Different edges for the same bets

14 January 2018

By John Grochowski

Even though the house edge at most casino games is unchanging on every play, you'll sometimes see different edges listed by different sources.

It's not necessarily that one source or another is wrong. It's just that they start with different assumptions.

Ray, who says he's been a regular reader for at least 10 years, e-mailed recently to ask about some of those differences.

"You list the house edge at baccarat as 1.06 on banker and 1.24% on player," he wrote. "But I've seen others list 1.17 percent on banker and 1.36% on player.

"There are others. You list the edge on don't pass in craps as 1.36%, but I've seen 1.40. You list edges on craps place bets as 1.52% on 6 or 8, 4% on 5 or 9, and 6.67 on 4 or 10, but my brother-in-law showed me a page that has 0.46, 1.11 and 1.67, which is way different.

"Why the differences, and which are right?"

All those figures are correct, but tell you different things about the bets:

• Baccarat: The house edges I use assume a push is a legitimate outcome of a bet. They tell you that on average, the house will keep 1.06% of all money wagered on banker and 1.24% of all money on player.

The higher figures assume bettors are interested only on the outcomes where money changes hands. They throw out the pushes before the calculation is made.

In an average 10,000 hands, banker will win 4,586 times, player will win 4,462 times and there will be 952 ties. If you want the house edge with all results taken into account, you'll use all 10,000 hands in the calculation. If you want to consider only the non-pushes, you'll base your house edge on the 9,048 hands where either banker or player win and ignore the 952 pushes.

I prefer to focus on all 10,000 hands to ignoring more than 9% of them.

I choose not to ignore the pushes.

• Craps, don't pass: A similar thing is at work as in baccarat. The 1.36% edge on don't pass includes pushes, while the 1.4% figure throws out pushes and considers only the bets in which don't pass wins or loses money.

On the comeout roll, don't pass bets lose on 7 or 11 and win on 2 or 3. If the roll is 12, don't pass pushes. On any other roll the number becomes the point, and don't pass wins if the shooter rolls a 7 before repeating the point.

Only one of the 36 combinations of two six-sided dice yields a total of 12 — a 6 on each die.

Including the 1 in 36 comeouts in which the dice total 12 results in a house edge of 1.36%. Ignoring that roll and focusing only on the 35 other rolls results in a house edge of 1.4%.

Craps, place bets: Place bets are multi-roll bets. If you place 6, then you win if the shooter rolls a 6 before rolling a 7, and lose if the 7 comes first. No other rolls count in deciding the bet.

If the roll is neither your number or a 7, most players leave the bet in action. However, you may take the bet down if you wish.

The higher figures, such as 1.52%, assume the bet is left in action until a decision is made — it is the house edge per decision. The lower numbers, such as 0.46% on 6 or 6, is the house edge per roll.

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