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Best of Alan Krigman

Gaming Guru

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What Slot Machine Payout Schedules Mean to You

29 September 1997

Payout schedules - lists of each possible return and its associated probability - are at the crux of all slot machines. These schedules determine the statistical properties of the games, including long-term averages and short-term phenomena, such as:
o sizes of various payouts;
o how often bettors can expect one payout or another;
o how much of what's bet is paid out as winnings;
o likelihood that solid citizens will be ahead - or have money left - after specified numbers of tries, starting with various bankrolls.

Everything else - from graphics to buttons, bells, and whistles - is about as relevant as the fins on a '57 DeSoto. Sadly, complete schedules for individual reel-type slots are closely-kept secrets. Players see winning combinations of symbols and corresponding amounts, but not the all-important probabilities.


Normally, builders and buyers of one-arm bandits start by specifying two parameters. Payback - the percentage of what's dropped into the slot that should be returned to players on winning spins. And hit frequency - the fraction of spins that should return at least something. Both parameters are theoretical averages over many spins. They're chosen to yield what experts think will be a "good game" - paying out sufficiently often and in adequate amounts to keep bettors interested, yet holding enough to cover the casino's costs and generate a profit.

Specific payout schedules are developed mathematically from the paybacks and hit frequencies. The accompanying table shows figures for four typical reel-type machines that would look the same to players. Here's how to interpret the table.
Payback: On the average, bettors will be returned 86.75 percent of the money played in machines A, B, and C; they'll be returned 90.00 percent of the money played in machine D.
Hit frequency: Machines A, B, and D will return one or more units to bettors on an average of 39.57 percent of all spins; machine C will return something on 50 percent of all tries.
Payout schedule: Bettors will be paid 2-for-1 an average of 10.1 percent of all spins on machine A, 6.1 percent on machine B, 1.776 percent on machine C, and 7.209 percent on machine D.


Implied in the table are features of slots that few people appreciate. For instance, machines A and B have identical paybacks and hit frequencies; schedules differ, however, such that machine B pays 5-for-1 at almost triple the rate of machine A - gratifying certain slot buffs but not affecting their overall chances. Similarly, machines B and C have equal paybacks; but hit frequency is higher in Machine C - pleasing some bettors but not altering their long-run chances. Conversely, machines A and D have the same hit frequencies; nevertheless, payback is higher on machine D, so bettors have more chance of landing in the money.

Payout schedules also determine how many spins bettors with given bankrolls can expect before reaching their goals or busting. The relationships are complex but some trends can be stated. Revising schedules without changing payback or hit frequency (machines A and B) has almost no effect on expected session length. Increasing hit frequency for the same payback (machines B and C) has only minor influence on expected length. Raising payback at fixed hit frequency (machines B and D) tends to lengthen sessions.

More significantly, players can stretch their sessions independently of payout schedules. The key is bankroll size, or - more correctly - sizing bets to bankroll. As an example, computer simulation shows that starting with 250 rather than 100 bet units on machine A improves chances of surviving 1,000 spins from 9 to 55 percent; for 2,000 spins, survival rate rises from 2.5 to 12 percent. So if you've got $100 and expect to play for several hours, betting over $0.25 per spin isn't likely to get you there. Yet another instance of luck favoring the well-prepared. Or, as the poet Sumner A Ingmark wrote:


If battles are with knowledge planned,
Then fortune gets a helping hand.


 
machine A
machine B
machine C
machine D
parameters
 
 
 
 
Payback
86.75%
86.75%
86.75%
90.00%
Hit frequency
39.57%
39.57%
50.00%
39.57%
 
 
 
 
 
payout schedule
 
 
 
 
return per
coin played
probabilities (%)
1
27.5000
30.500

46.773

30.000
2
10.100
6.100
1.776
7.209
5
0.525
1.525
0.000
0.000
10
0.915
0.915
0.915
1.831
15
0.305
0.305
0.305
0.305
50
0.152
0.152
0.152
0.152
100
0.076
0.076
0.076
0.07
2500
0.003
0.003
0.003
0.003

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.