Last update: September 19, 2001

GAM 470

Slot Machine Notes

Wizard’s single-line fruit Slot

Paytable

Center Payline	Pays
Three bars	5000
Three cherries	1000
Three plums	200
Three watermelons	100
Three oranges	50
Three lemons	25
Any two cherries	10
Any one cherry	2

Physical Reel Strip, with weights

Symbol	Reel 1	Reel 2	Reel 3
Cherry	3	2	1
Blank	2	3	3
Plum	3	2	2
Blank	2	3	3
Watermelon	3	3	2
Blank	2	3	3
Orange	4	3	3
Blank	2	3	3
Lemon	4	3	3
Blank	5	5	8
Bar	4	3	1
Blank	5	5	7
Cherry	2	2	1
Blank	2	3	3
Plum	3	2	1
Blank	2	3	3
Watermelon	3	2	2
Blank	2	3	3
Orange	3	2	3
Blank	2	3	3
Lemon	4	3	3
Blank	2	3	3
Total	64	64	64

Number/Reel

Symbol	Reel 1	Reel 2	Reel 3
Bar	4	3	1
Cherry	5	4	2
Plum	6	4	3
Watermelon	6	5	4
Orange	7	5	6
Lemon	8	6	6
Blank	28	37	42
Total	64	64	64

The next table shows the number of combinations of each paying combination and the contribution to the total return (combinations * win).

Center Payline	Pays	Formula	Combinations	Return
Three bars	5000	431	12	60000
Three cherries	1000	542	40	40000
Three plums	200	643	72	14400
Three watermelons	100	654	120	12000
Three oranges	50	756	210	10500
Three lemons	25	866	288	7200
Any two cherries	10	54(64-2)+5(64-4)2+(64-5)42	2312	23120
Any one cherry	2	5(64-4)(64-2)+(64-5)4(64-2)+(64-5)(64-4)2	40312	80624
Total			43366	247844

The lower row shows the total combinations is 43,366. The total possible combinations (including losing plays) is 64*64*64 = 262,144. So the hit frequency (ratio of wins to plays) is 43,366/262,144 = 16.54%.

The lower row also shows the total return to the player over all possible combinations is 274,844. The expected return of the game is the total return over all possible combinations divided by the total number of combinations. In this case 247,844/262,144 = 94.54%.

Mills Five Cent Bell

This is an early slot machine made by the Mills company. The design is found in Scarne's New Complete Guide to Gambling, Simon and Schuster, 1974, p. 445. A working model of this game can be found at www.wizardofodds.com/play/slot-21bell/.

Following is the pay table.

Win	Pays
7, 7, 7	200
bar, bar, bar	100
melon, melon, melon	100
melon, melon, bar	100
bell, bell, bell	18
bell, bell, bar	18
plum, plum, plum	14
plum, plum, bar	14
orange, orange, orange	10
orange, orange, bar	10
cherry, cherry, any	5
cherry, any, any	2

Next are the reel strips.

Stop	Reel 1	Reel 2	Reel 3
1	orange	cherry	bell
2	melon	plum	orange
3	plum	cherry	plum
4	cherry	7 and orange	bell
5	plum	cherry	orange
6	orange	bell	lemon
7	7	plum and bar	bell
8	bell and bar	bell	melon and orange
9	orange	cherry	bell
10	cherry	orange	plum
11	bar	bell	lemon
12	plum	melon and orange	bell
13	orange	plum	plum
14	plum	bell	bell
15	melon	cherry	7 and bar
16	plum	bar	lemon
17	orange	orange	bell
18	plum	cherry	melon and orange
19	bar	bell	bell
20	plum	melon and orange	lemon

The next table shows how often each symbol appears on each reel.

Symbol	Reel 1	Reel 2	Reel 3
7	1	1	1
Bar	3	2	1
Melon	2	2	2
Bell	1	5	8
Plum	7	3	3
Orange	5	5	4
Cherry	2	6	0
Lemon	0	0	4

The next table shows the number of combinations of each win over all 20³=8000 possible. The return combinations are the product of the probability combinations and what the win pays.

Win	Pays	Probability Expression	Probability Combinations	Return Combinations
7, 7, 7	200	111	1	200
bar, bar, bar	100	321	6	600
melon, melon, melon	100	222	8	800
melon, melon, bar	100	221	4	400
bell, bell, bell	18	158	40	720
bell, bell, bar	18	151	5	90
plum, plum, plum	14	733	63	882
plum, plum, bar	14	731	21	294
orange, orange, orange	10	554	100	1000
orange, orange, bar	10	551	25	250
cherry, cherry, any	5	2620	240	1200
cherry, any, any	2	2(20-6)20	560	1120
Total		202020	1073	7556

The hit frequency is 1073/8000 = 13.41%. The expected return is 7556/8000 = 94.45%.