Slot maths help

A 5 reel slot machine is played 2500 times and the jackpot symbol appears with the following frequency:

Reel 1: 31
Reel 2: 30
Reel 3: 43
Reel 4: 37
Reel 5: 40

To win the one of the jackpots, the symbol must appear on at least 3 reels.

Any 3=mini jackpot
Any 4=major jackpot
Any 5=mega jackpot

What are the odds of hitting each jackpot based on the given information?

Quote: FatDumbNBroke

A 5 reel slot machine is played 2500 times and the jackpot symbol appears with the following frequency:

Reel 1: 31
Reel 2: 30
Reel 3: 43
Reel 4: 37
Reel 5: 40

To win the one of the jackpots, the symbol must appear on at least 3 reels.

Any 3=mini jackpot
Any 4=major jackpot
Any 5=mega jackpot

What are the odds of hitting each jackpot based on the given information?

If you hit the first JP symbol on the first reel, then blank on the 2nd reel, then line up the rest on the last 3 reels do you still get the major?

Okay, so you "clocked" a slot machine for 2500 spins... hope it ain't too expensive to do that.

IF 30 to 43 is representative, ie if those 2500 spins are a large enough sample, then what is it a combination of 2500 things taken 5 at a time?

Yes, any 3 mini, any 4 major, all 5 mega.

Quote: FatDumbNBroke

A 5 reel slot machine is played 2500 times and the jackpot symbol appears with the following frequency:

Reel 1: 31
Reel 2: 30
Reel 3: 43
Reel 4: 37
Reel 5: 40

To win the one of the jackpots, the symbol must appear on at least 3 reels.

Any 3=mini jackpot
Any 4=major jackpot
Any 5=mega jackpot

What are the odds of hitting each jackpot based on the given information?

For 1 spin,

The mega jackpot is 59,185,199-to-1.
The major jackpot is 336,379-to-1.
The mini jackpot is 4,800-to-1,

For 2500 spins, the odds that the jackpot hits at least once are,

The mega jackpot is 23,674-to-1.
The major jackpot is 134.0-to-1.
The mini jackpot is 1.50-to-1.

Quote: teliot

For 1 spin,

The mega jackpot is 59,185,199-to-1.
The major jackpot is 336,379-to-1.
The mini jackpot is 4,800-to-1,

For 2500 spins, the odds that the jackpot hits at least once are,

The mega jackpot is 23,674-to-1.
The major jackpot is 134.0-to-1.
The mini jackpot is 1.50-to-1.

Would you mind showing your work? (For full credit, of course)

Quote: FatDumbNBroke

Would you mind showing your work? (For full credit, of course)

After the current school term is over...

Seriously, it depends on what you mean by "frequency" in the original post. Did the jackpot symbol on reel 1 appear 31 times in the 2500 spins, or 1/31 of the time?

Whichever it is, here's how you do it:
Let the numbers a, b, c, d, and e be the probabilities of the jackpot symbol appearing on reels 1, 2, 3, 4, and 5, respectively.
The probability of winning the mega jackpot is (1/a) x (1/b) x (1/c) x (1/d) x (1/e).
There are five ways to win the major jackpot: calculate the probabilities of each one happening, and add them up.
1,2,3,4 is (1/a) x (1/b) x (1/c) x (1/d) x (1 - 1/e)
1,2,3,5 is (1/a) x (1/b) x (1/c) x (1 - 1/d) x (1/e)
1,2,4,5 is (1/a) x (1/b) x (1 - 1/c) x (1/d) x (1/e)
1,3,4,5 is (1/a) x (1 - 1/b) x (1/c) x (1/d) x (1/e)
2,3,4,5 is (1 - 1/a) x (1/b) x (1/c) x (1/d) x (1/e)
There are ten ways to win the mini jackpot: again, calculate the probabilities of each one happening, and add them up
1,2,3 is (1/a) x (1/b) x (1/c) x (1 - 1/d) x (1 - 1/e)
1,2,4 is (1/a) x (1/b) x (1 - 1/c) x (1/d) x (1 - 1/e)
and so on for 1,2,5, 1,3,4, 1,3,5, 1,4,5, 2,3,4, 2,3,5, 2,4,5, and 3,4,5.

