# Nightmare Math / maths (betting question)

**URL:** <https://boards.straightdope.com/t/nightmare-math-maths-betting-question/740535>\
**Category:** Factual Questions\
**Created:** [December 15, 2015, 3:16pm UTC](https://boards.straightdope.com/t/nightmare-math-maths-betting-question/740535 "2015-12-15T15:16:19Z")\
**Posts on this page:** 3\
**Page:** 2

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**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\
**Post date:** [December 22, 2015, 4:54pm UTC](https://boards.straightdope.com/t/nightmare-math-maths-betting-question/740535/21 "2015-12-22T16:54:20Z")

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> [@Lance\_Turbo](#):
>
> These calculations are not trivial so I will not include them in this post, but the counterintuitive result is that we should wager approximately 12.4% of our bankroll on A and 0% on B. The high volatility of bet B counters its higher expectation. In this case the low risk low reward of A is the way to go.

The lack of precision may be unnecessarily complicating things here. More precisely…

Wager 12.40830% on A and 0.33333% on B. The amount we should wager on the more favorable bet is greater than zero, but it is much smaller than the amount we should wager on A.

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**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\
**Post date:** [December 22, 2015, 5:21pm UTC](https://boards.straightdope.com/t/nightmare-math-maths-betting-question/740535/22 "2015-12-22T17:21:02Z")

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You’re correct that the push condition means Remark 1 cannot be applied directly. However the claim that no money is placed on the 1-1 draw at optimality was still incorrect.

> [@Lance\_Turbo](#):
>
> Wager 12.40830% on A and 0.33333% on B. The amount we should wager on the more favorable bet is greater than zero, but it is much smaller than the amount we should wager on A.

OK. Now we’re in sync. The 0.333% bet is tiny but it isn’t zero. 😃

BTW, **Lance** , had you ever seen the Theorem that your wager should equal p times your bankroll where p is the probability of an outcome when you have the chance to bet (against an oddsmaker basing his payoffs on probabilities which sum to 100%) on all outcomes? It seems very elegant. Is it well-known?

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**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\
**Post date:** [December 22, 2015, 5:53pm UTC](https://boards.straightdope.com/t/nightmare-math-maths-betting-question/740535/23 "2015-12-22T17:53:10Z")

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That theorem is new to me, but the vast majority of the gambling math I have done professionally involves minimizing loss (either per ante or per total bet) in games where the house has an edge. Kelly betting and related concepts are merely a hobby of mine.

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