Personal slot RTP and meaningful sample size
July 27th, 2026 at 10:53:36 AM
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I have been looking at exported slot histories and grouping the results by game. Over shorter periods the personal RTP can sit far above or below the published RTP, which is expected, but it raises a practical question: is there any rough number of spins or total wager at which comparing a player's result with the theoretical RTP becomes statistically meaningful? Also, should bonus buys be separated from regular spins when making that comparison, since their cost and payout structure are different?
July 27th, 2026 at 12:36:15 PM
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I'd say somewhere between 10,000 and 100,000 spins you might be getting an estimation of your RTP. But 100 spins may just wind up being 50% RTP without the Bonus rounds.
July 27th, 2026 at 2:01:19 PM
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Usually you need at least 10,000,000 sims to get within 0.1% of the true RTP. Depends on the volatility of the machine.
Maybe a few hundred thousand could get you within 1%.
Maybe a few hundred thousand could get you within 1%.
July 27th, 2026 at 2:11:52 PM
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The answer depends on the variance of the game in question. Here are my quick estimates:
You need 9,604 coin flips getting paid 1:1 to be 95% confident that your result is within 1% of the expected breakeven outcome.
If you are rolling one die and getting 5:1 for a 6, you need 341,880 rolls to get within 1%.
If you are rolling two dice and getting paid 35:1 for boxcars, you need 1,344,560 rolls to get within 1%.
The variance of most slots is around 40, which is a bit higher than the 35:1 boxcars example. Some volatile slots have a variance of 60, 80, 100, or even more. There are a few lower-variance slots out in the wild, but you need many millions of spins on a typical slot to get an estimate of RTP to within a fraction of a percent. Testing labs can do many millions of spins. It is not easy to do it in real online casino play.
I did 470K spins on one particular slot over the course of 20 days in June and had an actual RTP slightly more than 1% above expectation. This was about 3K spins per hour, so almost 160 hours of play.
You need 9,604 coin flips getting paid 1:1 to be 95% confident that your result is within 1% of the expected breakeven outcome.
If you are rolling one die and getting 5:1 for a 6, you need 341,880 rolls to get within 1%.
If you are rolling two dice and getting paid 35:1 for boxcars, you need 1,344,560 rolls to get within 1%.
The variance of most slots is around 40, which is a bit higher than the 35:1 boxcars example. Some volatile slots have a variance of 60, 80, 100, or even more. There are a few lower-variance slots out in the wild, but you need many millions of spins on a typical slot to get an estimate of RTP to within a fraction of a percent. Testing labs can do many millions of spins. It is not easy to do it in real online casino play.
I did 470K spins on one particular slot over the course of 20 days in June and had an actual RTP slightly more than 1% above expectation. This was about 3K spins per hour, so almost 160 hours of play.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
July 27th, 2026 at 2:21:11 PM
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Quote: harrisUsually you need at least 10,000,000 sims to get within 0.1% of the true RTP. Depends on the volatility of the machine.
Maybe a few hundred thousand could get you within 1%.
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I agree with your estimates. It is really pointless for civilians to try and verify the RTP for each game they play. It is more useful to evaluate your W/L after a year or more and see if your actual RTP is consistent with the weighted RTPs of the games you play. I am thrilled by my actual realized RTP, but then I play a lot of very high RTP games.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
July 27th, 2026 at 3:22:06 PM
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Quote: harrisUsually you need at least 10,000,000 sims to get within 0.1% of the true RTP. Depends on the volatility of the machine.
Maybe a few hundred thousand could get you within 1%.
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I think you really need to take into consideration the frequency of the large jackpots. A game like Megabucks the jackpot symbols will only align between 25 million and 50 million spins. It was so much easier before the Telnaes patent.
You can't know everything, but you can know anything.
July 27th, 2026 at 4:04:48 PM
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Quote: HouseKnowsAlso, should bonus buys be separated from regular spins when making that comparison, since their cost and payout structure are different?
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Based on my extremely small sample size, I have no reason to think that buying a bonus substantially alters the RTP.
May the cards fall in your favor.
July 27th, 2026 at 4:19:08 PM
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There are a number of games where the RTP for bonus buys is significantly different from the base game (a 1.3% or more increase in RTP). I also know of several that have the same RTP to four significant figures (White Rabbit).
The variance is always much lower than the base game, but the absolute volatility (std. dev.) is always much higher due to the higher bet.
The variance is always much lower than the base game, but the absolute volatility (std. dev.) is always much higher due to the higher bet.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
July 27th, 2026 at 4:27:00 PM
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Quote: DRichQuote: harrisUsually you need at least 10,000,000 sims to get within 0.1% of the true RTP. Depends on the volatility of the machine.
