Probability Of Getting All Four Same Symbols In Slot Machine

I'm very new to probability and my professor hasn't gone into detail with it but we must know it for the class. I'd appreciate help with these questions. Suppose a slot machine has $3$ reels with $7$ different symbols on each, jackpot is when all $3$ reels have the same symbol.

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rogga

Hi,
after reading a lot about slot machine payout calculations there is still something that I just don't get:
All of the payout calculations on the Wizard of Odds Website seem work the same way:
- define the reel strips/symbol frequency,
- define the payout table,
- calculate combinations/probabilities
- calculate return percentage
I have seen slot machines (at least in europe) that enable the owner to change the payout percentage of the machine.
How would that work? Does the machine/game create new reels? How would you calculate the symbol frequency, based on your payout table?
Best regards,
rogga

ChumpChange

Thanks for this post from:

Interview with a Slot Manager - 1999
https://www.americancasinoguide.com/slot-machines/interview-with-a-slot-manager.html

Hi,
after reading a lot about slot machine payout calculations there is still something that I just don't get:
All of the payout calculations on the Wizard of Odds Website seem work the same way:
- define the reel strips/symbol frequency,
- define the payout table,
- calculate combinations/probabilities
- calculate return percentage
I have seen slot machines (at least in europe) that enable the owner to change the payout percentage of the machine.
https://burgernin3.netlify.app/prohibition-era-table-top-nickel-slot-machine.html. How would that work? Does the machine/game create new reels? How would you calculate the symbol frequency, based on your payout table?
Best regards,
rogga

The return is based on the frequencies.

Wizard
Administrator

How would that work? Does the machine/game create new reels? How would you calculate the symbol frequency, based on your payout table?

As a general rule, casino slot executives will reward players betting on higher denomination machines with an overall better payback percentage. The thinking goes that the average bet on a higher denomination machine will be higher than the average bet on a lower denomination machine. https://burgernin3.netlify.app/lower-denomination-slot-machines.html.

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The returns are easily configurable in any slot machine that has a computer chip inside.
In a mechanical slot (with actual spinning reels), the weighting of the stops on the reels are adjustable.
In video slots the actual reel strips are adjustable. For example, increasing the return might be achieved by adding more wilds to the reel strips.

Probability Of Getting All Four Same Symbols In Slot Machines

In both cases, the idea is to make the change invisible to the player.

It's not whether you win or lose; it's whether or not you had a good bet.

charliepatrick

Sometimes it is done by altering how much the feature pays, so although the hit rate might be the same the average payout for it can be changed.

rogga

I'm not sure what exactly changes when the payout rate is changed, but I would assume that, exactly like you said, the reel strips would just change. I have read a couple of your articles on how the payout rate can be calculated, but it always comes down to the same procedure (definition of payout table, definition of reel strips, then do the math). In this case I am interested in the math too, but the other way around.
Is there a way to first specify a payout table, then a payout rate (e.g. 90%) and then automatically generate the reels in a way so their setup results in a 90% payout probability? I could not find an article that explains the math for this scenario.
I'm sorry if my question is not clear enough to understand, english is not my first language.
thank you all for your help and also the very interesting interview (even though I am still sure I've seen a possibility to change the payout quote - but that was like 10 years ago and I might of course be wrong - but I still enjoyed reading it).

p13man

Probability of getting all four same symbols in slot machines

Thanks for this post from:

The 'display' reels are fixed. But the symbols that are displayed in a spin are determined by a random number generator (RNG) and multiple sets of VIRTUAL reels. The RNG picks a number which is an index into the virtual reel. This is then mapped to the actual or display reel. The machine can have multiple sets of virtual reels - one set that increases the chances of a free games feature; one that increases the chances of a Hold-and-Spin feature; one that increases the chances of wild symbols appearing. And so on.
All modern slots are programmed with multiple RTP (return to player) rates. The operator can adjust the payout from 86% to 88% or 90% etc. The display reels remain the same - but the virtual reels are different for different RTPs.
Here is a good explanation of virtual reels and their role in determining the odds of any particular symbol landing on the payline /watch?v=Ur53m9zQ5sY