5 ms·

A process with a particular expected value can still be random.

kelnos 3y ago
I think in this case it's not a legally mandated expected value, but a legally mandated payout rate. As in, it actually must pay out a percentage of what's taken in, over a certain time period. I don't think a fully random process can guarantee that.
- masklinn 3y ago
  Of course it can. Unless you start playing word games to manipulate what “fully random” means. You can set the odds of a fully random process, just take an rng returning a uniform distribution between 1 and 100 and set the bar at whichever threshold you want, or do the same with dice, the odds of any given face is 1/faces, so get however many faced dice you need then set the faces (or a threshold again for numbered faces) e.g. on a 20-faced dice you set the threshold at 3+ and you’ve got a 90% payout rate.
  - vl 3y ago
    This is obviously incorrect: Let’s say they have to pay on each 500-play window, on true random, operator can end up with all 500 plays as non-paying and break the law. This is why they are programmed to increase payout odds if there was no payout for long time, and this is why some players wait for such machines. (In modern casinos machines are pooled, so it’s actually more complicated)
    - alexb_ 3y ago
      An operator ending up with all 500 plays as non paying is not breaking the law, they are just incredibly unlucky. The spins are independent, and no amount of waiting for a machine to be "due" is going to do anything.
  - kelnos 3y ago
    That's not how randomness works. In your example, there is no guarantee that 90% of rolls will be a 3 or above. Statistically, over the long term, that will be the case, but I wouldn't expect the payout laws to be written in such a way that "eventually" you'll "probabilistically" hit your payout targets. More likely it's something like "you must pay out X over time period Y". You can't 100% guarantee that with a random process. It's possible (and not even all that unlikely) that, over the span of a day (week, month, whatever), you'd end up with only 89.9% of rolls being a 3 or above, and that would violate the payout laws.
    - silasdavis 3y ago
      I think there's a few missing pieces of information (in this discussion, probably could be looked up by some intrepid soul) Firstly what is the payout rate against, I could imagine it being: - Plays - Time - Stake Secondly, how is compliance defined: - Convergence in expected value - Degree of breach of threshold On the second one, it's kind of interesting if the degree of breach is 'never breach threshold', because when a machine is 'first turned on' the first play must always be a win (crudely speaking), if the second play has a sufficiently large stake (such that a loss would break the payout rate threshold) then that probably has to be a win too, etc until people can't keep exponentially raising the stages... This is a boot-strapping problem really but still. If compliance is in expected value then I think any of the rates can be made to work For a rate in terms of plays or stake then you can just have a binomial variable with some probability. In this case each player/play would be exposed to the same probability; each play would be independent. For a rate in terms of time the plays would not be independent because the duration of previous plays and payout would affect what payout with subsequent plays would be, so you would need a dynamic adjustment of odds over the time domain, but this can still converge. For a threshold like you describe then at such a point you would breach the threshold you may need to payout in a situation where you would have not paid out when converging in expectation. I think what you are saying is that this shunting of probabilities would make the process not random. However, I think the probability that a 'shunt' occurs could itself be modelled as a random variable dependent on the play history. Assuming some random properties to the sequence of plays (which is a reasonable modelling assumption), this would still be random. It wouldn't be 'fair' in the sense of giving each player the same probabilities or for plays to be independent, but it would still be random just a distribution weirder than a bernoulli one. Also FWIW: > I wouldn't expect the payout laws to be written in such a way that "eventually" That is exactly how I'd expect them to be written, seems the most natural way to do things, with the same ultimate benefit.
- seanhunter 3y ago
  They do not have a legally mandated rate, they have a legally mandated expected value and there are strong statistical tests done of the RNGs. Source: have worked with a situation which required me analyzing the process of getting betting software through regulatory approval. Edit to add: Here's the relevant regulations in Nevada. https://gaming.nv.gov/modules/showdocument.aspx?documentid=4548 https://gaming.nv.gov/modules/showdocument.aspx?documentid=4... The thing to search for in the regulations is the "Theoretical hold percentage", which is the expectation for the house expressed as a percent. The fact that they call it "theoretical" is probably enough to demonstrate that it isn't a mandated rate, but the theoretical average rate.

