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Best of Alan Krigman

Gaming Guru

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What's Your Shot at the Slots?

5 May 1997

What are your chances at the slot machines? As is often the case in gambling, this is far simpler to ask than answer.

For starters, slots that look, sound, smell, and feel alike can be set up differently. So, what applies to one may not hold for the next. Compounding the confusion, the question doesn't have the same meaning to everybody. One player may want to know the chances of any size win on any particular try, another may be interested in the odds of earning a profit during a certain length session, someone else may care only about the probability of hitting the jackpot, and a bettor who's too shrewd by a half may be asking for the "house advantage."

Ambiguity also results because three parameters, which a manufacturer can specify independently, combine to define each machine.
o Payback percentage: the portion of the "handle" - all money bet - returned to players, averaged over a long interval.
o Hit frequency: the fraction of individual tries, averaged over an extended period, in which something is paid out.
o Payout schedule: the tally of probabilities and associated amounts returned for each winning combination.

The accompanying table characterizes a particular two-coin three- reel progressive-jackpot machine. The figures show the odds and payouts for one coin, two coins at the starting jackpots, and two coins with the progressive bank at the "full-pay" level where players have a theoretical edge in the game. All relevant statistical properties can be derived from the data shown.

The payback percentage with one coin in play is 76 percent of the money bet. With two coins and the progressive meters at the base or "reset" values of 500 and 1000, payback rises to 85 percent. When two coins are played and the progressive jackpots are 1700 and 3400, the machine offers players 101.6 percent of the handle.

The hit frequency is 14.2 percent, regardless of coins in play or jackpot size. Players can therefore expect 142 returns of one size or another every 1,000 tries. Expressed in an alternate way, the odds against receiving a payout on any round are 6-to-1.


More important to most solid citizens are the chances of picking up either of the top two prizes. The odds against hitting on any try are shown directly in the table. They're 4,680-to-1 for the lower jackpot and 32,767-to-1 for the higher. The odds against a big score at least once during a session improve with extent of play. In 100 tries, they are approximately 46-to-1 and 325-to-1, respectively. In 1,000 rounds, the odds drop to about 4.5-to-1 and 32-to-1. And in 5,000 bids, they become better than 1-to-1 for the smaller jackpot and around 6-to-1 for the larger.

There's no magic in raising the odds of hitting a jackpot by playing longer. The catch is the correspondingly steeper odds against breaking even or making a profit without such a stroke of luck. For instance, in 20 tries, players have about 40 percent probability of being out of the soup on this machine if they don't hit a jackpot. In 100 rounds, prospects are roughly 30 percent. After 1,000 non-bell-ringing plays, the likelihood of being ahead is only 4 percent. And after 5,000 pulls, the chance is essentially nil - and half of all players who haven't made either of the top two scores will be over 1,100 bets down.

The songster of the slots, Sumner A Ingmark, summarized this situation splendidly when he said:


It's jackpot wins for which we strive,
Secure them early then we thrive,
Or hit them late just to survive.

TABLE: Odds and corresponding payouts
for a representative 3-reel 2-coin
progressive jackpot slot machine
Odds
against
winning
1-coin
payout
2-coin
payout
with
base
progressive
2-coin
payout
with
full-pay
progressive
12-to1
2
4
4
20-to-1
5
10
10
57-to-1
10
25
25
330-to-1
50
125
125
4,680-to-1
200
500
1700
32,767 - to -1
400
1000
3400

 

 

 

 

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.