> In fact, due to gambling laws, these games have to publish exact probabilities.
These pre-determined fixed odds make it such that the games support the opposite of your argument.
If outcomes were independent probability then it would be possible to for example win 100 games in a row (with astronomical probability, but it's still possible). In fact the machine owner neuters it so that the house won't lose in such a streak.
Similarly, the machines have a fixed payout %. If each outcome were truly independent, it would be possible for the machine to never pay out, just like it's possible to flip Heads any arbitrary number of times in a row.
Anyone sucked into these games thinking 'the next one will hit' is not committing to gambler's fallacy because these outcomes are not independent.
The fixed odds do not guarantee that a certain payout will happen. You seem to have misunderstood how it works. The odds determine the likelihood on any individual roll, not some theoretical "payout per hour."
Slot machines are based on RNGs.
> If each outcome were truly independent, it would be possible for the machine to never pay out
It is possible for a machine to never pay out. That would probably trigger an audit to see if there's a bug, but there is no guarantee that th
This may be jurisdiction dependant, but in the UK, the small prize fruit machine style games you find in pubs are required by law to payout a fixed percentage of their income over time. I believe it's 70%, but I think there are variations and exceptions to the rule.
So if £1000 is paid in during the day, the machine by law must pay out at least £700 in prizes. This is not allowed to be fully random, the odds of each game are not independent because they must by law ensure the minimum payout.
It's semi-common knowledge that the way to win at these machines is to watch them until you have seen someone else have a long losing streak, then take your turn when they leave as the machine is now 'behind' and overdue a payout.
You're right, this actually does vary by jurisdiction. I looked into and was quite surprised that the UK allows something called "compensated game control" to adjust the odds dynamically so the observed payout matches the expected one. [0]
Nevada has the opposite rule: machines must only incorporate chance when paying out and the theoretical payout is what the gaming commission analyzes. They can't dynamically adjust odds to favor a preferred payout. [1]
> These pre-determined fixed odds make it such that the games support the opposite of your argument.
> If outcomes were independent probability then it would be possible to for example win 100 games in a row (with astronomical probability, but it's still possible). In fact the machine owner neuters it so that the house won't lose in such a streak.
I don't really know anything about it, but it was one of the first on wikipedia's list of gacha games that I googled "pity system" and got "no it doesn't have one".
Someone has made a simulator for it. If I go to https://ae-encounter-sim.github.io/ and click on "Weapon Discovery Manifestation", it shows me two characters on "rate up" (more common). The official probability of getting each of them is 0.8% chance for each "encounter".
I'll click until I get the first character (5star Melina apparently) and post my results:
1. First time, 360 encounters (36 10 bundles), cost of $959.88 USD.
2. Another try, 480 encounters, cost of $1,200 USD
3. Last try, 130 encounters, cost of $319.
It is very possible to get the desired outcome in 1 "encounter", or to run out of money first and never get it.
> the machines have a fixed payout % [that isn't independently random per trial]
There's no fixed payout if there's no pity system. Why would there be, they're just giving away jpeg images.
A lot of casino machines also don't necessarily have fixed payout. Over long enough time periods, the casino still wins, they don't really need to worry about incredibly improbable events. For those, they have insurance anyway.
> not committing to gambler's fallacy because these outcomes are not independent.
These pre-determined fixed odds make it such that the games support the opposite of your argument.
If outcomes were independent probability then it would be possible to for example win 100 games in a row (with astronomical probability, but it's still possible). In fact the machine owner neuters it so that the house won't lose in such a streak.
Similarly, the machines have a fixed payout %. If each outcome were truly independent, it would be possible for the machine to never pay out, just like it's possible to flip Heads any arbitrary number of times in a row.
Anyone sucked into these games thinking 'the next one will hit' is not committing to gambler's fallacy because these outcomes are not independent.