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I have been using Top X% of hands to determine a preflop HU range like normal (ie if the villain raises 80% of buttons I am putting him on top 80% of hands etc) but I think it is just not a realistic representation of what players actually play with. The villains calling range can really be off I have noticed. This discrepancy been bugging me for awhile. Does anybody have any average data on this from real HH files?

you have to assign a bluffing range as well. Sure, for 80% it doen't matter but if the positional PFR is e.g. 35% there are some bluffs involved. Its clear thar the Bluff percentage depends on the opponent.

The harder part is to define which hands are these bluffs. Is he is bluffing small Axs or other hands like SC-> this is very important for defining your defending range.

Yeah that is really difficult. There is really no accurate way to do it without a bunch of history on the villain. The only real solution I have found to that problem is to try to end the hand preflop by heavy use of the 3 and 4 bet and putting him on the defensive and see how he reacts. Most players will not 4 bet or shove air so if they call you can really narrow the range down to hands from top 10 to 25% area or typical flatting hands. The only way to get information without data is to raise

Hi,

Using an action % to polarize an opponents probability distribution of hands in that way can be very inaccurate.

e.g. if someone raises 25% of the time in a certain spot - then assigning zero probability to the bottom 75% of hands is far from realty I think.

Instead you want an opponent model which will bump up the stronger hands but still leave some probability on the others.

I would recommend getting away from the frame of mind of an opponent having a 'range' - ie a set of hands that are still deemed possible - instead think of a probability distribution of all possible hands. Some hands may be much more likely than others - but the only hands with zero probability are those that have been excluded because the cards are on the board (or in your hand).

As a hand progresses this probability distribution will evolve with the actions - and can become very confident that an opponent has or doesn't have a given hand.

Well that was always my approach anyway .

- PeppaPig

Hey. Yeah that makes sense but I do not use models but stats to assign a range to the villain since I use range equity entirely. 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?

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.

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.

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

Hmm..this is very interesting. Yes I have seen the bot do exactly that and get itself into trouble. But I tell myself it cannot be right all the time so I have not done anything about it. It does tend to make the right play more often then not.

But now you have me thinking that it can be improved. Most of what you say is a bit over my head as I have a rule based bot and I am a bit clueless when it comes to CFRM, NN, etc. It is all kind of greek to me. I did read your reply on my other thread and now I am thinking that I should be using a combination of both rules and sims (or a lookup table of prior run sims)