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Best of Alan Krigman

Gaming Guru

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How Long Must You Play before the Edge Costs You One Bet?

21 February 2001

House advantage on most casino bets is obscured in the fog between the chance of winning and the payoff. Confusion is compounded by the fact that chances and payoffs are commonly described in terms of "odds," which most solid citizens readily envision, while edge is usually stated as a "percentage," which folks frequently find flustering. You can get a clearer picture of the impact of house advantage by changing from percentage to a number of decisions at which edge is equivalent to a single bet.

I'll illustrate with a specific case. The edge when you place the five or nine at craps is 4 percent. This implies that every time you bet $5, you give the house $0.20 -- 4 percent of $5. But, you never actually fork over $0.20. You either lose the $5 or win $7. So how do the bosses take their bite?

Technically, 4 percent on the five or nine arises from beating odds of 3-to-2 but only getting paid 7-to-5. At 3-to-2, making the bet 25 times mean you "expect" to lose 15 decisions and win 10. When the statistically correct proportion ensues, though, you don't break even. Betting $5, you win $7 x 10 or $70 and lose $5 x 15 or $75. You'll be $5, one bet, behind. The $5 loss amounts to $0.20 for each of 25 bets, since $0.20 x 25 = $5.

It's easy to convert edge, in percent, to number of decisions at which house advantage is equivalent to losing a single bet. Just divide edge into 100. On any calculator, punch in 100, hit the "divide" key, enter the percent edge, and press "equals." For the example we're using, 100 divided by 4 equals 25.

Slot buffs may have to change "payback percentage" to edge before doing the division. This is also simple, since edge is 100 minus payback percentage. So, a 92 percent machine gives the house 100 - 92 or 8 percent edge. Divide 8 into 100 to get 12.5 pulls. Don't worry about the fraction. Figuring 12 or 13 rounds in this situation is adequate to estimate the effect of house advantage.

The following list gives edges and decisions for some typical bets. Use the values directly, or as a way to check that you're using your calculator correctly when you want to find equivalent numbers of decisions for situations I haven't selected.

Number of Decisions at which
House Advantage becomes Equivalent
to a Single Bet
Bet
Edge
Number of
Decisions

Craps, Place 6 or 8
1.52%
66
Craps, Place 4 or 10
6.67%
15
Craps, hard 4 or 10
11.11%
9
Double-zero roulette, inside
5.26%
19
Single-zero roulette, any
2.70%
37
Blackjack, typical player
0.65%
154
Baccarat, Player
1.17%
85
Slot machine, 86% return
14.00%
7
Slot machine, 95% return
5.00%
20

On some bets, such as Player at baccarat or red at single-zero roulette, wins get 1-to-1. On these, winning one more than the statistically correct share of the edge-equivalent number of decisions puts you at break-even. Over one excess win in this many decisions pays the devil its due and puts you in the pink.

A few bets, like Banker at baccarat or lays at craps, return under 1-to-1. You're still down a unit if the edge-equivalent number of rounds ends at the statistically correct proportion. But you have to win more than one excess decision to be ahead.

Most wagers pay multiples of the money at risk -- for instance 7-to-1 on a hard 10 at craps, 35-to-1 for straight-up spots at roulette, and varying amounts on slots and tables whose returns depend on the odds against particular results. On these bets, a lone win above the statistically correct proportion can swamp the edge and leave a player flush. Sometimes substantially so.

The edge-equivalent number of decisions at which you're one unit behind provides a good intuitive sense of house advantage. And the reward for winning a single excess wager explains why so many bettors eagerly take longshots despite the high edge they often carry. Sumner A Ingmark, the versifier venerated as the Chaucer of chance, reflected on the latter in his laconic lyric:

Though I seem stuck, the game's not over,
One stroke of luck, I'm in the clover.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.