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Best of Alan Krigman

Gaming Guru

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It's Time to Go Beyond Edge in Characterizing Bets

4 October 2001

As a player, it's nice to know the house advantage or edge on the various bets you can make in a casino. It's even useful. Sort of.

For instance, you can evaluate edge from the returns shown on the fronts of poker machines and use it to pick the most favorable games. Or, knowing that edge is lower at single- than double-zero roulette, opt for the former when feasible. Or, take comfort from following Basic Strategy at blackjack, confident that it's based on edge so you're optimizing potential gain in every situation.

Edge, coupled with game speeds and bet sizes, is a vital statistic for casinos to project profits and allocate the comp credits solid citizens so solicitously seek. The bosses have therefore spent heavily to calculate it. And, since the figures are time-honored, they serve as standards everybody acclaims.

To players, though, edge is, at best, abstruse. Partly because it's a small fraction of what's won or lost on any particular round. Also owing to its usually being buried in the odds of and payoffs for winning. These considerations mean that edge isn't at all an intuitive betting criterion. Especially when you take a quick shot at a few bucks on the way to the all-you-can-eat buffet, in the brief span of an adequately funded session at the tables or slots, or even during a casino visit of several days' duration. Dabblers who flout edge by drawing to three-card low unsuited inside straights and such at video poker are barely less apt to get rich on $20 investments in quarter machines than crackerjacks who respect it by adhering to expert strategy.

In contrast, lots of measures could really help players make betting choices that satisfy their personal preferences. An illustration might be the chance of being even or ahead after some specified ?? typically short ?? period of play.

I'll show you what I mean using Place bets at craps as an example. For reference, here are values of edge and the theoretical loss they imply after only 10 throws of the dice.
Six or eight: edge is 1.51 percent; after 10 throws, betting $6 to win $7, theoretical loss due to edge is $0.28.
Five or nine: edge is 4.00 percent; after 10 throws, betting $5 to win $7, theoretical loss due to edge is $0.56.
Four or 10: edge is 6.67 percent; after 10 throws, betting $5 to win $9, theoretical loss due to edge is $0.83.

The weakness of edge to classify and compare bets jumps right out of the above data. First, the percentages don't seem tied to any realities ?? for instance, what insights do you get from the six having 1.51 percent edge? Likewise, is a $6 six 4.42 times better than a $5 four because edge is this much less, three times better because theoretical loss it causes is a third as much, or what? Further, why does theoretical loss only triple when edge rises by a factor of 4.42? Besides, you can't be $0.28, $0.56, or $0.83 behind after 10 throws, so what do the amounts represent, anyway?

In pre-digital days, calculating edge was tough; finding anything more meaningful was almost impossible. Today, assuming you know how to set up the formulas, ascertaining something like the chance of being even or ahead after some number of bets in most casino games is a piece of cake. The accompanying list shows the probabilities for 10 throws of the dice on the Place bets.

Probability of being even or ahead on the Place
bets at craps after 10 throws of the dice

bet
even/ahead
ahead
$6 six or eight
55.2%
52.6%
$5 five or nine
49.0%
45.2%
$5 four or ten
43.8%
38.2%

 

Computers allow gaming experts to characterize bets with many other parameters far more intuitive than edge. These include the likelihood of staying in action for some desired interval, the chance of reaching an arbitrary profit before depleting a stake, and how far up or down the normal swings of a game are apt to drive a bankroll. Wider dissemination of such facts would give folks a basis for informed choices they might actually use. The immortal muse, Sumner A Ingmark, succinctly summarized the idea:

Explanations too obscure,
Cause more headaches than they cure.

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.