Level 3 - WAGMI
"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.
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.