-6-4.

That doesn't really eliminate very many hands, and the strategy adjustment doesn't really cut much into the house edge. The only hands we'd fold using Stern's strategy instead of staying with Frome's are Queen-6-3, Queen-6-2, Queen-5-4, Queen-5-3, Queen-5-2, Queen-4-3, Queen-4-2 and Queen-3-2.

Let's review the rules for Three Card Poker play vs. the dealer. The player antes and is dealt three cards. If he likes his hand, he makes a bet equal to the ante -- not double the ante, as in Caribbean Stud. If not, he folds, losing the ante.

If the player bets and the dealer does not have a qualifying hand of a Queen or better, then the dealer pays the ante at even money and ignores the bet. If the dealer has a qualifying hand that beats the player's hand, the player loses both ante and bet. And if the dealer has a qualifying hand and the player's hand wins, both the ante and bet are paid at even money.

The player also receives bonuses of even money on a straight, 4-1 on three of a kind and 5-1 on a straight flush, regardless of whether the player hand beats the dealer. Players who want to keep it simple and follow Frome's strategy of making the bet anytime they have a Queen or better will be close to optimal play. But those who want to squeeze every last drop out of the game will follow Stern and bet only with hands of Queen-6-4 or higher.

Stern's work does not apply to the other betting option in Three Card Poker, called Pair Plus. In Pair Plus, the player bets on whether his hand will contain a pair or better. The player is paid even money on any pair, 4-1 on a flush, 6-1 on a straight, 30-1 on three of a kind and 40-1 on a straight flush.

The dealer's hand does not matter in this portion of the game. There are no decisions to make after the initial bet, so there are no strategies to learn.

TRE CARD STUD: Mikohn Gaming, which owns progressive table games such as Caribbean Stud and Caribbean Draw, distributes a game similar to Three Card Poker called Tre Card Stud.

Just as in Three Card Poker, the player makes an ante to start, then, after seeing a three-card hand, must either fold or make a bet equal to the ante.

If the dealer doesn't have a qualifying hand of Queen-8 or better, the ante is paid at even money and the bet ignored. If the dealer qualifies and has the higher-ranking hand, the player loses both ante and bet. If the dealer qualifies and the player has the higher-ranking hand, the ante is paid at even money and the bet is paid according to a pay table that may vary from casino to casino.

The big difference that makes Tre Card Stud an eye-catcher is the addition of a progressive jackpot. It requires a \$5 side bet to be eligible for the progressive jackpot, a much larger risk than the \$1 side bet on Caribbean Stud or Caribbean Draw. The big payoff comes when both the player and the dealer have three of a kind.

How often does that happen? Using a standard deck of 52 cards, there are 22,100 possible three-card combinations, and there are 52 possible three of a kind hands. In the long run, a player can expect to be dealt three of a kind about once per 425 hands. If the player has three of a kind, the dealer's chances of also having three of a kind increase to once per 383.83 hands. Player and dealer should get three of a kind at the same time once per 163,129 hands.

The top progressive jackpot should hit about four times as often in Tre Card Stud as in Caribbean Stud or Caribbean Draw, where the top payoff is on royal flushes that occur on average once per 649,740 hands. If you play 55 hands per hour at Tre Card Stud, you could expect to hit the big one about once per 3,000 hours of play.

If you play for a couple of hours once a week, that brings you to a jackpot about once every 30 years, and that's not guaranteed. And it's well within normal probability that you could go 60 years or 90 years between jackpots instead.

At the starting point of \$10,000, the house edge on the progressive bet is a whopping 16 percent, and drops 1 percent for every \$8,155 added to the jackpot.

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Best of John Grochowski
John Grochowski

John Grochowski is the best-selling author of The Craps Answer Book, The Slot Machine Answer Book and The Video Poker Answer Book. His weekly column is syndicated to newspapers and Web sites, and he contributes to many of the major magazines and newspapers in the gaming field, including Midwest Gaming and Travel, Slot Manager, Casino Journal, Strictly Slots and Casino Player.

Listen to John Grochowski's "Casino Answer Man" tips Tuesday through Friday at 5:18 p.m. on WLS-AM (890) in Chicago. Look for John Grochowski on Facebook and Twitter @GrochowskiJ.

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John Grochowski
John Grochowski is the best-selling author of The Craps Answer Book, The Slot Machine Answer Book and The Video Poker Answer Book. His weekly column is syndicated to newspapers and Web sites, and he contributes to many of the major magazines and newspapers in the gaming field, including Midwest Gaming and Travel, Slot Manager, Casino Journal, Strictly Slots and Casino Player.

Listen to John Grochowski's "Casino Answer Man" tips Tuesday through Friday at 5:18 p.m. on WLS-AM (890) in Chicago. Look for John Grochowski on Facebook and Twitter @GrochowskiJ.