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Kelly Can't Fail

(win-vector.com)
389 points jmount | 1 comments | 19 Dec 24 23:07 UTC | HN request time: 0.203s | source
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pcthrowaway ◴[20 Dec 24 02:34 UTC] No.42467756[source]▶
Note that you need to be able to infinitely divide your stake for this to work out for you all the time.

For example, if the deck has 26 red cards on top, you'd end up dwindling your initial $1.00 stake to 0.000000134 before riding it back up to 9.08

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boothby ◴[20 Dec 24 03:06 UTC] No.42467915[source]▶
If you start out with a $1e12 stake, you're able to avoid catastrophic rounding errors even in the worst case. There's probably a life lesson here.
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cbsks ◴[20 Dec 24 05:01 UTC] No.42468417[source]▶
My simulation shows that with a 52 card deck, if you round the bet to the nearest $.01 you will need to start with $35,522.08 to win a total of $293,601.28.

If you start with $35,522.07 or less, you will lose it all after 26 incorrect cards.

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1. boothby ◴[20 Dec 24 06:37 UTC] No.42468808[source]▶
Nearest rounding does seem like a mistake here. Rounding down is quite safe: rather than lose it all, you end up with at least 2^26 pennies.