I remember in one of Bart's podcasts (DPP or SO) that he talks about the appropriate % of the time that a good, thin value bettor should be value-owning (VO) themselves. I seem to recall the stat at something like 60-70% for maximum profitability. Does anyone know if/how this has been calculated? I've been trying to work on it with limited success. Here's what I have so far:
Net won per bet (EV) = Amt won*%won + Amt lost * % lost
=(1 unit)*(1-VO%) + (-1 unit) * VO%
This makes sense because your ROI will be 100% if you never VO, 0% if you're 50/50, and -100% if you always VO. This works for a single bet. But overall value bet ROI (the optimal 60-70% that was quoted in the podcast) needs to take into account frequency and sizing. You can plug in numbers for VO to look at spot ROIs, but VO% itself is a function of both frequency and sizing. So VO is related to frequency and sizing with something like:
VO ~ frequency*sizing
I think this makes sense, since the greater frequency you value bet, the more likely it is you will VO, and the bigger the bet sizing, the more likely that you will VO. We could plug in some different sizings; maybe something like a different curve for average thin value bet sizings as a % of the pot. But how to determine frequency? Maybe frequency would be a function of the relative strength of your "thin" hands to possible better hands? Something like if you're betting with a hand that beats say, 10% of possible hands on the river, vs 20%, 30%, etc? Obviously this is quite situationally dependent IRL, but is it possible to generalize for math's sake?
The ideal outcome to this exercise would be to get some sort of peak overall ROI values based on VO% to show the optimal point that Bart discussed (or find that, based on sizing, etc, that it's at a different spot!)