Calculating the payback percentage

[Simple Sam]

I'm having some trouble calculating the payback percentage on my Bally 1075 from the Reno Hilton.  It's a three reel, three line, 25 cents machine, similar to an 831.  I calculated the payback on the first two lines at 87.8% but the third line is at 105%.  I'm pretty sure that the Hilton wasn't offering games with that high of a payback!


Here's the calculations I used:

	Reel Symbols
	first	second	third
symbol	reel	reel	reel
cherry	3	3	0
orange	7	1	4
plum	4	4	1
bar	3	3	1
watermelon	3	7	5
bell	1	3	10
7	1	1	1
total	22	22	22
			Table of winning combinations
winning		winning	# winning	award
	combination	symbols	combination	total
1 cherry = 3		3x19x22	1254	3762
2 cherry = 5		3x3x22	198	990
	3 orange = 10	7x1x4	28	280
	2 orange bar = 10	7x1x1	7	70
3 plum = 14		4x4x1	16	224
	2 plum bar = 14	4x4x1	16	224
3 bell = 18		1x3x10	30	540
	2 bell bar = 18	1x3x1	3	54
	3 watermelon = 20	3x7x5	105	2100
3 bar = 100		3x3x1	9	900
	3 7 = 200/2000	1x1x1	1	200
	total potential awards		1667	9344
	payback percentage			0.878
					This is a 22 stop game so 22x22x22 = 10,648 combinations And here's the table when I switch the top award to 2,000 coins: Table of winning combinations winning winning # winning award combination symbols combination total 1 cherry = 3 3x19x22 1254 3762 2 cherry = 5 3x3x22 198 990 3 orange = 10 7x1x4 28 280 2 orange bar = 10 7x1x1 7 70 3 plum = 14 4x4x1 16 224 2 plum bar = 14 4x4x1 16 224 3 bell = 18 1x3x10 30 540 2 bell bar = 18 1x3x1 3 54 3 watermelon = 20 3x7x5 105 2100 3 bar = 100 3x3x1 9 900 3 7 = 200/2000 1x1x1 1 2000 total potential awards 1667 11144 payback percentage 1.047 What am I doing wrong?

[Herbie21]

the payback formula for playing three coins, according to me and using your numbers, is:


(((9344*3)+2000-200)/(10648*3))=93,4 %

cheers Herbie

[Herbie21]

((9344 * 3) + 2000 - 200) / (10648*3) = 93.4%

this is better lees two brackets

cheers Herbie

[wolftalk]

wrt what you are doing wrong, it's true the payback percentage for line 3 is 104.7%


the overall percentage of the game over three lines tho is  (.878 + .878 + 1.047) / 3


or looking at it another way, the average 777 win is (2400 / 3).


or the way herbie did it ... all come out to herbies number.

[Simple Sam]

Thanks for the responses!  I get it now.  I had been thinking of each line being an independent game (which is true) but failing to account for the fact that line 3 can't be played independent of lines 1 and 2. 


It might be kind of weird but I like to calculate the odds on each of my games.  By doing so, I found out that my 831 had been changed.  It has a marque stating that there are "1767 ways to win" but when I did the math, I realized that there were only 1,575 winning combinations.  It appears that one of the bars had been removed which changed the payout percentage from about 83% to only 75% for lines 1 and 2. 

[Herbie21]

Hi Sam, sure for me it was an eyeopener that the payout for the same machine could be so different, not only the total percentage but also the 'distribution' of payouts ie lots of small winns or more big wins, making some model versions much more fun to play. I use an excel sheet for the calculations, adding things like:percentage of winning pulls, average pulls for a win, averages wins with a cherry etc see sample of a 1114 attched, cheers Herbie

[Simple Sam]

Hi Sam, sure for me it was an eyeopener that the payout for the same machine could be so different, not only the total percentage but also the 'distribution' of payouts ie lots of small winns or more big wins, making some model versions much more fun to play. I use an excel sheet for the calculations, adding things like:percentage of winning pulls, average pulls for a win, averages wins with a cherry etc see sample of a 1114 attched, cheers Herbie

That's a pretty comprehensive spreadsheet! Mine (shown above, poorly formatted) is not anywhere near as comprehensive.  I especially like how you layout each winning combination as it makes it very clear, particularly the one versus two cherries as well as winning combinations with bars in them.  It's interesting to see the layout for a wins right/wins left machine as I hadn't tried to lay that out on the one machine I have that is a right/left machine.  I may try to do the calculations on my 847 but there are so many winning combinations (17 each side including 6 duplicates).