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Arbing: Betspread does not effect EV

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tombos21
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Arbing: Betspread does not effect EV

Sat Mar 02, 2019 11:16 pm

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, $1999 on the other gives the same EV as $1000 on one, $1000 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). I'm new here - not sure if this is common knowledge already  :P
Here's a spreadsheet which calculates EV and proves my claims.

Interesting side note for other math geeks out there:
The equation for calculating your return on an arb is the same equation for calculating resistors in parallel... Weird.

Return = 1 / (1/odds1 + 1/odds2 + 1/odds3...)
Resistance = 1 / (1/r1 + 1/r2 + 1/r3...)

Finding a way to make money with math feels amazing :)

https://docs.google.com/spreadsheets/d/1z0TSx5eaRzMYHnK9HS7D22lHIV-zT_Ywf1sulYctLMU/edit?fbclid=IwAR1y84CsHUbCIP_lNgXlK1225GSIFTMlGjFWrq6-e20ihOrXjMic_Bn-ZIw#gid=81043287
Chipmunk
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Re: Arbing: Betspread does not effect EV

Sun Mar 03, 2019 12:42 pm

Makes sense.

You could go a step further, and radically reduce your stakes on the sharp side. More variance than arbing, but less than pure "value-betting".
vinciguerra
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Re: Arbing: Betspread does not effect EV

Sun Mar 03, 2019 12:51 pm

"The way you spread your bet has no effect on your expected value. "

of course it does.  assuming one side of your bet is the "sharp" side, and one side of the bet is "soft" side, you will increase EV by decreasing stakes on the sharp side, and increasing stakes on the soft side. Your model seesm to be implying you can increase stake on either side, and EV remains the same, which is only true if both lines are equally soft. Good luck with that. You can't just ignore the fact the implied probability of lines you arb on don't have the same correlation to the event actually happening when you model something.

The real challenge is determining what the soft side and the sharp side actually are, as this isn't always as straightforward as it may seem. You arb to avoid this challenge and to decrease variance,  by valuebetting you increase EV (and, no matter what, you increase variance) as long as you're succesfully in determining what the soft line is.
Last edited by vinciguerra on Sun Mar 03, 2019 12:54 pm, edited 1 time in total.
tombos21
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Re: Arbing: Betspread does not effect EV

Sun Mar 03, 2019 3:53 pm

You're absolutely right vincigurrra. The fundamental math says EV stays the same, but that oversimplification doesn't account for the fact that some bookmakers are better at estimating event probability than others. I wonder if there is a way to model "sharpness" on a spreadsheet  :)

Your guy's suggestion to shift part of the bet over to the softer bookie is fascinating! Something in between a value bet and arb haha.

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