October 24th, 2014 at 1:07:32 PM permalink
I was trying to figure out how many pulls (on average) it would take to spell BONUS on an antique slot machine with the bonus feature. Old machines had reels, each with 20 symbols. Of these 20, 5 symbols were (one each) the letters B,O,N,U,S. The first reel was the ONLY REEL to have these letters. To win the bonus, you had to first pull the lever and get the "B". On successive rolls you would then need to complete the "O", "N","U" and "S" in order to obtain an 18 coin payout. While the odds of obtaining the "B" is one in 20, and the odd of obtaining an "O" is also one in 20, it cannot be true that the odds of getting all the letters is 1/20^5. That would take more than 3.2 million pulls. What is the correct probability? I was thinking that on average it would take 10 pulls to get a "B" (it could be the first pull or the 20th pull) on average. Then it might be the same for each of the next letters so on average it might take 50 pulls to spell BONUS. Any thoughts???
October 24th, 2014 at 2:40:24 PM permalink
On average, it would take 20 spins to complete each letter. So, it would take an average of 100 spins in total to get all 5 letters.
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