"With some clever assumptions on the relationship between the odds on one outcome and the others we could come up with a similar plot/figure as in the exchange case."

Not sure if you check comments on old posts, but I'd really like to see your profit graph for the American case where you're hedging with other books instead of exchanges.

I wrote my own script exploring this. I'm assuming a 2 outcome game, and my relationship between the odds is that I assume the implied probabilities always sum to 22/21 (the case in the -110/-110 and most normal situations; it breaks down when odds get to +2000 or more but that's a whole other discussion).

I'm finding you maximize profit when the freebet is used on odds broadly between +250 and +500 (max at +360), but on longer odds your profit goes back down pretty sharply.

Also, the max profit is around $60 for a $100 freebet, which is sorta the worst case of assuming you can only get odds from one book. Presumably shopping around a bit can get you back to your ~$70 profit, but it's not continuously increasing at longer odds like your plot with the exchanges.

Hi ser, yes you are correct in what you're saying & what's said in the text is, as you mention, slightly off.

For the US case I'd recommend generalizing the plot into a 3D plot with (vig, odds) as variables to correctly represent all paths the problem can take. If you're having problems generating such a graph on your own, please get back to me.

& feel free to share your scripts with other readers if you'd like to! :)

Hm yeah interesting. As you lower the vig, the profit margin goes up (duh) but the odds to bet to get that maximum profit get longer. Looks like it asymptotes to 0 vig and +infinity odds gets you the full value of your bet back, which I think makes sense.

Anyway, here's my code to make the 2D vig/odds with profit plot and a line showing where the maximum odds are. And also showing for any given vig, what is the max profit you can expect. Looks like you need to get down to 2.5% vig to get up to your 70% return though.

"With some clever assumptions on the relationship between the odds on one outcome and the others we could come up with a similar plot/figure as in the exchange case."

Not sure if you check comments on old posts, but I'd really like to see your profit graph for the American case where you're hedging with other books instead of exchanges.

I wrote my own script exploring this. I'm assuming a 2 outcome game, and my relationship between the odds is that I assume the implied probabilities always sum to 22/21 (the case in the -110/-110 and most normal situations; it breaks down when odds get to +2000 or more but that's a whole other discussion).

I'm finding you maximize profit when the freebet is used on odds broadly between +250 and +500 (max at +360), but on longer odds your profit goes back down pretty sharply.

Also, the max profit is around $60 for a $100 freebet, which is sorta the worst case of assuming you can only get odds from one book. Presumably shopping around a bit can get you back to your ~$70 profit, but it's not continuously increasing at longer odds like your plot with the exchanges.

edited Aug 3, 2023Hi ser, yes you are correct in what you're saying & what's said in the text is, as you mention, slightly off.

For the US case I'd recommend generalizing the plot into a 3D plot with (vig, odds) as variables to correctly represent all paths the problem can take. If you're having problems generating such a graph on your own, please get back to me.

& feel free to share your scripts with other readers if you'd like to! :)

Hm yeah interesting. As you lower the vig, the profit margin goes up (duh) but the odds to bet to get that maximum profit get longer. Looks like it asymptotes to 0 vig and +infinity odds gets you the full value of your bet back, which I think makes sense.

Anyway, here's my code to make the 2D vig/odds with profit plot and a line showing where the maximum odds are. And also showing for any given vig, what is the max profit you can expect. Looks like you need to get down to 2.5% vig to get up to your 70% return though.

https://gist.github.com/ethankruse/e242cab8b235faf4018f6e79fe21b597

Post now updated with plots for the American case. Thanks for sharing code, will hopefully come to great use for a bonus rugger or two at some point.

Perfect timing with football about to start up in the US.

And rest assured, you’ve tapped into a community with plenty of nerds/autists who will track through the math.

Indeed.

The community was chosen for a reason! ;)