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Three Card Poker and Pair Plus

8 July 2021

QUESTION: I've been reading about Three Card Poker and Pair Plus, including something you've said about the house edge on the original version being 2.32 percent while the common edge today is 7.28 percent.

The only difference between the two is that flushes pay 4-for-1 on 3-for-1 on the other. The rest are all the same: 40-1 on straight flushes, 30-1 on three of a kind, 6-1 on straights and 1-1 on pairs.

I get that you want the higher payoff and that the house edge would go up with the lower pay on flushes. But is that little difference on a pretty rare hand really enough so the house edge on one is more than three times as high on the other?

ANSWER: Flushes aren't all that rare in Three Card Poker. You'll see one an average of once in 20.16 hands. Changing flush payback makes a big difference in our overall return.

In three-card games, there are 22,100 possible hands in which card order doesn't matter. Those include 48 straight flushes, 52 threes of a kind, 720 straights, 1,096 flushes, 3.744 pairs and 16,440 losing hands.

Imagine betting \$1 on each of 22,100 hands in which each possible combination was dealt once. With a 4-1 payoff, the 1,096 flushes would bring \$5,480 back to your side of the table, including the payoffs plus getting your bet back on winners.

If flushes pay only 3-1 instead, then the 1,096 winners bring only \$4,384 to your side.

The house keeps an extra \$1,096 per \$22,100 wagered when flushes pay 3-1 instead of 4-1. That's a huge difference. That \$1,096 shortfall in payoffs represents 4.96 percent of \$22,100 in wagers. And not so coincidentally, 4.96 percent is the difference in house edge between the original 2.32 percent and the 7.28 percent on the most common version today.

QUESTION: Craps newbie here. Maybe you can explain something to me.

I tried betting don't pass for the first time. It was fine. I didn't win much or lose much. One thing bothered me. When the shooter rolled 12, the pass players all lost, but I just got my money back.

That seemed wrong to me. If pass loses, don't pass should win. Was the casino pulling a fast one?

ANSWER: The odds that follow from the game's setup lead to pass losing more often than it wins. That's how the house gets its 1.41 percent edge on the pass line.

If don't pass was set up as the exact opposite of pass, with don't bettors always winning when pass loses, then don't pass bettors would have a 1.41 percent edge.

The house wouldn't make any money. In fact, it would lose money because players in the know would gravitate to the bet that gave them the edge. More players would bet with a 1.41 percent edge than would bet pass and give the house the edge. The books wouldn't balance and the house would have to change the game or close it down.

The adjustment that was made was to make 12 on the comeout roll a push for don't pass bettors. other than that tweak, pass and don't pass are mirror images of each other, with bettors on each side winning when those on the other side lose.

That little tweak is enough to give the house a 1.36 percent edge on don't pass.

Both sides have edges narrow enough that winning sessions are frequent for both pass and don't pass players. But overall, the odds of the game will lead to profit for the casino no matter which bet you make.
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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.

Books by John Grochowski:

Winning Tips for Casino Games
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.