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Say you are playing a completely random game. You have a (7/8) chance to win, and a (1/8) chance to lose.

What are the chances that you would lose 5 times in a row?, if you played the game 4,320 times?

What is the formula for this?

m0a
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    What will help you here is Markov chains. I have an old answer for a variation of this problem somewhere on the site. – mathreadler Dec 18 '17 at 15:11
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    You mean lose 5 times in a row at least once or exactly once? Either way Markov chains will help you but one case is a bit more complicated than the other. – mathreadler Dec 18 '17 at 15:12
  • @mathreadler At least once. And thank you for helping me out. – m0a Dec 18 '17 at 15:13
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    $\frac{1}{8}^5=\frac{1}{32768}$, maybe that'd help....? – Alexander Day Dec 18 '17 at 15:15
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    https://math.stackexchange.com/a/2214416/213607 here is one practical method, you just need to exchange the values in the matrix with 1/8 on the "stairs" and 7/8 along the edge. The $k$ value you raise the matrix to is $4320$ and the number of steps of the stairs is the number of loss in a row. – mathreadler Dec 18 '17 at 15:17
  • I'm new to these concepts, so I will need time to figure out how to calculate this even though you gave me the setup to do so. – m0a Dec 18 '17 at 15:35

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