why actual RTP is lower by using scatter?
March 18th, 2024 at 12:58:29 AM
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Hi, I'm facing some problems with the scatter method. the actual RTP is lower than the theoretical RTP.
here is some background info.
3 x 3 slot games. each reel has one Scatter symbol, a total of 32 stops for each reel. I'm giving some free spins that are triggered by different scatter combinations.
3 scatters: each reel has one scatter, it can be anywhere on the reel. so it will (1*3) * (1 *3) * (1*3) =27 events.
left 2 scatters: only left 2 reels' scatter, it will (1*3) * (1 *3) * (32 - 1*3)= 261 events.
total events: 32*32*32= 32768
3 scatters can trigger 25 free spins: the probability = 27 / 32768 = 0.08240%. expected free spins= 0.08240% * 25 = 0.02059936523
left 2 scatters can trigger 5 free spins: the probability = 261 / 32768 = 0.79651%. expected free spins = 0.79651% *5 =0.03982543945
total expected free spins: = (0.02059936523 + 0.03982543945 )/ (1-0.02059936523 -0.03982543945) = 0.06431077043
the free spins game is the same as the base game, the base game RTP is 91.29%.
the RTP with free spins is 97.17% = 91.29% + 91.29% * 0.06431077043
now after 1,000,000 time simulations @ 1 payline or 5 paylines. the actual RTP is only at around 95.6%. lower than 97.17%
can anyone tell why so?
here is some background info.
3 x 3 slot games. each reel has one Scatter symbol, a total of 32 stops for each reel. I'm giving some free spins that are triggered by different scatter combinations.
3 scatters: each reel has one scatter, it can be anywhere on the reel. so it will (1*3) * (1 *3) * (1*3) =27 events.
left 2 scatters: only left 2 reels' scatter, it will (1*3) * (1 *3) * (32 - 1*3)= 261 events.
total events: 32*32*32= 32768
3 scatters can trigger 25 free spins: the probability = 27 / 32768 = 0.08240%. expected free spins= 0.08240% * 25 = 0.02059936523
left 2 scatters can trigger 5 free spins: the probability = 261 / 32768 = 0.79651%. expected free spins = 0.79651% *5 =0.03982543945
total expected free spins: = (0.02059936523 + 0.03982543945 )/ (1-0.02059936523 -0.03982543945) = 0.06431077043
the free spins game is the same as the base game, the base game RTP is 91.29%.
the RTP with free spins is 97.17% = 91.29% + 91.29% * 0.06431077043
now after 1,000,000 time simulations @ 1 payline or 5 paylines. the actual RTP is only at around 95.6%. lower than 97.17%
can anyone tell why so?
March 18th, 2024 at 1:02:41 AM
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Please stop making duplicate threads.
May the cards fall in your favor.
March 18th, 2024 at 5:45:40 AM
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You have not mentioned whether free spins can retrigger more free spins.
You do not specify the variance for your game. If your game has a variance of 100 bets^2, then the standard deviation divided by coin in is sqrt(1,000,000*100)/1,000,000 = 1% for your simulation. You could easily get your result by being 1.5 SD below the true value. You should be able to run trillions of MC simulations for such a simple game. For a simple game with only 32,768 outcomes, it should be easy for you to enumerate all the possible outcomes in a spreadsheet or computer program.
You do not specify the variance for your game. If your game has a variance of 100 bets^2, then the standard deviation divided by coin in is sqrt(1,000,000*100)/1,000,000 = 1% for your simulation. You could easily get your result by being 1.5 SD below the true value. You should be able to run trillions of MC simulations for such a simple game. For a simple game with only 32,768 outcomes, it should be easy for you to enumerate all the possible outcomes in a spreadsheet or computer program.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
March 19th, 2024 at 7:13:24 PM
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Hi, yes, it is infinite free spins, free spin can re-trigger free spins
RTP(with infinite free spins): 97.17%
base game RTP: 91.29%
Variance: 38.39772674
Std. Div.: 6.196589928
Confidence Interval: 90.00%
Volatility Index: 10.19339043
Hit Frequency: 50.78%
based on the above info. theoretical RTP outcome range is
(number of free spins) 1,000,000 96.15%(min) - 98.18%(max)
(number of free spins) 10,000,000 96.84%(min) - 97.49%(max)
I only did 1,000,000 spins simulation, the actual RTP only around 95.6%, it is out of the theoretical range
test data:
1st round, 5 line, spins 1000000
total payout/total stake = 4772457.95/5000000
total free-spin payout = 222292.90
RTP 95.45
2nd round,
total payout/total stake = 4784066.65/5000000
total free-spin payout = 212657.55
RTP 95.68
3rd round,
total payout/total stake = 4785460.25/5000000
total free-spin payout = 218577.75
RTP 95.71
RTP(with infinite free spins): 97.17%
base game RTP: 91.29%
Variance: 38.39772674
Std. Div.: 6.196589928
Confidence Interval: 90.00%
Volatility Index: 10.19339043
Hit Frequency: 50.78%
based on the above info. theoretical RTP outcome range is
(number of free spins) 1,000,000 96.15%(min) - 98.18%(max)
(number of free spins) 10,000,000 96.84%(min) - 97.49%(max)
I only did 1,000,000 spins simulation, the actual RTP only around 95.6%, it is out of the theoretical range
test data:
1st round, 5 line, spins 1000000
total payout/total stake = 4772457.95/5000000
total free-spin payout = 222292.90
RTP 95.45
2nd round,
total payout/total stake = 4784066.65/5000000
total free-spin payout = 212657.55
RTP 95.68
3rd round,
total payout/total stake = 4785460.25/5000000
total free-spin payout = 218577.75
RTP 95.71
Quote: MentalYou have not mentioned whether free spins can retrigger more free spins.
You do not specify the variance for your game. If your game has a variance of 100 bets^2, then the standard deviation divided by coin in is sqrt(1,000,000*100)/1,000,000 = 1% for your simulation. You could easily get your result by being 1.5 SD below the true value. You should be able to run trillions of MC simulations for such a simple game. For a simple game with only 32,768 outcomes, it should be easy for you to enumerate all the possible outcomes in a spreadsheet or computer program.
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