If we assume that he is raising 2.5x 44% of the time, his range is approximately 22+, A2o+, A2s+, K9o+, K2s+, Q9o+, Q8s+, J9o+, J8s+, 76o+, 54s+, 86o+, 64s+. This does not need to be exact, as he will be folding out the weakest part of this range virtually* every time. The important thing is getting his raising frequency correct, which we have already determined.
Now we must figure out his calling frequency of 56% (since he is folding 44%). This not quite exact either, but still easy to figure out, particularly when reviewing my hand histories to find specific examples of hands he has called with. In so doing, we get a calling range of 22+, A5o+, A2s+, KTo+, K9s+, QJo+, QTs+, JTs. This is an admittedly broad calling range, but in so doing, he prevents getting heavily exploited by shortstackers.
By factoring in the stakes of $2/4, rake and dead money from the blinds and then running the simulation 5000k times with a 20BB stack, here is what we end up with:
Voila! The highlighted hands are the profitable reshoving range and the number below is the exact amount in $ that we can expect to profit per trial, on average. Depending on the stack size, we can begin to shove more or less hands, but now his calling frequency will also be affected as well. However, if we were to deduct just 3BB from the effective stack (this will not likely change his default calling range), the grid now appears as thus:
Amazing! Now the next time you hear someone complain about a shortstacker having a mathematical advantage you will have a true understanding of what they are talking about.
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*Even good players sometimes get frustrated and go on tilt and will call with a ridiculous hand like 97s. For players who do this consistently, you now must fold your "non-showdown" hands such as low off-suit broadways and middle suited connectors.