John Grochowski

John Grochowski John Grochowski John Grochowski John Grochowski

A shuffle through the Gaming mailbag:

Q. I was just at a craps table where the shooter just never rolled sevens. He made his points, and he didn’t even roll 7s on the comeouts. There had to be 20 rolls in a row without a 7. It was uncanny. What re the odds of a streak like that?

A. On any given roll, the odds are 5 in 6 that the roll will be something other than 7, so there’s an 83 percent chance that any given roll will be a non-7.

For streaks, the chances are calculated by multiplying 5/6 by itself as many times as there are rolls. For a two-roll streak, you’d square 5/6, giving you 25/36. Converted to percent, that’s a 69.4 percent chance that two rolls in a row with be non-7s.

Make the streak five in a row, and you need (5 5 5 5 5)/(6 6 6 6 6), or 3,125/7,776. That’s 40.2 percent.

You think there might have been 20 in a row, so you need 5 to the 20th power divided by 6 to the 20th power. That takes you to some really large numbers — 95,367,431,640,625 / 3,656,148,440,062,976.

That boils down to a 2.6 percent chance of rolling 20 non-7s in a row. It’s not something you expect to see on any give trial, but given thousands of trials a day in a casino, such streaks are inevitable.

Q. When you play Three Card Poker, do you play both ante-play and Pair Plus? If you do, do you bet more on one than the other? What’s the best balance of bets?

A. Three Card Poker has evolved, and so has my play.

In the game as initially devised by Derek Webb at Prime Table Games, the house edge was 2.32 percent on Pair Plus vs. 3.37 percent of your ante or 2.01 percent of total action on the ante-play option.

In games with multi-stage betting, such as Three Card Poker’s ante-play, Mississippi Stud and Caribbean Stud, the house edge on total action — the figure Wizard of Odds Michael Shackelford calls “element of risk” — is my preferred comparison to other bets. You can’t win if you don’t make bets beyond the ante, so the house edge on the total of my wagers is the figure I need.

In its original configuration, Three Card Poker had house edges close enough on its two options that I usually played both, with an ante equal to my Pair Plus bet. I knew that overall I’d be betting more on ante-play once my play bets were made, but then ante-play had the somewhat lower edge.

Since then, the Pair Plus pay table has changed. The original version paid 40-1 on straight flushes, 30-1 on three of a kind, 6-1 on straights, 4-1 on flushes and 3-1 on three of a kind. For several years, that was the only pay table, and it had the 2.32 percent house edge.

Today, Pair Plus is offered in a number of pay tables, nearly all with higher house edges. The most common looks like the original, except the payoff on flushes is reduced to 3-1. That increases the house edge to a whopping 7.28 percent.

I will not play a game with anything near a 7 percent house edge, so today if I play Three Card Poker, I stick to ante-play and don’t bet on Pair Plus. I once played in a casino that required players to make both bets. That’s not common, but if I encountered it today, I’d skip the game entirely.

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