What are the odds of....(math question)

[HaiKarate]

Slot machine, 3 reels each containing 9 different symbols. What are the odds of stopping on 3 identical symbols?

And what are the odds of gambling that on the next spin I correctly predict the actual 3 symbols, ie, three sevens?

Thanks for any info.

[LimaDelta]

Assuming each symbol has an equal chance of appearing then...

1/9 x 1/9 x 1/9 = 1 in 729

Unless I'm missing something obvious?

edit: Should have stated this is the probability of predicting the correct three symbols

The probability of three matching are 1/9 x 1/9 = 1 in 81

Edited by LimaDelta on Saturday 26th January 09:49

[The Mad Monk]

HaiKarate said:

Slot machine, 3 reels each containing 9 different symbols. What are the odds of stopping on 3 identical symbols?

And what are the odds of gambling that on the next spin I correctly predict the actual 3 symbols, ie, three sevens?

Thanks for any info.

Er

3 identical symbols? 64 to 1?

Predict 3 symbols? 512 to 1?

What's wrong with my maths?

[HaiKarate]

Different answers. Which one?

[The Mad Monk]

LimaDelta said:

Assuming each symbol has an equal chance of appearing then...

1/9 x 1/9 x 1/9 = 1 in 729

Unless I'm missing something obvious?

The odds on each reel are 8 to 1, not 9 to 1.

1 (a)You want all three reels to show the same unspecified symbol.

1 (2) The first reel stops, let's say it's cherries. It is 8 to 1 against the next reel being cherries and 8 to 1 again against the third reel being cherries. That is 64 to 1 against an unspecified symbol.

2 you want a specified symbol on each reel, so that is 8 x 8 x 8 = 512.

[The Mad Monk]

HaiKarate said:

Different answers. Which one?

You asked to different questions.

1, three unspecified symbols the same.

2, three specific symbols the same.

[HaiKarate]

Thank you Mad Monk. That makes sense, even to me. Appreciated.

PS. I meant the two different answers from two members.

[Fast and Spurious]

1/81 and 1/729.
One in nine probability per reel.

[LimaDelta]

The Mad Monk said:

LimaDelta said:

Assuming each symbol has an equal chance of appearing then...

1/9 x 1/9 x 1/9 = 1 in 729

Unless I'm missing something obvious?

The odds on each reel are 8 to 1, not 9 to 1.

1 (a)You want all three reels to show the same unspecified symbol.

1 (2) The first reel stops, let's say it's cherries. It is 8 to 1 against the next reel being cherries and 8 to 1 again against the third reel being cherries. That is 64 to 1 against an unspecified symbol.

2 you want a specified symbol on each reel, so that is 8 x 8 x 8 = 512.

Why 1/8 if there are 9 outcomes?

[HaiKarate]

I wondered why the 1 in 8. Can someone please confirm?

[ReallyReallyGood]

LimaDelta is correct. 1/9is the same as 8-1 in bookie parlance but not probability. E.g a 50/50 event is 1/2 but evens 1-1 in bookie terminology.

[The Mad Monk]

HaiKarate said:

I wondered why the 1 in 8. Can someone please confirm?

As I understand it, it's because there is one chance it will be, say, cherries - eight chances it won't. Therefore it is 8 to 1 against - I think!

[CanAm]

The Mad Monk said:

As I understand it, it's because there is one chance it will be, say, cherries - eight chances it won't. Therefore it is 8 to 1 against - I think!

Think of it as only one reel. There are 9 possibilities, so the probability of 1 particular number coming up is 1/9, but the ODDS against that number coming up are 8:1.
There are 729 different combinations of symbols and 9 possibilities of 3 identical symbols, 9/729 or 1/81, but the odds are 80:1.

[LimaDelta]

ReallyReallyGood said:

LimaDelta is correct. 1/9is the same as 8-1 in bookie parlance but not probability. E.g a 50/50 event is 1/2 but evens 1-1 in bookie terminology.

Yes, some confusion (on my part) between 'odds' and 'probability'.

[silentbrown]

The Mad Monk said:

Er

3 identical symbols? 64 to 1?

Predict 3 symbols? 512 to 1?

What's wrong with my maths?

Even using bookies terminology, those are wrong.

It would be 80 to 1 for any 3 identical, and 728 to 1 for three stars, say.

Imagine there's 10 reels with 2 symbols, A and B.

the odds of A on the first reel are 1:1 but what are the odds of 10 'A's in a row?

[HaiKarate]

Thanks everyone. I really should’ve tried harder at school.

[thelawnet1]

Just FWIW, most 3-reel slots are weighted. In other words the chances of each position are not the same, so it is pretty much never going to be 1/729 for the scenario described.

For 5-reel slots they are less likely to be weighted, but you would never have 9 distinct symbols occurring once - you might have 9 distinct symbols, but the lower-paying symbols might appear say 5 times and the jackpot symbol only once or twice. Also typically each reel is different in a 5-reel machine, so that for example if there are 25 symbols per reel (the number is not fixed, so it could different between reels), that results in 25^5 = 9.8 million combinations, and then if you had say 3 symbols on reel 1, 2 on reel 2, 2 on reel 3, 1 on reel 4 and 1 on reel 5, then that gives 12 combinations, for a ~1 in 800,000 chance of getting the jackpot (per line - noting that a 5-reel slot is almost invariably played with multiple lines (patterns within the 3 symbols per reel visible on screen))

[The Mad Monk]

thelawnet1 said:

Just FWIW, most 3-reel slots are weighted. In other words the chances of each position are not the same, so it is pretty much never going to be 1/729 for the scenario described.

For 5-reel slots they are less likely to be weighted, but you would never have 9 distinct symbols occurring once - you might have 9 distinct symbols, but the lower-paying symbols might appear say 5 times and the jackpot symbol only once or twice. Also typically each reel is different in a 5-reel machine, so that for example if there are 25 symbols per reel (the number is not fixed, so it could different between reels), that results in 25^5 = 9.8 million combinations, and then if you had say 3 symbols on reel 1, 2 on reel 2, 2 on reel 3, 1 on reel 4 and 1 on reel 5, then that gives 12 combinations, for a ~1 in 800,000 chance of getting the jackpot (per line - noting that a 5-reel slot is almost invariably played with multiple lines (patterns within the 3 symbols per reel visible on screen))

Are you saying that putting your money into a slot machine may not be a wise investment?