Otherwise I agree totally with your thoughts!

I don’t find anything wrong with your method. By and large it works fine on all but the closest calls. I think most math minded players do a lot of quick and dirty math at the table, at least I do.

In the above example, my thought process is “I know 1500:700 is a little over 2:1 and I know 15 outs with one card to come is a little over 2:1, so I can either call or fold without making too much of a mistake.” I do have to point out though that on the turn there are 46 unseen cards left (you forgot about the turn card).

I believe the odds against making your hand on the river is 32:15 = 2,13:1. There are 47 unseen cards left in the deck on the turn when you subtract your two hole cards and the three cards on the flop. But you’re right that with this more exact calculation of the odds against making your hand on the river, the call is actually +EV (barely though). The mistake I made was to use the easy rule of thumb to calculate poker probabilities, which isn’t exact.

Thanks for your feedback!!!