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How do I calculate the probability of a very basic slot machine? Answered

Hi folks and thanks for taking the time with this one.
For the school fayre we are planning to make a slot machine with three wheels and three images on each wheel. What are the odds or what is the probability of a 'win' ?

Obviously we don't want to make the chance of getting three identical images as likely as a Vegas jackpot, but it would be nice to understand the maths behind such things - just in case there are curious minds on the big day who want to know more. I've looked at the web and read a bit about AND / OR situations for three events happening - tell you the truth I think I need something levelled at the lay-person.




My brain has started to dribble with all the permutation calculation.

I need to lie down in a darkened room for a few days. However I keep getting a painful reminder from the Instructables robot that I need to decide on the best answer.

So a big thank you to all responders for your time.

While my brain's regenerating:-  Lemonie (  irrational tendency towards fellow countryperson ( and you are PRO) and Seandogue ( keep your miss-spelled maps to yourself ( and you are PRO too ) please submit your final pitch in this Maths-Off because I still need to feel that I know what I'm talking about when I try to explain it to my kids - and although you seem to know of what you speak of,  I can see both your answers are very different. 

Remember: Three wheels each contain three identical images - in the same order. The chances of three matching images coming up are?........



DOH! I forgot to ask "Please show your workings".

If your three wheels are truly random, the 3 symbol-match is:
1/(the number of symbols on each reel X the number of reels)
E.g. 1/(3 x 3 x 3)
1 out of 81 times (plays)


Ding, ding, ding. I think you're right. I forgot about the three possible combination to win.


8 years ago

Yep, you're right. I don't know where my brain was at when I typed that in.


8 years ago

RD is correct, it is 1 to 27. 3x3x3 or 3 cubed. In your example, if there were 4 images on 3 wheels it would be 1 to 62.

I hated statics.

And frankly after half a bottle of wine I wouldn't trust my math/cognative skills or my spelling.

I come up with either 1 in 27 OR 1 in 455.

I hope steve, or lemonie or nacho or somebody is looking tonight and can either confirm (doubtful) or correct (thanks) my projection.

P.S. since it's not easily available anymore I finally got the next patch.