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Lets say you’re a $100 (flat bet) blackjack player. In three hours, which we will assume is the average length of a sporting event, you would normally play about 180 hands of blackjack. Assuming a 0.5% house edge and SD of 1.14, your expectation would be -$90 +/- $1,529.

If you multiply that SD by (2/π)^.5 you get the weighted average of all possible results for for either side of the distribution, which is $1,220

Going by that logic, $1,220 would be the appropriate sports bet for that blackjack player since, over the long term, his blackjack results will average $1,220 above or below expectations for a three-hour session. For bet size calculations, I generally only pay attention to variance since expected loss is quite small, relatively speaking

Does this calculation makes sense ?

Quote:Ace2If you multiply that SD by (2/π)^.5 you get the weighted average of all possible results for for either side of the distribution, which is $1,220

I recognize the (2/π)^.5 from the Gaussian curve, but otherwise you lost me with that step.

Can't we just use Kelly to get a very close estimate? I suspect you may be overthinking this.

Quote:Ace2Last night I had a bet on the college basketball championship. It got me thinking about what is the appropriate size for a sports bet. Here’s what I came up with

Lets say you’re a $100 (flat bet) blackjack player. In three hours, which we will assume is the average length of a sporting event, you would normally play about 180 hands of blackjack. Assuming a 0.5% house edge and SD of 1.14, your expectation would be -$90 +/- $1,529.

If you multiply that SD by (2/π)^.5 you get the weighted average of all possible results for for either side of the distribution, which is $1,220

Going by that logic, $1,220 would be the appropriate sports bet for that blackjack player since, over the long term, his blackjack results will average $1,220 above or below expectations for a three-hour session. For bet size calculations, I generally only pay attention to variance since expected loss is quite small, relatively speaking

Does this calculation makes sense ?

I'd say no. A $100 BJ player will rarely lose $1220 in a session, while a $1220 sports bet will lose about half the time.

The same goes for winning. A $100 BJ player will not will $1220 very often, but a $1220 sports bet will win about half the time.

I'd guess 99% or more of BJ sessions will end somewhere between the two extreme outcomes while a sports bet only has the two results.

I'm comfortable betting $100 a hand but not with betting $1200 on a single outcome. I don't think the time of the event should matter.

Using your criteria, what should a $100 BJ bettor bet on an NBA playoff series that might take two weeks to complete?

With a three hour $100 blackjack session having an expectation of -$90 and SD of $1,529, the result will differ from expectations by more than $1,220 (0.8 of a SD) about 42.5% of time, not 1% of the timeQuote:billryanI'd say no. A $100 BJ player will rarely lose $1220 in a session, while a $1220 sports bet will lose about half the time.

The same goes for winning. A $100 BJ player will not will $1220 very often, but a $1220 sports bet will win about half the time.

I'd guess 99% or more of BJ sessions will end somewhere between the two extreme outcomes while a sports bet only has the two results.

I'm comfortable betting $100 a hand but not with betting $1200 on a single outcome. I don't think the time of the event should matter.

Quote:Ace2With a three hour $100 blackjack session having an expectation of -$90 and SD of $1,529, the result will differ from expectations by more than $1,220 (0.8 of a SD) about 42.5% of time, not 1% of the time

Those have not been my experiences but I won't argue with your math. My personal experiences differ.

Quote:TomGAs the time it takes for a bet to resolve increases, the size of the bet should decrease.

That makes sense. Tying up money long term can get expensive.