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Best of Alan Krigman

Gaming Guru

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How Much Money Should You Bring to Play the Game?

17 February 2004

Everyone who's pitched pennies in the schoolyard knows you gotta pay to win. So, enough of a wad to outride cold streaks is vital to casino gambling. You can stay alive foolishly by visiting a credit card or cash terminal for a transfusion. Or, wisely, by sizing bets to a bankroll that made sense before you left home.

Experience playing a particular game a certain way is an asset. It yields good intuition about how much moolah buys acceptable prospects of keeping solvent for sessions of different durations.

But neophytes, or seasoned solid citizens trying unfamiliar games or strategies, needn't go without guidelines. It's a matter of degree of confidence, say 95 percent, in being in action after some desired interval. Hopefully ahead; if not, at least with the resources to continue. The relevant variables are the edge and volatility of the game, the typical number of bets resolved per unit time, and the average amount wagered in each round.

A practical way to get at the necessary nest egg is to establish a reference point then explore how funding pressures change with each contributing factor. Single-zero roulette, betting on one 12-number column, offers a convenient baseline. House edge is 2.7 percent. The wager pays 2-to-1 and has a standard deviation (a measure of volatility characterizing average spin-to-spin changes in your fortune) of 1.4 times the amount bet. A well-paced game clocks about 50 spins per hour. At $25 per spin, $1,100 would leave you 95 percent sure of being at the table for four hours.

Altering the size of your bet increases or decreases demands for reserves proportionally. Doubling the wager to $50 dictates twice as much -- $2,200. Cut the wager by a factor of five to $5 and you're down to one fifth of the $1,100, just above $200.

Back-up requirements also track changes in house advantage, although the correlation is weaker than widely believed. A $25 one-column bet at double- rather than single-zero roulette, where the sole major parameter modification is an increase in edge from 2.7 to 5.26 percent, suggests $1,200 rather than $1,100 for the same 95 percent confidence in surviving four hours. As a rough rule of thumb, raise or lower bankroll needs by a single bet unit per 100 rounds for every percent increase or decrease in edge.

Volatility has a stronger impact. With higher volatility, larger but less frequent payoffs, you can soar or plummet rapidly. Lower volatility moderates the swings. Assume that, on a double-zero table, you switch from $25 on a one 12-number column to $5 each on five non-overlapping four-number corners. The total bet and edge stay the same but $25 wins $20 instead of $50. The standard deviation drops from 1.4 to 0.9 times the $25 bet. The lower fluctuations trim bankroll requirements from $1,200 to $850.

Decisions per hour are another critical element. Say you play blackjack and adhere closely to Basic Strategy. The edge is 0.5 percent; wins are mostly 1-to-1 with some pushes and a few higher returns, putting standard deviation at 1.13 bet units. For 200 rounds at $25 apiece, $800 is about right. But, at a table with three spots in action in addition to your own, you'd expect 300 to 350 hands in four hours and $1,000 would be more appropriate.

Slots usually have greater house edge than table games, along with higher volatility and more decisions per hour. Bets are generally lower. A machine with a 7.5 percent edge and a standard deviation of 10 calls for a stash of $525 per dollar bet playing 300 rounds per hour for two hours, and $650 for three hours.

Gambling for high stakes can be gratifying. The more you wager, the more you can earn. Plus, the more attentive and solicitous the caring casino crew becomes. But illusions of grandeur fall through, from your musing about bagging those big bucks to their tactless toadying, as soon as the well runs dry. Barring an unlimited budget, a bet-to-bankroll compromise seems prudent. The penurious poet, Sumner A Ingmark, caught the conundrum thusly:

Acting rich is OK long as you can afford it,
But the folks with real money don't risk it, they hoard it.

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.