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Best of Alan Krigman
What You Really Need to Know: A New Formula for Video Poker3 August 2000
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.
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:
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:
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,
Best of Alan Krigman