The probability of hitting a particular jackpot at least once in 2500 spins = 1 minus the probability of not hitting it in 2500 spins
= 1 minus (the probability of not hitting it in one spin)²⁵⁰⁰
= 1 - (1 - p)²⁵⁰⁰, where p is the probability of it happening in one spin

Quote: FatDumbNBroke

Would you mind showing your work? (For full credit, of course)

What that Don guy said is what I did.

Quote: teliot

What that Don guy said is what I did.

Saved you some typing! haha

And given the results, I wonder if the OP is running below average on the jackpot symbols. I would be surprised if any slot machine in the US had top prize odds greater than 1 in 50M since they are legal in very few states. GLI-11 recommends that probability being the minimum top prize chance. If this is an foreign or online casino, then who knows.

Can someone check the mega odds for me? It's 3am and for the life of me I can't seem to get my numbers to match. TWas bugging me earlier.

Here's my attempt at the easiest one(mega).

(1/(31/2500))= .0124
(1/(30/2500))= .012
(1/(43/2500))= .0172
(1/(37/2500))= .0148
(1/(40/2500))= .016

.0124*.012*.0172*.0148*.016= .000000000606056
1/.000000000606056= 1,650,011,320.4
1 in 1.65 billion

Quote: Mooseton

Can someone check the mega odds for me? It's 3am and for the life of me I can't seem to get my numbers to match. TWas bugging me earlier.

Here's my attempt at the easiest one(mega).

(1/(31/2500))= .0124
(1/(30/2500))= .012
(1/(43/2500))= .0172
(1/(37/2500))= .0148
(1/(40/2500))= .016

.0124*.012*.0172*.0148*.016= .000000000606056
1/.000000000606056= 1,650,011,320.4
1 in 1.65 billion

If someone has already posted the correct answer and someone else has explained the method, why bother posting a wrong answer?

Quote: Mooseton

Can someone check the mega odds for me? It's 3am and for the life of me I can't seem to get my numbers to match. TWas bugging me earlier.

Here's my attempt at the easiest one(mega).

(1/(31/2500))= .0124
(1/(30/2500))= .012
(1/(43/2500))= .0172
(1/(37/2500))= .0148
(1/(40/2500))= .016

.0124*.012*.0172*.0148*.016= .000000000606056
1/.000000000606056= 1,650,011,320.4
1 in 1.65 billion

If you mean why your answer isn't 1 / 59,185,200, it's because that answer appears to be under the assumption that the probabilities for the five reels are 1/31, 1/30, 1/43, 1/37, and 1/40, instead of 31/2500, 30/2500, 43/2500, 37/2500, and 40/2500 - teliot misunderstood what you meant when you said the jackpot symbols hit with a particular "frequency." Your answer is correct given the 31/2500, 30/2500, etc. probabilities for each reel.

Quote: ThatDonGuy

If you mean why your answer isn't 1 / 59,185,200, it's because that answer appears to be under the assumption that the probabilities for the five reels are 1/31, 1/30, 1/43, 1/37, and 1/40, instead of 31/2500, 30/2500, 43/2500, 37/2500, and 40/2500 - teliot misunderstood what you meant when you said the jackpot symbols hit with a particular "frequency." Your answer is correct given the 31/2500, 30/2500, etc. probabilities for each reel.

Yes, if an audit of the wheel based on 2500 spins is used to determine the relative weight of the jackpot symbols and that is meant to answer the question of the likelihood on any one spin for the mega. But then things are very rough. It would be much wiser to use those same 2500 spins to try and reconstruct each reel strip.

Edit: deleted response

Cool thanks for the explanation guys. :)