Maybe a few hundred thousand could get you within 1%.
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I think you really need to take into consideration the frequency of the large jackpots. A game like Megabucks the jackpot symbols will only align between 25 million and 50 million spins. It was so much easier before the Telnaes patent.
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The OP is clearly about online slots (unless you know how to export slot game histories for B&M slots). Only a few percent of online slots have a mega jackpot feature. Most of those jackpot slots have a low meter contribution rate and are not among the highest volatility slots.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
July 27th, 2026 at 4:33:55 PM
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Quote: MentalThere are a number of games where the RTP for bonus buys is significantly different from the base game (a 1.3% or more increase in RTP). I also know of several that have the same RTP to four significant figures (White Rabbit).
The variance is always much lower than the base game, but the absolute volatility (std. dev.) is always much higher due to the higher bet.
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I can believe that we are both right, for a number of reasons that do and do not overlap.
Do you think it is safe to assume the expected return of a buy a bonus is still less than the price of the buy a bonus?
May the cards fall in your favor.
July 27th, 2026 at 5:15:06 PM
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Since every buy-a-bonus game is well under 100% RTP, that is true by the definition of RTP.Quote: DieterQuote: MentalThere are a number of games where the RTP for bonus buys is significantly different from the base game (a 1.3% or more increase in RTP). I also know of several that have the same RTP to four significant figures (White Rabbit).
The variance is always much lower than the base game, but the absolute volatility (std. dev.) is always much higher due to the higher bet.
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I can believe that we are both right, for a number of reasons that do and do not overlap.
Do you think it is safe to assume the expected return of a buy a bonus is still less than the price of the buy a bonus?
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Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
July 27th, 2026 at 6:40:59 PM
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Many states have a law that BAB RTP has to be 0.5%+ higher
July 27th, 2026 at 8:50:00 PM
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I see a lot of YouTube slot players trying their luck with 20 pulls per denom. Some have luck, some don't. My latest two tries with a $10 free play with 50 cent spins is about a 10%-20% RTP. I win a buck or two back which gives an extra 2-4 free spins.
July 28th, 2026 at 2:03:27 AM
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Quote: harrisMany states have a law that BAB RTP has to be 0.5%+ higher
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Can you give a citation?
May the cards fall in your favor.
July 28th, 2026 at 8:10:06 AM
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Quote: DieterQuote: harrisMany states have a law that BAB RTP has to be 0.5%+ higher
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Can you give a citation?
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Uhhh...
Sorry, I can't, but I was told this was a legal requirement at work, when I started developing Buy-A-Bonus rounds on slot machines. So it is a rule... somewhere.
July 28th, 2026 at 10:02:05 AM
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With 1 million spins (at the same bet), the RTP spread can be +/- 3%
July 28th, 2026 at 10:28:51 AM
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So that means if it's set at 93%, it would wind up between 90% and 96%. You'll be down $200K to $500K with a million $5 spins. I don't know how many Grand JP's behind that would be but it'd be more than dozens at $10K to $18.8K per Grand JP.
I expect these slot YouTubers are not winning on slots unless they hit the million Grand recently. If they are betting $2,500 per spin for 50,000 spins, that's a total of $125 million bet and a 96% RTP would mean a loss of $5 million. They are already behind. If they had a RTP of 102%, they'd be up $2.5 million. Imagine having over $100 million in W-2G's and you have to document 90% of your losses. Whatever you won is going to be eaten alive by taxes.
I expect these slot YouTubers are not winning on slots unless they hit the million Grand recently. If they are betting $2,500 per spin for 50,000 spins, that's a total of $125 million bet and a 96% RTP would mean a loss of $5 million. They are already behind. If they had a RTP of 102%, they'd be up $2.5 million. Imagine having over $100 million in W-2G's and you have to document 90% of your losses. Whatever you won is going to be eaten alive by taxes.
Last edited by: ChumpChange on Jul 28, 2026
July 28th, 2026 at 10:53:07 AM
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Quote: DobrijWith 1 million spins (at the same bet), the RTP spread can be +/- 3%
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The standard deviation for a slot with variance of 40 will be +/- 0.63%. It is possible to have results +/- 3%, but only if you are talking about a slot with unusually high variance or counting extremely improbable sessions at +/- 5 SD from the mean.
The standard deviation is the square root of the total variance =sqrt{40 * 1,000,000} approx = 6,325 units
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
July 29th, 2026 at 7:52:14 AM
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To answer both of your questions:
Sample Size: You need a minimum of 100,000+ spins on a single game to get anywhere near a statistically meaningful confidence interval. Anything under 10,000 spins is just short-term noise and standard deviation.