I think in this case it's not a legally mandated expected value, but a legally mandated payout rate. As in, it actually must pay out a percentage of what's taken in, over a certain time period. I don't think a fully random process can guarantee that.

masklinn 3y ago
Of course it can. Unless you start playing word games to manipulate what “fully random” means. You can set the odds of a fully random process, just take an rng returning a uniform distribution between 1 and 100 and set the bar at whichever threshold you want, or do the same with dice, the odds of any given face is 1/faces, so get however many faced dice you need then set the faces (or a threshold again for numbered faces) e.g. on a 20-faced dice you set the threshold at 3+ and you’ve got a 90% payout rate.
- vl 3y ago
  This is obviously incorrect: Let’s say they have to pay on each 500-play window, on true random, operator can end up with all 500 plays as non-paying and break the law. This is why they are programmed to increase payout odds if there was no payout for long time, and this is why some players wait for such machines. (In modern casinos machines are pooled, so it’s actually more complicated)
  - alexb_ 3y ago
    An operator ending up with all 500 plays as non paying is not breaking the law, they are just incredibly unlucky. The spins are independent, and no amount of waiting for a machine to be "due" is going to do anything.
- kelnos 3y ago
  That's not how randomness works. In your example, there is no guarantee that 90% of rolls will be a 3 or above. Statistically, over the long term, that will be the case, but I wouldn't expect the payout laws to be written in such a way that "eventually" you'll "probabilistically" hit your payout targets. More likely it's something like "you must pay out X over time period Y". You can't 100% guarantee that with a random process. It's possible (and not even all that unlikely) that, over the span of a day (week, month, whatever), you'd end up with only 89.9% of rolls being a 3 or above, and that would violate the payout laws.
  - silasdavis 3y ago
    I think there's a few missing pieces of information (in this discussion, probably could be looked up by some intrepid soul) Firstly what is the payout rate against, I could imagine it being: - Plays - Time - Stake Secondly, how is compliance defined: - Convergence in expected value - Degree of breach of threshold On the second one, it's kind of interesting if the degree of breach is 'never breach threshold', because when a machine is 'first turned on' the first play must always be a win (crudely speaking), if the second play has a sufficiently large stake (such that a loss would break the payout rate threshold) then that probably has to be a win too, etc until people can't keep exponentially raising the stages... This is a boot-strapping problem really but still. If compliance is in expected value then I think any of the rates can be made to work For a rate in terms of plays or stake then you can just have a binomial variable with some probability. In this case each player/play would be exposed to the same probability; each play would be independent. For a rate in terms of time the plays would not be independent because the duration of previous plays and payout would affect what payout with subsequent plays would be, so you would need a dynamic adjustment of odds over the time domain, but this can still converge. For a threshold like you describe then at such a point you would breach the threshold you may need to payout in a situation where you would have not paid out when converging in expectation. I think what you are saying is that this shunting of probabilities would make the process not random. However, I think the probability that a 'shunt' occurs could itself be modelled as a random variable dependent on the play history. Assuming some random properties to the sequence of plays (which is a reasonable modelling assumption), this would still be random. It wouldn't be 'fair' in the sense of giving each player the same probabilities or for plays to be independent, but it would still be random just a distribution weirder than a bernoulli one. Also FWIW: > I wouldn't expect the payout laws to be written in such a way that "eventually" That is exactly how I'd expect them to be written, seems the most natural way to do things, with the same ultimate benefit.
seanhunter 3y ago
They do not have a legally mandated rate, they have a legally mandated expected value and there are strong statistical tests done of the RNGs. Source: have worked with a situation which required me analyzing the process of getting betting software through regulatory approval. Edit to add: Here's the relevant regulations in Nevada. https://gaming.nv.gov/modules/showdocument.aspx?documentid=4548 https://gaming.nv.gov/modules/showdocument.aspx?documentid=4... The thing to search for in the regulations is the "Theoretical hold percentage", which is the expectation for the house expressed as a percent. The fact that they call it "theoretical" is probably enough to demonstrate that it isn't a mandated rate, but the theoretical average rate.