Stay informed with the
Recent Articles
Best of John Grochowski

# Big craps rolls and big house edges

19 October 2017

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.
Recent Articles
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:

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.