Bonus Buys: You should 100% separate bonus buys from base game spins. Feature buys alter both the volatility profile and often carry a slightly different published RTP rating than standard spins.
Sample Size: You need a minimum of 100,000+ spins on a single game to get anywhere near a statistically meaningful confidence interval. Anything under 10,000 spins is just short-term noise and standard deviation.
Bonus Buys: You should 100% separate bonus buys from base game spins. Feature buys alter both the volatility profile and often carry a slightly different published RTP rating than standard spins.
July 29th, 2026 at 4:16:39 PM
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Quote: MentalQuote: DobrijWith 1 million spins (at the same bet), the RTP spread can be +/- 3%
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The standard deviation for a slot with variance of 40 will be +/- 0.63%. It is possible to have results +/- 3%, but only if you are talking about a slot with unusually high variance or counting extremely improbable sessions at +/- 5 SD from the mean.
The standard deviation is the square root of the total variance =sqrt{40 * 1,000,000} approx = 6,325 units
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Choosing the right SD value for slot games is difficult. I prefer to use simulation results, although they are only suitable for each game individually.
Probably, to answer more precisely, need to have a specific table of probabilities of combinations for a specific slot.
July 29th, 2026 at 5:12:02 PM
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Quote: DobrijQuote: MentalQuote: DobrijWith 1 million spins (at the same bet), the RTP spread can be +/- 3%
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The standard deviation for a slot with variance of 40 will be +/- 0.63%. It is possible to have results +/- 3%, but only if you are talking about a slot with unusually high variance or counting extremely improbable sessions at +/- 5 SD from the mean.
The standard deviation is the square root of the total variance =sqrt{40 * 1,000,000} approx = 6,325 units
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Choosing the right SD value for slot games is difficult. I prefer to use simulation results, although they are only suitable for each game individually.
Probably, to answer more precisely, need to have a specific table of probabilities of combinations for a specific slot.
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And I have stored 6.4M lines of data about my slot transactions and I have written programs to extract the variance for individual games or classes of closely related games. If you have 100K results from a slot game, you don't need to do simulations. You can just calculate the variance of the set of results (where the win and bet amounts are normalized to a unit bet)
You may not consider DK Digits to be a slot game, but it is listed by DK as a slot game and the user can choose the odds for each game, which means they can select the variance over an extremely wide range. The variance at the minimum setting is 0.0294 units². The variance at the maximum setting is 96.04 units². The number of spins needed to verify the RTP to 1% or 0.1% varies tremendously for this single game. Anyone giving a number of trials needed without specifying the variance of the game is just pulling numbers out of their nether regions. In general, you can only get the variance of a slot game by gathering data.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
July 30th, 2026 at 11:59:36 PM
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Quote: harrisQuote: DieterQuote: harrisMany states have a law that BAB RTP has to be 0.5%+ higher
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Can you give a citation?
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Uhhh...
Sorry, I can't, but I was told this was a legal requirement at work, when I started developing Buy-A-Bonus rounds on slot machines. So it is a rule... somewhere.
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I asked at work and they said it's not actually a law, but it's something really common for reasons that are beyond my current understanding. I imagine that casinos want the BABs to have a higher RTP to encourage people to spend money more quickly (Depends how quickly you spin and depends on the nature of the BAB round, but I imagine that BABs take more money per hour for casinos than normal spins).
Extremely rare instance where I was incorrect about something ;) Fortunately I get paid for being a mathematician not a legal expert
July 31st, 2026 at 6:01:31 AM
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Quote: ChumpChangeSo that means if it's set at 93%, it would wind up between 90% and 96%. You'll be down $200K to $500K with a million $5 spins. I don't know how many Grand JP's behind that would be but it'd be more than dozens at $10K to $18.8K per Grand JP.
I expect these slot YouTubers are not winning on slots unless they hit the million Grand recently. If they are betting $2,500 per spin for 50,000 spins, that's a total of $125 million bet and a 96% RTP would mean a loss of $5 million. They are already behind. If they had a RTP of 102%, they'd be up $2.5 million. Imagine having over $100 million in W-2G's and you have to document 90% of your losses. Whatever you won is going to be eaten alive by taxes.
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The range is found using RTP +/- little sigma * z critical/sqrt(n), which means it is dependent on the underlying statistical distribution of the game, the chosen "confidence interval," and number of plays.
The resulting plot of averages is normalish (central limit theorem), but all plots are not not equally kurtosed. In normal play lengths, the results are highly skewed and kurtosed.
Singh et al sort of discuss it in this paper, but they only did 4000 trials.
https://oasis.library.unlv.edu/grrj/vol17/iss2/4/
