# A's die has sides 1, 2, 3, 4, 5, and 6. B's die has sides 1, 1, 1, 6, 6, and 6. Who is more likely to win?

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A and Bare each rolling a fair, six-sided die. They roll their dice simultaneously, individually keeping a sum until someone reaches 100; whomever reaches 100 first wins. (If they reach 100 on the same roll, it's a tie.)

A's die has sides 1, 2, 3, 4, 5, and 6. B's die has sides 1, 1, 1, 6, 6, and 6. Who is more likely to win?

Thanks Gaurav for sharing...

posted Jul 22, 2017

both are equally likely to win
In first case expected outcome /average is ((1+2+3+4+5+6)/6)=3.5
In second case expected outcome /average is ((1+1+1+6+6+6)/6)=3.5

'A' is more likely to win
I haven't applied any in-depth mathematics, but here was my answer.

When either die is rolled twice, 7 is the most likely result. (Albeit, with differing probabilities for each die)

As a multiple of 7, both players are more likely to have 98 after 28 rolls than any of the surrounding values; However, Andrea has a 5/6 chance of reaching 100 from 98, but Raleigh only has a 3/6 chance.

With that, I concluded that 'A' was more likely to reach 100 first.

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