shalako wrote:
...I do not use models but stats to assign a range to the villain
The stats are the input, the model is how you go from stats to probabilities. Your model is one where (I guess) the probabilities are uniform across a range, then zero for all other hands. That kind of model can work fine for lots of cases - because in lots of cases the range you use is representative enough of a more realistic distribution that it doesn't make much difference - but I still think there will always be compromises with that approach.
shalako wrote:
since I use range equity entirely.
Note you can use a similar approach with a full probability distribution. ie your equity against a full distribution of 1326 hands is the sum of your equity against each hand multiplied by the probability of that hand. You can pre-calculate equity matrices of every hand against every hand (for every board!) to make those calculations lightning fast.
shalako wrote:
If a guy has a low 3 bet % then its pretty straightforward (as he is tight) but if he has a high 3 bet % then I know there has to be some air in his range. The problem is what type of air is it? This is where a model could really fail. For example..some players will 3 bet the very best of hands (AA, KK etc) and the very worst of hands (32, 72 etc), others will 3 bet nuts, AX, KX (blocking type hands) and suited hands of all types. So players could have identical stats but completely different ranges. Having a model would have same issue yes?
If you can observe such differences in behavior you can calibrate your opponent model to reflect them - or you can take a more humble approach and make sure that your model doesn't impose too much contrast in those areas where you know it might be inclined to be too confident an opponent doesn't hold a particular hand.
If we define the contrast of a model as being the ratio of the probability of the most likely hand to the probability of the (still possible) least likely hand - then there are two types of mistakes you can make - not adding enough contrast - and adding too much. In my experience adding too much is the more dangerous of the two - i.e. you end up making really insane bluff re-raises on the river as you your model is so sure the opp can't have a certain hand - when clearly he somehow does have it!
- PeppaPig