Comment by nwsm
4 years ago
The bookie odds go into the formula as b- the net fractional odds received on the wager.
We have our own models for our confidence, and the Kelly criterion decides our wager size (though we don't use a full Kelly bet).
Yes, the sportsbook minimizes their own risk by setting a spread or odds with respect to how patrons are wagering. This actually makes it easier to make money if your model is much better than the average bettor. There will be games where public opinion and the majority of bets are on the wrong side of a matchup, and the bookie adjusts the odds accordingly, so the correct bet's payout is bigger than it should be.
In high school I tried to do more what you are asking- use one bookie's odds (which I deemed the most accurate) as the "true probability", and another as the payout. This was not successful, but theoretically could be if the two bookies' clientele were consistently better or worse than each other, therefore influencing their odds consistently.
I can attest to this. Successful sports betting is about betting on gamblers, not games.
As for your last points: bookies often book bets with each other in order to even out the odds. Otherwise you would be able to arbitrage bookies against each other. (Which would also result in their odds evening out, of course, but then the bookies wouldn't get the proceeds so they prefer to do it themselves.)