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How Bankroll, Bet Size, and Edge Affect your Staying Power

4 April 2006

How many spins can you expect to get on a slot machine with a certain edge or return percentage, starting with a specific bankroll and bet some amount per try? There are lots of ways to answer this question. One of the simplest involves averages.

But, a caution. Averages can be misleading unless you understand that while they're convenient, they're also fictions. Convenient because they indicate trends. Average housing prices are up, or are greater in one city than in another. But fictions because they don't describe any particular situations. An average of \$213,465 for a home in a given area is unlikely to be exactly the amount you'd pay there for your version of the American Dream.

That's the way it is with the numbers generally cited for casino gambling. You can think of the house edge in your favorite game in terms of what the casino expects to earn from the average player. Assume a solid citizen plays 1,000 rounds at a slot machine during a visit, betting \$1 per spin, and the edge is 10 percent. Using averages, the casino figures that person for a gross profit equal to 10 percent of \$1,000 or \$100. It's entirely possible that the figures could work out precisely this way for someone; however such a result would be pure coincidence.

Rather, some individuals would make money, a lot or a little; others would lose less or more than \$100. The bosses book enough action that the averages serve as reliable predictors of earnings across their wide base of patrons. Bettors can also gain insights that may help them derive the most value and enjoyment from their casino visits. Here's how it might work on the question of the spins your money will buy you at the slots.

Make believe a player bets 1 percent of a bankroll per spin. This could be \$1 beginning with \$100, \$0.50 with \$50, and so forth, on a machine having 90 percent return. After 100 spins, the law of averages says \$90 will remain. The player goes 90 rounds on this residual and on the average would have \$81 left. Think of each such set of rounds as a cycle. Every cycle leaves 90 percent of the amount with which it began. Eventually, there won't be enough at the end of one cycle to start the next. With the stated parameters, "eventually" is 44 cycles and a total of 990 rounds.

How much less or more action would a smaller or bigger ratio of bankroll-to-bet buy at the same game? No definitive answer covers any given case. But the averages for different bankroll-to-bet ratios may help players make strategic decisions with which they can tailor the casino experience to suit their preferences.

With a bankroll equal to 25 times the bet (for instance, \$50 for bets of \$2, or \$250 for bets of \$10), the average is 240 spins.

For a bankroll-to-bet ratio of 50-to-1, it's 490 spins. At 200-to-1, the average is 1,990. Going to a bankroll of 500 times the bet, it's 4,990 spins. And at 1,000-to-1, it's 9,990 spins. The duration of play with a fixed return percentage rises roughly in proportion to the bankroll-to-bet ratio. So, for instance, doubling a bankroll for the same bet, or halving the wager for the same stake, gives twice as much action on the average.

The effect of return percentage at a given bankroll-to-bet ratio is a bit more complex. Using the 100-to-1 as a reference, 90 percent return gives an average of 990 rounds. The same bankroll and bet yield averages of 1,238 rounds at 92 percent return, 1,650 rounds at 94 percent return, and 2,475 rounds at 96 percent return. What may seem like minor improvements in percent return have a major impact on staying power. As a point of reference, the average of 2,475 rounds obtained at a 96 percent machine with \$1 bets on a \$100 bankroll would require a stake of \$250 with \$1 bets on a game having only 90 percent return.

Of course, there are and probably always will be folks who think one bet's as good as another. You pay your money and you take your shot. It's all just gambling anyway. No skill is needed. These are the hapless who never heeded the hortation of the punters' poet, Sumner A Ingmark, when he perceptively penned:

Your chance of success is tenaciously lifted,
Applying the knowledge with which you are gifted.
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Best of Alan Krigman
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.