d20 rolling puzzle

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DataGenetics
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Location: Seattle

d20 rolling puzzle

Postby DataGenetics » Fri Feb 12, 2016 8:44 pm UTC

I have a single (fair and unbiased) d20. We play a game.

You roll the die, and can elect to bank, or roll again. If you bank, you walk away with the dollar amount shown on the die, and the game ends.

If you elect to re-roll, it costs you $1 for each new roll. You can re-roll as often as you like. (Your first roll is free).

What is the optimal strategy to adopt to maximize expected return?, and what is this expected return?

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DataGenetics
Posts: 24
Joined: Sat Jan 01, 2011 1:12 am UTC
Location: Seattle

Re: d20 rolling puzzle

Postby DataGenetics » Fri Feb 12, 2016 8:46 pm UTC

This is a great little problem because it's so simple, and you can test your hypothesis with a simple Monte Carlo Simulation.

Once you think you have a good 'strategy' write a few lines of code and test it out by running it a few million times with a random number generator.

zukenft
Posts: 44
Joined: Mon Dec 20, 2010 11:34 am UTC

Re: d20 rolling puzzle

Postby zukenft » Sat Feb 13, 2016 7:52 am UTC

in your own blog you said
Spoiler:
to continue rolling until you got a 15 or above.


now what about a general solution? for different entry/play costs, and for different sided dice?

EDIT : is this is basically roulette? well, except for the fair payout...

Please, spoiler answers. -jr

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DataGenetics
Posts: 24
Joined: Sat Jan 01, 2011 1:12 am UTC
Location: Seattle

Re: d20 rolling puzzle

Postby DataGenetics » Sun Feb 14, 2016 4:54 am UTC

Yes. If the price to re-roll is constant, *and* there is no limit to the number of times you are allowed to re-roll, then the optimal strategy will be a fixed limit stopping strategy. You can use the technique in the blog to find out what this is depending on the cost/dice-range.

If there is a limit to the number of re-rolls allowed (or the price to re-roll is variable) then the stopping condition will be a function of the number of rolls in and the current count (For example of how to calculate this, look two articles earlier in my blog for the puzzle about rolling the d6).


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