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What You Really Need to Know: A New Formula for Video Poker

3 August 2000

By Alan Krigman

An avalanche of advice, some even accurate, abounds about video poker. A lot of it tells how to play each hand -- what to hold or discard. A fair fragment helps bettors interpret the coin-back charts on the belly glasses to estimate payback percentages. And a smidgen suggests how big a bankroll players need at various betting levels to be reasonably assured they won't run dry during a normal downswing, not -- at least -- before amassing enough bonus points for a comp to the all-you-can eat buffet.

In practice, the last of these is more vital to bettors than the first two, despite getting less attention. For instance, on hands where the strategy isn't a gimme, differences between best and next best tend to be trifling; further, flouting rules doesn't preclude winning. Similarly, casinos may have poker machines with munificent, moderate, or miserly payback percentages, although a single joint rarely offers a spectrum of house advantages within any particular denomination; knowing what to look for therefore doesn't guarantee you'll find what you seek. But, premature insolvency can ruin any gambler's day; solid citizens court disaster by betting too big for their bankrolls or overestimating the playing time their stakes can be expected to support, despite having control over just these factors.

Until now, the few available survival guidelines have been vague. Typical is "bankroll should be at least 100 times the bet per spin," say $125 to play five coins in a 25-cent machine. Or, marginally more informative, along the lines of "a stake of 200 times the total bet per spin affords 95 percent confidence of being in the game for at least two hours." These milestones are useful, as far as they go. However, they don't tell players quite enough. How does edge enter the picture? What about playing longer? Would $100 more significantly improve my position? Can I raise my probability of survival to 99 percent?

These limitations have finally been overcome. I've developed a formula linking bankroll, bet size, spins per session, confidence you'll remain in action, and house advantage. Starting with any four of these variables, you can find the other -- provided you can use a calculator, spreadsheet, or paper and pencil to do addition, subtraction, multiplication, and division.

Before I present the formula, I'll mention it's "empirical." That is, it's based on data from video poker simulated on a computer, not strictly on the theory of probability. I'll also caution that results are approximate -- not exact, but close enough to use for decisions in a milieu where uncertainty reigns supreme.

Here's the primary version of the formula:
B = [(R) x (W)]/[29.3 + (53.1 x E) - (22.7 x S)]

B is bankroll, in dollars.
R is rounds per session; if you think in terms of time, figure 500 rounds per hour is average and go up or down from there.
W is the total wager per round, in dollars.
E is the house edge on the machine, expressed as a decimal; it equals the payback, also expressed as a decimal, minus 1.
S is the confidence you want to have in surviving the session, expressed as a decimal probability.

I'll illustrate how to use the formula. Make believe you want to be 90 percent sure (S = 0.9) your stake will last at least three hours (R = 3 x 500 = 1,500), betting five coins in a $1 machine (W = $5), knowing that the payback on your game is 95 percent (E = 0.95 - 1 = -0.05). With these numbers, the formula shows you need roughly $1,200. For 95 percent confidence of endurance (S = 0.95), the required bankroll rises to $1,475. At 98 percent payback (E = -0.02), 95 percent survival confidence takes $1,120.

Here are the alternate versions of the formula to use in starting with other parameters and calculating what you'd like to know:
S = 1.29 + (2.338 x E) - (0.044 x R x W)/B
R = (B/W) x [29.3 + (53.1 x E) - (22.7 x S)]
W = (B/R) x [29.3 + (53.1 x E) - (22.7 x S)]

Maybe you think it's asking too much to do a little homework before risking your dough in a video poker game. Maybe you think gambling is all luck, so why bother? Maybe you think I'm nuts. If so, I recommend this refrain by the rhymer, Sumner A Ingmark:

Though luck is a factor, astute preparation,
Helps you and your money avoid separation.

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 were focused on those interested in gambling probability and statistics. He passed away in October, 2013.