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Best of Alan Krigman

Gaming Guru

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How to get broader bankroll swings without paying more in edge

7 June 2010

Everybody knows that house advantage or edge in the casino is bad for players. Not many solid citizens know exactly why, how much it's responsible when they lose, or the reason folks often wrap up sessions or visits with a profit despite its negative effect.

Hardly anybody knows anything about volatility. It can help or hurt. It's the parameter underlying losses far exceeding those predicted by house advantage, wins that swamp the negative impact of edge, and differences among sessions in which fortunes drift gradually up and down or rise and fall sharply. Picture games with frequent small payouts versus those with big low-probability jackpots. Or bets held constant from round to round as opposed to those pressed aggressively to capitalize on previous wins or try to recover past losses. In all of these situations, the first of the items bespeaks low volatility and the second high.

Other than by counting cards at blackjack, you can't eliminate edge. At best you can choose machines or tables, propositions within games, and strategies giving the joint as edge it as it's willing to take. Conversely, you can do a lot about volatility to tailor the gambling experience to your personal preferences for tolerance of or aversion to risk and your fantasies of reward.

Make believe your punting passion is minibaccarat and you always bet on Player, an even-money wager. The probabilities are to win 44.6 percent, lose 45.8 percent, and push the other 9.6 percent.

Including rounds with ties, the house has 1.2 percent edge. After 200 hands betting an average of $10 each, your gross wager would be $2,000. The value to the house of this action would be 1.2 percent of $2,000 – $24. You might, in fact, finish $24 behind. But it would be coincidence. More likely, owing to volatility, you'd be showing a profit or be deeper than $24 in the hole.

On a single-round basis, betting $10, your chances would be 44.6 percent of going up by $10, 45.6 percent of going down by $10, and 9.6 of not changing. The characteristic jumps in your bankroll per hand would be $9.50, a figure the statisticians call "standard deviation." The 200 rounds will be a mix of ecstasy and agony. For this much play, the characteristic overall change in your bankroll, the standard deviation for the session, would be $134. What this means to you is there's a 63 percent chance you'll finish $134 below or above the $24 average loss ascribed to edge. That is, you'll be from $158 in the hole to $110 ahead. The unbalance illustrates the interaction between volatility – which may be up or down, and edge – which is always down.

Pretend you'd like to stick with Player at minibaccarat but want to earn a bit more when the table is hot and are willing to watch your stake shrink marginally further when it's cold. You could do this betting, say, $12 per hand. In 200 rounds, you'll sacrifice more to edge, $28.80 instead of $24. Characteristic bankroll jumps will also go up, to $11.41 rather than $9.50 per hand and $161 as opposed to $134 for 200 rounds. The range for 63 percent chance of finishing is also wider, roughly $190 loss to $133 win.

Alternately, you can raise volatility without increasing loss to edge by varying your bets while keeping the same average per hand. For instance, the average in 200 rounds will be $10 with 110 bets at $5, 60 at $10, 28 at $25, one at $50, and one at $100. Standard deviation per hand is $11.98; after 200 rounds, you have 63 percent chance of being between $194 loss and $146 gain. The swing is $170 over or under $24 expected loss to edge.

Similarly, in 200 rounds, 100 bets at $5, 80 at $10, 12 at $25, and eight at $50 give a $10 average with characteristic jumps of $13.78 per hand and $195 per session. You therefore have 63 percent chance of finishing from $219 in the red to $171 in the black, $195 below or above the $24 loss projected solely by edge.

Of course, statistics that give you a 63 percent chance may not mean much if you lose a few of your more ambitious wagers and bust out. It's as the cynical songster, Sumner A Ingmark, said:

While math and statistics have meaningful places,
They do not anticipate definite cases.

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.