Big craps rolls and big house edges

19 October 2017

By John Grochowski

QUESTION: I was just at a craps table where the shooter just never rolled sevens. He made his points, and he didn't even roll sevens on the comeouts.

There had to be 20 rolls in a row without a 7. It was uncanny. What are the odds of a streak like that?

ANSWER: On any given roll, the odds are 5 in 6 that the roll will be something other than 7, so there's an 83% 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%.

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% chance of rolling 20 non-7s in a row. It's not something you expect to see on any given trial, but given thousands of trials a day in a casino, such streaks are inevitable.


QUESTION: 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?

ANSWER: 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% on Pair Plus vs. 3.37% of your ante or 2.01% 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 Shackleford 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 it's 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% 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%.

I will not play a game with anything near a 7% 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.