RNG random numbers/preset payout rate contradiction

Taking a casino slot machine for example: How can the probability of a payout TRULY be random with a preset payout rate?

If a casino has slots programmed to a specific rate or percentage of payout, how can probability of winning by RNG generated slot symbols TRULY be “random” while simultaneously being pre set by the controller?

What am I missing - Does the preset payout rate not contradict the simple and fundamental premise of random winning?

The moment preset payout rates are programmed, fundamentally you lose all chance (pun intended) of generating anything random.

Consider that I can "program" a six-sided die to a payout rate of...

• 0%, by designating that no sides win

• 16.67%, by designating that only a 6 wins

• 33.33%, by designating that a 5 or higher wins

• 50.00%, by designating that a 4 or higher wins

• 66.67%, by designating that a 3 or higher wins

• 83.33%, by designating that a 2 or higher wins

• 100%, by designating that all sides win

Does that mean I've reduced the randomness of the die by deciding which sides I'll count as a win?

No. And yet I can mathematically show that the overall win rate will tend toward the number I chose over large numbers of trials.

Real games have many more internal states than just the six faces of a die, so the percentages can be tuned to much finer increments. But the core idea remains: given a source of randomness that can put the system into each one of these states with some known probability, we can compute the overall probability of winning (or the expected value paid to the player on average) by summing over the probability of each winning state (multiplied by its payout value).

The trick here is that the win rate is an average of a large population of samples. We can know a great deal about the overall behaviour of a stochastic system in the long term, when all the antics of the RNG are smeared together over millions of runs, even if we can say nothing about how the next roll of the die will fall.

Of course, the exact degree of unpredictability depends on the quality of our source of randomness. But even with an RNG source as pure as radioactive decay, we can still reason precisely about the long-term rates of particular occurrences, despite the randomness of each sequential outcome.

It's sometimes misunderstood that this means probability itself has some kind of memory or agency. That if a coin comes up tails "too many" times, Lady Luck will notice and start tipping the scales in favour of heads in order to balance it out and hit her 50% target. This is known as the Gambler's Fallacy. If this were true, then it really would make things "less random". If we'd observed a number of tails flips in the past, we could use that to make better predictions that the next flip might come up heads.

But that's not what happens. It's not unusual, for instance, for difference between the number of observations of some event and its expected number of occurrences according to the probability to actually grow over time, rather than shrink back to zero. So how do the overall rates still approach the theoretical calculations anyway, even if one event doesn't "catch up"? It's the growth of the denominator that does it:

• 9 heads out of 20 flips is 1 behind what we'd expect, for a 10% error.

• 95 heads out of 200 is 5 behind what we'd expect (5x more), for only a 5% error (half as much)

• 975 heads out of 2000 is 25 behind what we'd expect (5x more again), for only a 2.5% error (half again)

This is how we can get more and more confident about the range of the overall results we expect to see over an interval as we increase the number of trials, even without any ability to predict the result of a particular trial.

• Thank you - in summary, a casino that has preset payouts of say 74% return would have a 74% of the possible combinations that the RNG could “land on” be winning combinations, is that fair? I can see now that I asked a stupid question. The preset payout rate doesn’t affect the end result of the RNG selection. Separately - What prevents a preset “program” of RNG from be faulty, or corrupted? Is it fair to say that it’s actual randomness is only as true or honest as the entity of which created or moderates it? Whether in a touch screen phone game or a casino?
– Bill
May 29, 2021 at 9:50
• I should add - what is random is the end resulting winning combination, what is not random is how much you will win. You will win 74% of the time over time, what is random is the combination on which you will win. I was brain farting.
– Bill
May 29, 2021 at 10:02
• As a game designer, I can only speak with authority about the game design — how we might adjust the rules of the game to achieve certain expected odds and payouts. I've never worked in the gambling industry, so I know only a little of what kinds of RNGs they use and how they're vetted. I understand that any new hardware or software used in a casino is subject to extensive testing by an independent agency, though I don't know their exact protocols. For smartphone software, you are trusting the author to write their pseudorandom algorithms honestly and correctly to avoid bias or exploits. May 29, 2021 at 11:08
• The payout % is known as the RTP (return to player). Last Vegas strip machines have an RTP of around 90%. I think as players expect it to be much lower but its skewed by the players who win big and walk away. rickross.com/payout-percentage-slots onlinegambling.com/slots/payout-percentages Aug 1, 2021 at 18:26