about expectation value to get winning on slot
June 23rd, 2018 at 8:45:13 AM
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Hi all,
I saw a funny game weeks ago (forget what is the name of the game) but it is a 1024 ways game. Upon each spin, no matter if you win or lose, you get a chance to respin one of the reel by pay extra cost. Of course, as player, I will only do that in a losing spin and see the potential of winning with respin. I am wondering how do they calculate the extra cost for respinning a reel so the casino won't lose money. I am trying to do the math by making a simple assumption: only allow player to respin the 1st reel. To figure out what extra cost is appropriate, I calculate the expectation value of all potential winning from the current last 4 reels symbols and all possible symbol from the first reel, i.e. looping the 1st reel, compose a new screen along with last 4 reels symbols, estimate the winning and record the probability of getting that winning. Mathematically, we could compute the expectation of win. And so I use this expectation of win as the extra cost of 1st reel respin.
To simulate that, I repeat the same procedure.
1) randomize the reel stops to get a new screen, if win, no extra respin
2) if lost, compute the EV, player pay the extra cost (=EV) and respin the 1st reel
Without the respin feature, the payback of this game is about 51.5%, but with the respin feature, assuming player only pay the extra cost for respin during losing game, the payback increased to 57.5%. I am curious why with respin feature will decrease the house edge. I know someone said it is just 6% different but for casino, even 1% is huge in revenue. I would like to know how to even that out with extra cost of repin, if EV is not what I should use as the cost, any other idea? Thanks.
I saw a funny game weeks ago (forget what is the name of the game) but it is a 1024 ways game. Upon each spin, no matter if you win or lose, you get a chance to respin one of the reel by pay extra cost. Of course, as player, I will only do that in a losing spin and see the potential of winning with respin. I am wondering how do they calculate the extra cost for respinning a reel so the casino won't lose money. I am trying to do the math by making a simple assumption: only allow player to respin the 1st reel. To figure out what extra cost is appropriate, I calculate the expectation value of all potential winning from the current last 4 reels symbols and all possible symbol from the first reel, i.e. looping the 1st reel, compose a new screen along with last 4 reels symbols, estimate the winning and record the probability of getting that winning. Mathematically, we could compute the expectation of win. And so I use this expectation of win as the extra cost of 1st reel respin.
To simulate that, I repeat the same procedure.
1) randomize the reel stops to get a new screen, if win, no extra respin
2) if lost, compute the EV, player pay the extra cost (=EV) and respin the 1st reel
Without the respin feature, the payback of this game is about 51.5%, but with the respin feature, assuming player only pay the extra cost for respin during losing game, the payback increased to 57.5%. I am curious why with respin feature will decrease the house edge. I know someone said it is just 6% different but for casino, even 1% is huge in revenue. I would like to know how to even that out with extra cost of repin, if EV is not what I should use as the cost, any other idea? Thanks.
Last edited by: konglify on Jun 23, 2018
June 23rd, 2018 at 10:19:15 AM
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I don't know about your algorithm but your post sure gave me a pain in my algorithm. I didn't understand a word of it which, given my utter lack of math skills, is understandable but wading thru all those calculations for a 0.6 percent change in the edge would be negated by just one tip to the cocktail waitress.Quote: konglifyI am more interesting in what's wrong with my algorithm. Thanks.
