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# Slot Payback Percentages Do Affect Your Chances

8 January 1996

ou may have heard that slot machines in some casinos have higher "payback percentages" than in others. In New Jersey, where the mandatory minimum is 85 percent, casinos can't advertise payback rates but results for various size machines in each establishment are reported to and made public by the State every month. In Nevada, where laws are looser and competition keener, some casinos tout paybacks of 96 percent or more on their marquees.

But do you know anyone who started with \$100, played for a while, and ended with \$85 or \$96? A few folks make big bucks on the banditos; almost everyone else taps out.

So, what does payback percentage really mean? And, does it affect your play, especially your chance of hitting a jackpot?

Payback percentage is the fraction of the "handle" ─ the money actually wagered ─ returned or credited to players. Say you start with 100 \$1 tokens, play them all, and rack up 120 units on the credit meter. The machine tallied \$100 in bets and \$120 in payouts; so far, your payback percentage is 120/100 or 120 percent. You continue, "cashing out" and playing your \$120. After this round, imagine 78 units on the credit meter. Since you began, the machine counted \$100 + \$120 = \$220 in bets and \$120 + \$78 = \$198 in payouts. Your payback percentage is 198/220 or 90 percent, even though you have 78/100 or 78 percent of your initial stake. Now play the \$78 and assume you end with \$70. The machine clocked \$100 + \$120 + \$78 = \$298 in bets and \$120 + \$78 + \$70 = \$268 in payouts. The payback percentage is 268/298, still 90 percent, but you have only 70/100 or 70 percent of your original stake.

Sadly, if you keep trying for the big jackpot and continue to experience average payback below 100 percent, you'll eventually go broke. Gladly, the higher the payback rate you encounter, the more bets you can cycle through the machine before your bankroll disappears. And, the greater the number of tries, the better your chances of eventually getting a bell-ringer.

You can see the effect in the accompanying table. It's for \$1 bets, starting with \$50, \$100, and \$1,000, and a jackpot whose probability is 1/100,000. Entries show how many shots you can expect to take by recycling winnings at various payback percentages, and the probability of a jackpot within this many tries.

The table indicates how the action and corresponding chances of a jackpot rise as payback percentage increases. The table further suggests that, for any payback percentage, wagering smaller portions of a bankroll per spin extends the expected number of tries and the associated likelihood of a jackpot.

The problem with the table is that it's based entirely on average payback and ignores deviations caused by "volatility." Averaged over long periods and many players, highly-volatile machines can achieve any payback percentages with small numbers of large payouts; low-volatility slots can achieve mathematically equivalent results with large numbers of small returns. High volatility is what makes the slots popular because it's the means by which players can score big. But increasing volatility reduces effective payback percentage over typical playing periods. In the extreme, picture a 98 percent average payback -- achieved with a \$99,000 jackpot whose probability is 1/100,000 and no intermediate payouts whatever. In theory, the table shows a \$1 bettor with a \$100 bankroll getting 4951 tries and corresponding probability about 1/21 of hitting the jackpot at least once. In practice, this bettor is likely to get only 100 tries ─ all losers ─ with an overall jackpot probability roughly 1/1,000.

Most slot players won't stop with a moderate win but will keep going for the gold. If this is your style, maximize your chances by getting the most play from your bankroll. You can't tell which slots have high payback percentages. You can identify low-volatility machines, those that seem to give lots of small returns. And, you can keep bets low, not over \$1 per \$100 bankroll. As succinctly stated by Sumner A Ingmark, singer of slot songs:

For some, gambling's goal is to earn a day's pay.
For others the aim's not to win but to play.
On slots, though, the force driving players to stay,
Is thinking a fortune's an arm's length away.

 payback \$1 bets starting with \$1 bets starting with \$1 bets starting with percent a \$50 bankroll a \$100 bankroll a \$1,000 bankroll total no prob of total no prob of total no prob of of coins hitting of coins hitting of coins hitting through jackpot through jackpot through jackpot 86 351 1/285 709 1/142 7137 1/15 88 410 1/244 827 1/112 8327 1/13 90 492 1/203 991 1/101 9991 1/11 92 614 1/163 1239 1/81 12,488 1/9 94 818 1/122 1652 1/61 16,651 1/7 96 1226 1/82 2476 1/41 24,977 1/5 98 2451 1/41 4951 1/21 49,951 1/3
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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.