Some books on gambling illustrated the following as a typical slot machine arrangement:
(%) Cherries 5 7 3 (O) Oranges 4 1 10 (@) Plums 6 1 4 (A) Bells 1 9 1 (C) Melons 2 1 1 (=) Bars 2 1 1
perhaps with payouts like these:
%.. 2 %%. 3 %%% 8 OOO, OO= 10 @@@, @@= 14 AAA, AA= 18 CCC, CC= 100 === 200
This is a more modern arrangement, of the general style favored in the postwar era. Lemons are completely removed from the machine; instead, the melon, a second jackpot symbol, is added. And now even a single cherry on the first reel wins. Note, however, that there were many different payout arrangements used in the postwar era; no one arrangement was nearly universal, as was the case with the prewar era.
Here, a greater effort has been taken to limit the number of times a winning combination occurs. There is only one bell on the first and third reels, so the second reel can savely have nine bells on it, and so there is only one orange, and one plum, on the second reel.
We can note that if every possible combination of the reels occurs exactly once in 8000 plays, then the machine takes in 8000 coins, it will give out the number of coins calculated as follows:
Reel Combinations Value Amount
1 2 3 Paid
5 * 13 * 20 = 1300 * 2 = 2600
5 * 7 * 17 = 595 * 3 = 1785
5 * 7 * 3 = 105 * 8 = 840
4 * 1 * 11 = 44 * 10 = 440
6 * 1 * 5 = 30 * 14 = 420
1 * 9 * 2 = 18 * 18 = 324
2 * 1 * 2 = 4 * 100 = 400
2 * 1 * 1 = 2 * 200 = 400
----
7209
for a profit of 9.8875%.
The following image illustrates some of the ways that slot machines have changed over the years.
In the top row, the first set of payouts shown are those of the first slot machine, as invented by Charles Fey. Note that these symbols, although different from those used on later machines, can be seen as corresponding to them: horseshoes become cherries, the star becomes the lemon, spades become oranges, the diamond becomes the plum, hearts become bells, and the bell becomes the bar.
The second set of payouts illustrates those offered on the earliest slot machines using fruit symbols. All the prizes are doubled, and the feature of allowing a bar on the last reel to complete most three-in-a-row combinations is added.
These early slot machines did not have payouts as large as became common later. The payout schedule shown in the diagram above for the earliest of the slot machines with fruit symbols is:
%%. 2 %%*, %%A 4 OOO, OO= 8 @@@, @@= 12 AAA, AA= 16 === 20
without a jackpot as such. These slot machines had a different arrangement of symbols on the reels from that shown in the example on the previous page, because, with the smaller prizes, the machine could still be profitable, even if the players would win more often.
One such machine had this arrangement of symbols:
(*) Lemons 1 1 3 (%) Cherries 4 4 - (O) Oranges 5 5 6 (@) Plums 3 3 5 (A) Bells 5 5 4 (=) Bars 2 2 2
With the payout scheme above, this machine's payout percentage can be calculated as follows:
Reel Combinations Value Amount
1 2 3 Paid
4 * 4 * 14 = 224 * 2 = 448
4 * 4 * 6 = 96 * 4 = 384
5 * 5 * 8 = 200 * 8 = 1600
3 * 3 * 7 = 63 * 12 = 756
5 * 5 * 6 = 150 * 16 = 2400
2 * 2 * 2 = 8 * 20 = 160
----
5748
for a percentage favoring the house of 28.15%. Although quite high, note that it is less than the 30.175% for the common design with the higher payouts given on the previous page. As well, that design offered 189 combinations paying 10 or more, while this design offers 421 combinations paying 8 or more. If players tend to put small prizes back into the machine, but quit while they are ahead after winning a larger prize, a machine with a low percentage, but which pays out most of the money in small prizes, is still very likely to take the money the player was willing to wager in the end. Of course, this depends on the setting; in some locations, players are likely to wager only one or two coins and move on, and then raw percentage is what matters.
The third set of payouts is that discussed in the example on the page on probability. This was the standard set of payouts for a slot machine; for many years prior to World War II, nearly every slot machine made used those payouts. Three bars paid 20 coins plus the jackpot, depicted here as 100 coins.
The fourth set of payouts is for the Mills Gold Award slot machine. This is one of the first machines to introduce an extra symbol which stood for an additional jackpot. Arbitrarily, the jackpot for three bars is depicted as 50 coins; winning the Gold Award provided either a larger jackpot, or a token redeemable for 100 times the amount wagered on different machines made by Mills with the new symbol.
The version of this machine with a low percentage had the following arrangement of symbols:
(*) Lemons - - 3 (%) Cherries 8 7 - (O) Oranges 3 4 5 (@) Plums 2 4 5 (A) Bells 2 3 4 (=) Bars 3 1 2 (o) Coins 2 1 1
an alternate version replaced two of the cherries, and one bar, on the first reel with lemons.
