Arbitrage betting: Why it doesn't matter how you spread your bets

Hey guys! I’ve been exploring the math of Arb betting and value betting lately. I’ve noticed something interesting. The way you spread your bet has no effect on your expected value. For example: $1 on one outcome, $999 on the other gives the same expected value as $500 on one, $500 on the other, regardless of the odds.
This means that you can round your bets drastically to avoid detection, without sacrificing long-term profit (although your variance will increase).

Here’s a spreadsheet which calculates EV and proves my claims.


Some of the pros at arbusers pointed out that some bookmakers are better at calculating the probability of an event occurring, which would skew the EV slightly. They suggested that you could shift part of your stake to the softer bookie (who is more likely to lose), in order to make a kind of arbistrage-value bet.

Finding a way to make money with math feels awesome!

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