Deal Me In: Math trumps kitchen table consensus

Dear Mark: This is not a question, but an observation about people. I was invited to play with a group of old-timers, mostly retired or soon-to, professors. Some of us play three-card games. The first time I had a winning three-card hand (straight) a player with a flush pulled in the chips. When I pointed out that in three-card, a flush doesn't beat a straight, and trips don't beat a straight flush, the response was, "Well, that's the way we've always played it.” OK, it's only nickel-dime, so as long as I know the house rules . . ." I was the only member of the math department, although one was a chemist and one a physicist. Any thoughts? Bill S.

Before playing any form of poker, one should familiarize oneself with the hand rankings of the game being played. You just can’t make a smart decision unless you know the value of your hand compared to that of others.

So, Bill, with single-mindedness, let’s focus on what you already know, the math of Three Card Poker. When it comes to this version of poker, you are correct: a straight beats a flush, and a straight flush thumps three-of-a-kind.

The probability of getting a flush in the game of Three Card Poker is 4.9593%, and the number of potential combinations forming that hand is 1,096. Whereas for a straight, the probability is 3.2579%, and the combination possibilities are 720, which makes for the stronger hand.

Likewise, Bill, where you noted to fellow players that trips (three-of-a-kind) do NOT beat a straight flush, again, you are correct. The differential isn’t as distinct as flush versus a straight, but the chances of catching a three-of-a-kind hand are 0.2353% with 52 possible combinations, whereas the chances of getting a straight flush are 0.2172% and 48 achievable groupings.

What I believe is happening within your group, is that they are confusing the hand rankings of Three Card Poker against that of a five-card game. In video poker, or five-card draw for that matter, flushes do beat straights. But, unlike 'normal' poker, a straight is much less likely with three cards and is accordingly ranked higher. The same holds true with a straight flush, which is less probable to appear than trips.

Here is a list of Three Card Poker hands from best to worst. The better the position, the stronger the hand:

• Straight flush: straight of one suit (8-9-10).
• Three-of-a-kind: three cards of one kind (J-J-J).
• Straight: three cards of sequential rank (4-5-6).
• Flush: three cards of the same suit (K-9-7 same suit).
• Pair: two cards of the same kind (10-10–4).
• High card: If nobody has any of the above, then whoever has the highest card wins.

Obviously, Bill, you are burdened by the house rules of whoever is gracious enough to let you spill beer and avocado dip all over their carpet. Still, I am sensing something very positive here. Dead money players (patsies) who don’t know the probabilities of the game, over the long run, tend to make for easy pickins.

Gambling Wisdom of the Week: “If after 10 minutes at the poker table you do not know who the patsy is — you are the patsy.” --poker proverb