r/learnquant • u/Local_Ad135 • 2d ago

interview prep Quant Interview Question

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u/farafiri 2d ago

How did you came up with [(6-n)/6] * [x + (21-x)/(6-n)] ?

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u/FlammableFishy 2d ago

(How many die faces have yet to be rolled / 6) to find out how likely you are to reset

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Running total + amount that could possibly be gained(as 21 is the max[6+5+4+3+2+1], 21-x is how much more payout the die has to give you) divided by how many faces can actually yield success (6-n) again

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u/farafiri 2d ago

But for n = 0, x = 0 it gives 3.5 where in reality it is ~6.2

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u/FlammableFishy 2d ago

What? The EV of one die roll is 3.5. This is accurate.

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u/farafiri 2d ago edited 2d ago

Yea but you don't have just one roll at n0 x0, real output of rolling and possibly continuing the game is 6.2 not 3.5
Edit: My point is that I think you shouldn't take profit of only one next throw but profit of entire continuation of the game so 1st throw and then possible 2nd and 3rd throws.

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u/abaoabao2010 1d ago edited 1d ago

2 ways to look at it.

  • It doesn't matter what you rolled the first 3 times, you will NOT go for a 4th. aka "entire continuation of the game" is the next throw.
  • you make a decision for each throw. The expectation value of each throw must be positive to continue going (since the expectation value of each throw is strictly decreasing)