Given the payouts of
%%. 3 %%*, %%A 5 OOO, OO= 10 @@@, @@= 14 AAA, AA= 18 === 70 ooo 120
we can calculate how many coins this paid out for each 8000 coins put in, on average:
Reel Combinations Value Amount
1 2 3 Paid
8 * 7 * 13 = 728 * 3 = 2184
8 * 7 * 7 = 392 * 5 = 1960
3 * 4 * 7 = 84 * 10 = 840
2 * 4 * 7 = 56 * 14 = 784
2 * 3 * 6 = 36 * 20 = 720
3 * 1 * 2 = 6 * 70 = 420
2 * 1 * 1 = 2 * 120 = 240
----
7148
for a profit of 10.65%.
The second row continues along, showing some more modern arrangements. A single cherry symbol on the first reel could now pay out a prize, but at first cherries were still only found on the first two reels.
The first arrangement shown on the second row shows the payouts of Mills' Melon Bell machine. Here, the new symbol, a half-watermelon, simply replaced the bar, as can be seen from the fact that it can complete three oranges, three plums, and three bells.
The set of payouts in the second arrangement is also for some machines by Mills. These payouts were used both with the 21 Bell slot machine, which was described in detail in John Scarne's Complete Guide to Gambling, whose house percentage was unusually low for a slot machine, being just over 5 percent, and which had a few positions on the three reels where two symbols were present in various combinations, so that any winning combination either symbol might make would pay out, and with the 7-7-7 HiTop machine, where the extra 7 jackpot symbol was in every case overprinted on another symbol so that both would pay out, and no other symbols were combined.
(*) Lemons - - 5 (%) Cherries 3 6 - (O) Oranges 5 4 2 (@) Plums 8 3 3 (A) Bells 1 5 8 (C) Melons 1 1 1 (=) Bars 2 1 1 (7) Sevens 1 1 1
Although it does not affect the odds, the 7 on the first reel was overprinted on a plum, the one on the second reel was overprinted on an orange, and the one on the third reel was overprinted on the bar.
Again, an alternate version of the first reel was available for a less generous payout; it had three lemons on the first reel, replacing two plums (including the one overprinted with a 7) and one of the bars.
Given the payout schedule:
%.. 2 %%. 5 OOO, OO= 10 @@@, @@= 14 AAA, AA= 18 CCC, CC=, === 120 777 200
its percentages can be calculated as follows:
Reel Combinations Value Amount
1 2 3 Paid
5 * 14 * 20 = 1400 * 2 = 2800
5 * 6 * 20 = 600 * 3 = 1800
5 * 4 * 3 = 60 * 10 = 600
8 * 3 * 4 = 96 * 14 = 1344
1 * 5 * 9 = 45 * 18 = 810
1 * 1 * 2 = 2 * 120 = 240
1 * 1 * 1 = 1 * 120 = 120
1 * 1 * 1 = 1 * 200 = 200
----
7914
As this gives an even lower profit of 1.975%, which would seem to be impractical for any slot machine, even in a major casino, I can only conclude that I have misunderstood my sources of information. Cutting the jackpot in size from 100 coins to 50 changes the percentage to 2.95%, still extremely low.
The third arrangement in the bottom half of the illustration is that of the Jennings Sun Chief, a popular model in tropical resorts. The contents of its reels are as follows:
(*) Lemons - - 10 (%) Cherries 1 7 - (O) Oranges 10 1 3 (@) Plums 5 1 5 (A) Bells 1 10 1 (=) Bars 2 1 1
Making lemons fully half of the symbols on the third reel seems something of an uninspired expedient to reduce the amount paid, but the standard measure of making symbols common on one reel, and rare on another, seems to have been pushed to its limits here as well. However, in addition to allowing bars to freely replace cherries on the first two reels, this machine also offered additional payouts for three bars in a row elsewhere than on the payline.
With its payout schedule of:
%.., =.. 3 %%., %=., =%., ==. 5 OOO, OO= 11 @@@, @@= 13 AAA, AA= 18 === 150
we can work out how much it pays (possibly allowing an extra 1200 coins for the additional jackpots):
Reel Combinations Value Amount
1 2 3 Paid
3 * 12 * 20 = 720 * 3 = 2160
3 * 8 * 20 = 480 * 5 = 2400
10 * 1 * 4 = 40 * 11 = 440
5 * 1 * 6 = 30 * 13 = 390
1 * 10 * 2 = 20 * 18 = 360
2 * 1 * 1 = 2 * 150 = 300
----
5610
If we add 1200 coins to cover the extra jackpots this machine provides, we get 6810, for a percentage of 14.875%.
The fourth arrangement shown in the bottom half of the illustration finally shows an example of payouts for a more modern type of machine, on which an award is made for three cherries in a row.
