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Best of Alan Krigman

Gaming Guru

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Overbetting Your Bankroll Hurts Your Chances at the Slots

1 September 1997

Slot fans frequently follow the King of Hearts rule in deciding how long to play. As the King of Hearts told Alice, the rule is: "Begin at the beginning, and go on till you come to the end; then stop." But, how do players know when they've "come to the end?" Easy! They run out of cash, run out of time, or hit a jackpot.

Folks who gamble this way aren't simply seeking a fair return on money placed at risk - say 20 or 30 percent. They're out for a big score. And they'll keep trying till they "come to the end."

Some of these solid citizens think it's pure luck. Others are sure they can sense which slots are set to pay, or when their machine is "due." A few cling to the conviction that the casino bosses or their clever computers decree who wins what, and when.

Forget about beneficent bosses, machine cycles, and hot slots. Luck? Yes, it's a factor, but not the whole story. Two further items affect how players are likely to "come to the end."

Inherent machine payback is one determinant. Savvy players rate poker machines on this basis, using the schedule of returns listed on the machines and the known chances of getting various hands. Casinos have similar data in the technical specifications of their reel-type slots, but the information isn't available to players or even personnel on the gaming floor.

Bankroll relative to bet size also impacts how players are apt to "come to the end." And while payback governs casino profits over many patrons, bankroll bears strongly on individual games. More, paybacks are fixed but players can pick their stakes and wagers.

I'll illustrate the importance of bankroll on the slot machine represented in Table I. At the indicated jackpot levels, this is a two-coin progressive "full-pay" device which returns everything players bet. In addition to payouts, the table gives probabilities - although players would have no way to know the latter.

Tables II and III show what players can expect from such a machine starting with bankrolls equivalent to 100, 200, and 500 bets - $100, $200, and $500 in a 50-cent slot played two coins at once. Action is assumed to stop after the entire bankroll is gone, a player hits a 3400-coin jackpot, or 3000 rounds.

Table II presents percentages of players who "come to the end" by losing their bankrolls after the designated numbers of rounds. As an example, 0.36 percent of those bankrolled with 100 bets will last between 1400 and 1499 rounds before going broke, compared to 1.56 percent starting with 200 and 4.21 percent with 500 bets.

Table III shows fractions of players who "come to the end" winning, or losing but having money left, after finishing 3000 rounds or hitting the 3400-coin jackpot. For instance, 0.40 percent of those starting with 100 bets will earn 900 to 999 bets, compared to 0.84 percent with 200 and 1.68 percent with 500.

Specifics differ on machines with other payback schedules, but the general conclusions hold. Higher bankrolls stretch playing time and lead to more players who "come to the end" as bigger winners - jackpot and otherwise.

Sumner A Ingmark, the gamblers' Goethe, who frequents a wonderland Alice never envisioned, thought about it like this:


Go play a slot you think is hot,
But have the clout to tough it out,
Cause stake's a key to victory.

Table I
Return schedule for two coins
in full-pay progressive slot machine
reel
pattern
probability
(%)
payout
(coins)
z z z
0.003
3400
z z ?
0.021
1700
z ? ?
0.300
125
a a a
1.600
25
a a ?
4.640
10
a ? ?
7.560
2
? ? ?
85.876
0

 

Table II
Percent of Players Who Lose Their Entire Bankrolls
within Various Numbers of Rounds
rounds
completed
% of players
with 100-bet
bankrolls
% of players
with 200-bet
bankrolls
% of players
with 500-bet
bankrolls
100-199
18.3
 
 
200-299
25.9
0.18
 
300-399
14.3
6.32
 
400-499
9.62
11.45
 
500-599
6.17
12.64
0.00
600-699
4.50
10.99
0.00
700-799
2.96
8.59
0.00
800-899
2.25
6.87
0.04
900-999
1.42
4.87
0.25
1000-1099
1.12
3.79
.99
1100-1199
0.80
3.26
1.68
1200-1299
0.65
2.60
2.96
1300-1399
0.54
2.02
3.21
1400-1499
0.36
1.56
4.21
1500-1599
0.32
1.33
4.19
1600-1699
0.29
0.97
4.22
1700-1799
0.16
0.85
3.89
1800-1899
0.10
0.72
3.90
1900-1999
0.08
0.50
3.42
2000-2099
0.07
0.40
3.27
2100-2199
0.07
0.29
2.96
2200-2299
0.03
0.35
2.65
2300-2399
0.04
0.13
2.55
2400-2499
0.03
0.20
2.51
2500-2599
0.05
0.14
1.66
2600-2699
0.04
0.10
1.64
2700-2799
0.03
0.14
1.38
2800-2899
0.14
0.17
1.11
2900-2999
0.14
0.09
1.28
Overall fraction
losing bankroll
90.43
81.52
53.97

 

Table III
Percent of Players Who Quit
with Various Wins and Losses
after Hitting 3400-Coin Jackpot or 3000 Rounds
win (W) or
loss (L)
(bets)
% of players
with 100-bet
bankrolls
% of players
with 200-bet
bankrolls
% of players
with 500-bet
bankrolls
400-499 L
 
 
2.38
300-399 L
 
 
2.38
200-299 L
 
 
1.65
100-199 L
 
0.63
1.55
0-99 L
0.41
0.84
2.08
 
 
 
 
0-99 W
0.55
1.25
3.10
100-199 W
0.66
1.70
4.09
200-299 W
0.87
1.51
4.03
300-399 W
0.78
1.23
3.19
400-499 W
0.43
0.95
2.10
500-599 W
0.29
0.64
1.12
600-699 W
0.17
0.36
0.82
700-799 W
0.22
0.51
0.95
800-899W
0.31
0.57
1.16
900-999 W
0.40
0.84
1.68
1000-1099 W
0.61
0.71
1.72
1100-1199 W
0.37
0.85
1.29
1200-1299 W
0.21
0.52
1.17
1300-1399 W
0.19
0.36
1.34
1400-1499 W
0.14
0.22
1.37
1500-1599 W
0.04
0.89
1.17
1600-1699 W
1.06
1.45
1.58
1700-1799 W
0.51
0.51
0.90
1800-1899 W
0.15
0.32
0.59
1900-1999 W
0.22
0.32
0.49
2000-2099 W
0.17
0.16
0.53
2100-2199 W
0.12
0.28
0.24
2200-2299 W
0.10
0.14
0.32
2300-2399 W
0.18
0.20
0.20
2400-2499 W
0.06
0.07
0.22
over 2500 W
0.35
0.45
0.62
overall fraction
with net win
9.16
17.01
35.99
jackpot winners
1.95
3.38
6.88

 

 

 

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.