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Best of Alan Krigman

Gaming Guru

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Your Whole Bankroll May Be Greater than the Sum of Its Parts

6 June 1994

You sometimes see or hear things so often you figure they must be true. Especially if they more or less make sense. More so when they have a technical ring. Such concepts comprise the canon of "conventional wisdom."

Sadly, conventional wisdom isn't always right. Take the axiom that the whole equals the sum of its parts. It's reasonable. And, words like equals and sum give it a mathematical aura.

But, ask yourself, if five sharply-honed hoopsters equal a championship basketball team, why aren't all-star games as good as the playoffs? Why couldn't all the king's men put Humpty Dumpty back together? The whole is frequently greater than the sum of its parts. Engineers call this "synergy."

The casino version of this conventional wisdom says to divide your gambling budget into four or five separate bankrolls and quit any game after losing one of these portions. It seems to make sense. Under the rubric, "money management," it sounds scientific. But, is it right?

Say you walk into the casino with $500 in your pocket. As a lump sum, this is about enough for a $10 line bet with double odds and one $10 or $12 place bet at craps, $25 blackjack or baccarat, a few inside and outside bets adding up to $25 on the layout at once at roulette, or three-to-five coin play at the dollar slots. It's enough because the peaks and valleys you can and should expect in the majority of games with this much at risk, the volatility, will be $400 or $500. Sure, you can get hot right away and be this much or more ahead. But, you're more apt to start with a few losses and be waiting for a series of hits to bring you up and over. You need a big enough bankroll to ride it out.

Suppose you divide your $500 into five $100 parts. The $100 bankrolls are adequate to survive normal cold streaks if you downsize your bets. Play $5 blackjack or mini-baccarat, a single outside bet at $5 roulette, a $5 on the line with double odds or two $5 or $6 place bets at craps, and single-coin dollar or multiple-coin quarter or nickel slot machines.

Mathematically, low-stakes games with small bankrolls and high-limit games with large bankrolls are equivalent, adjusting playing time for equivalent total risk. On this basis, the whole equals the sum of its parts and dividing a bankroll into segments for multiple games will help keep you in action longer.

But, there are two problems.

First, casinos don't have all that many $5-and-under tables these days. And it's not always easy to find free 5- and 25-cent slot machines on weekends or holidays. So, if you want to gamble, you may have to play at a level where a $100 bankroll is too vulnerable to wipe-out.

Second, there's human nature. You came with $500 to risk. You set your sights for profit accordingly. You'd like to win a few thousand, but you'd be happy with $300 or $400. Well, volatility works two ways. If you play a game in which $100 is enough to ride through most valleys, don't count on higher peaks. But few folks who divide their budgets into small bankrolls also divide their expectations. If they get $75 or $100 ahead at $5 blackjack, they figure they're hot and keep going. Instead of aiming for $100 profit in each of five games, they shoot for $400 or $500 every time.

You may not find or be happy with a low limit game. And you may not quit with a realistic profit for such a game. It's then that the conventional wisdom fails. The sum of the parts is less than the whole. And dividing your budget into separate playing bankrolls lowers the odds you'll make a profit. As Sumner A Ingmark, the bard of the big bettor, once wrote:

You haven't got too good a chance
To win a game played in short pants
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.