The arrangement of symbols on the reels of this slot machine, also by Jennings, is:
(%) Cherries 3 7 3 (O) Oranges 7 1 10 (@) Plums 6 1 5 (A) Bells 1 10 1 (=) Bars 3 1 1
and the payment schedule it had was the following:
%.. 3 %%. 5 %%% 11 OOO, OO= 11 @@@, @@= 13 AAA, AA= 18 === 150
Once again, we can attempt to calculate this machine's percentage:
Reel Combinations Value Amount
1 2 3 Paid
3 * 13 * 20 = 780 * 3 = 2340
3 * 7 * 17 = 357 * 5 = 1785
3 * 7 * 3 = 63 * 11 = 693
7 * 1 * 11 = 77 * 11 = 847
6 * 1 * 6 = 36 * 13 = 468
1 * 10 * 2 = 20 * 18 = 360
3 * 1 * 1 = 3 * 150 = 450
----
6943
for a percentage of 13,2125%.
Some machines use an upside-down horseshoe (as is favored to retain the good luck) instead of a melon, and Bally has used a target symbol on some of their slot machines as a jackpot symbol. As well, they made an early slot machine, the Bally Double Bell, where three lemons paid out 6 coins; also, the Jennings Sweepstake Chief used the pear as a fruit that ranked below the orange; here, three pears paid 5 coins.
More recently, slot machines had been designed to have 22, 23, or 25 positions per reel, and currently electronic machines are used in casinos that simulate a slot machine with perhaps 128 positions on each reel.
An unusual slot machine, called the Multi-Bell Seven Way, was devised by Adolph Caille after he had sold the Caille Brothers slot machine business, and so he started a new company, A. C. Novelty, to produce and sell it. (Eventually, the company was renamed to A. C. Manufacturing during the 1950s.)
It had twelve different kinds of symbols; the seven which could form a jackpot combination, and on which the player could wager: Strawberries, Bells, Lemons, Bars, Plums, Apples, and Oranges, and five others: Cherries, Pears, Apricots, Grapes, and Pineapples, which only appeared on the second and third reels.
The player could choose which one of the first seven symbols to wager on, and would win a prize if that symbol came up on the first reel. The amount of the prize was indicated on the last reel; it might be anything from twice to 20 times the amount wagered. If three of the same symbol came up, regardless of which symbol was chosen by the player, he would win a jackpot.
The payout odds were given on the third reel along with the third symbol; those odds appear not to have been the same for every occurrence of the same symbol.
I do not yet know the arrangement of the symbols on its reel strips, but they were likely similar to that shown in the diagram to the right, some segments of which were inferred from various photographs of the machine.
The first reel had the seven main symbols in a fixed sequence. I will assume that the reels each contained 21 symbols, to be close in size to those of conventional slot machines, so the sequence would occur three times over.
So that jackpots do not occur too often, I am assuming each of the seven possible jackpots can be made in only six ways, for a total of 42 possible jackpots out of 9261 spins. So, in the diagram to the right, I show the second reel containing two strawberries, two oranges, two lemons, and two bars, but only one each of the three other main symbols, apples, plums, and bells. The third reel, on the other hand, has two apples, two plums, and two bells, but only one of each of the other symbols.
On the first reel, each of the seven main symbols is overprinted with the number of the coin slot used to bet on it.
On the third reel, each fruit symbol is overprinted with the ordinary payout the player receives if his symbol comes up. The payouts shown average to less than 7, so some money is left for the jackpots.
Thus, out of 9,261 combinations, the odds for the reel strips shown are:
3 * 21 * 7 * 2 = 882
3 * 21 * 4 * 3 = 756
3 * 21 * 5 * 4 = 1260
3 * 21 * 2 * 5 = 630
3 * 21 * 2 * 10 = 1260
3 * 21 * 1 * 20 = 1260
----
6048
which does not leave enough for the 42 possible jackpots to pay 100 coins each, but if they paid 50 coins, 6048 + 2100 = 8148, which would give the machine a payout percentage of just under 87.98%; reasonable but still profitable.
While it is somewhat inelegant to have five kinds of fruit symbol that are not part of a jackpot combination, the fact that every symbol that appears on the first reel is one the player can bet on, and every symbol that appears on the last reel has a prize amount associated with it, more thoroughly reassures the player that he must have at least some chance of winning, an important consideration in the past when many slot machines were being operated illegally, and hence without oversight.
It might be possible to take the principle of this machine, and apply it to a slot machine of a more conventional type. The third reel might bear the symbols upon which a player could wager, and if that symbol came up, it would complete any combination which the first two reels might make. And, just as a normal slot machine allows one to win with a cherry on the first reel, in the absence of a pair of matching symbols on the first two reels, there would be a small fixed payout, perhaps 3 coins.