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Best of Alan Krigman

Gaming Guru

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How Much Bankroll Do You Need to Play the Machines?

25 October 2004

Casino patrons who favor the machines typically nurture three hopes in their hearts. First and foremost is to strike it rich by hitting a jackpot. Knowing the chance of this is small, though, they have the backup wish that they'll be able to stay in action for the whole of their planned visits. And third is the consolation desire for a comp to the all-you-can-eat buffet.

All three certainly involve luck. But luck isn't the only factor. Bankroll is involved, too. Not because it affects the edge. Rather, owing to its influence on a bettor's ability to withstand the normal downswings of the game. That is, to avoid running out of money in short order, and by surviving, to have more shots at the big score while amassing the points needed to earn a comp.

Bankroll adequacy depends in part on elements beyond a player's control. The edge, volatility, and skewness inherent in the probabilities and paybacks at various levels are among these determinants. But bankroll needs are also functions of choices made by the individual. These alternatives include the amount bet on each coup, the speed at which a person operates the machine, the goal for session duration, a player's exit strategy, the level of confidence a solid citizen will accept in not going broke, and the price a gambler is willing to pay to raise the probability of hitting the jackpot at a particular sitting.

Each situation is unique. However, conclusions drawn from a computer simulation for a specific set of circumstances can be instructive on their own, and as a starting point for extrapolation to other conditions.

Assume 25-cent video poker machines, five coins ($1.25) bet per spin. Say the games pay 8-for-1 on full houses and 5-for-1 on flushes, such that payback is about 95 percent. Also, posit bettors who get 600 rounds per hour and want three hours of action but will quit earlier if the jackpot hits or their initial stakes are depleted. For these ground rules, the simulation gives the probabilities in the accompanying table for busts, jackpots, and completing three hours without reaching either extreme.

Probabilities of busting, hitting a jackpot,
and surviving three hours at an 8-5 video poker game
playing 600 rounds per hour at $1.25 per round

bankroll
$50
$100
$200
$250
$300
$400
$500
bust
77%
51%
11%
4%
1%
~0%
~0%
jackpot
2%
3%
4%
4%
4%
5%
5%
play 3 hrs
21%
46%
84%
92%
95%
95%
95%

The simulation shows a breakpoint around $200 or $250 -- 160 or 200 times the bet. With such bankrolls, someone can be reasonably confident of surviving and therefore has about as good a shot at the jackpot as can possibly be achieved in 1,800 tries. Playing slower than 600 spins per hour extends the time at the machine but doesn't help with jackpots or comps. When payback percentage goes up, bust-out frequency declines while jackpot and survival rates rise; conversely, when payback percentage goes down.

The data are most striking in showing the danger of underfunding a game. A $200 bankroll exposes $1.25 players to only 11 percent chance of biting the dust before the end of three hours. Halve the bankroll to $100 and this probability soars to 51 percent. More, there's a message here for folks with something like $500 burning a hole in their fanny packs, who think they're ready to join the elite at the dollar or higher denomination slots. A $500 bankroll in a dollar game is like $125 at a quarter, with almost 50 percent probability of going belly-up within three hours.

Also, be wary of the new machines you can supposedly play for a nickel but end up betting multiple coins on each of 10 or more hands simultaneously. Think in terms of more hands per hour, raising the probability of busting and lowering that of remaining in action for the time you have in mind. Of course, all may not be lost because the money the casinos earn from the edge on your gross wager or "handle" may get you that coveted comp in a shorter period. Still, this poses the enigma evoked in the enduring epigram by the esteemed elegiast, Sumner A Ingmark:

Casinos have action for those in the clover,
But, run out of dough and the thrill is all over.

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.