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Hello,

Well its late I have been drinking. In the back of my mind I have been thinking about a routine that would tell me how many combos of nut hands I can rep based on my actions. I suppose the solution would be to take the board and figure out what hands make the nuts, 2nd nut, third nut etc. Then I can determine how many of those hands could be in my "perceived range". To make a successful bluff I think you need to be able to rep at least 10 combos. Poker is not only about analyzing EV against his range but also analyzing how he perceives my range as well. I think this is a hole that I have missed.

What is interesting about this can I also want to represent a bluff when I have value. So it works both ways.

Has anybody else worked on this? This is the kind of stuff that keeps me up at night. I need a life...

I finally figured this out after it came to me. It was staring me in the face as to the best way to do this for weeks and only took a few minutes to implement. The best way to rep value is to take the bots general stats that a villains HUD would see and form a likely or "perceived range" for various situations (basically only three: button raise ip, bb call oop or 3B. Then run thru each hand combo to see if its top pair+ or strong draw. This will give me the exact percentage of my range that I could bet for value on this particular board. I think that if I can rep at least 10 combos of value then I can make a successful bluff along with other factors. The other factors would be if I am in position and he checks in front or I see his range as being weak heavy using combinatorics.

This doesn't only apply to rules based bots.

I suspect a reason that the MCTS approach hasn't worked well is that it hasn't taken self image into account. Sonia did though.

Also there are two aspects to this. The short term issue - is the bluff I'm about to make plausible? - and the long term issue - can I really maintain these stats over 100's of hands without someone noticing?

Yeah that is what I am trying to figure out..is the bluff plausible based on the villains read of my range.

I have posted in other forums trying to get more GTO advice on this problem. One bit of info I got was the max % of the time I should be bluffing in any given spot. The formula is based on the betsize:

X = BetSize/1+2*BetSize

So if you make a standard cbet of half pot you should not be bluffing more the 25% (0.5/1+1) of the time. So basically it needs to work 25% of time to be profitable.

So now we take the combinatorics of a particular hand. Lets say I am 3 betting 200 combos pre and on the flop I can only value bet 39 combinations of my perceived range. So of that range I can only be bluffing 25% of it or 9.25 combinations. I believe that is how it works but I am not really positive yet.

So according to what I had heard that I should be repping at least 10 combinations when bluffing then the above scenario does not meet the criteria and I should not bluff.

I took this routine to the next level as I thought it was missing something. What I forgot about was I needed to factor in how much of villains range is likely folding if I make a raise. So I took the combinatorics of his range which includes all air and some marginal pairs and calculated EV as follows

Win = PotSize * FoldEquity
Lose = PotSize+BetSize * (1-FoldEquity)
EV = Win-Lose

So in order to pull off the bluff you not only have to be able to rep 10+ value combos but also calculate what part is his range is going to fold.

Well I changed this routine even more making it even more sophisticated. One thing I had forgotten about was the bots calling range. If the bot is not leading the betting then it cannot rep as many value hands when it decides to bluff. So if the bot gets to the turn or river by calling then the value combos it can rep are greatly reduced. It could if it was slowplaying but some hands would not make sense such as a set on a two flush flop. Any decent player would eliminate those hands from the bots turn range as they would generally be protected by raising or jamming the flop depending on the preflop action. So repping 10+ value combos is not as easy as it sounds. It obviously is very board and action specific.

I also simplified the fold equity math:



So the process of selling a bluff was not as easy as I had first thought. Hand combinatorics of both the villain and the bot play a huge part of it.

Shalako, you do this kind of bluffs in HU or also in 6 max / 9 max ?
And also are you going to exploit all of your opponents, or it depends by their stats, and if yes, what stats?

This is for HU but it would be the same for 6 or 9max. I only have it bluffing if I have no showdown value/equity. I am not really using any stats but if the guy is folding too many turns and rivers then none of this really matters anyway. Like if the guy is folding to 60% of turn bets then you have to bet 100% of turns until he adjusts. The villains folding stats are the most useful.

As far as stats to determine whether to bluff or not the hand combinatorics is the place to start which is not really a stat. So to pull off a bluff you need two major items of info. 1: can you rep a 10+ combos and 2: how much fold equity is in the villains range. To do this your going to have to break down ranges which is a royal pain.

One thing to remember is that if your leading the betting and the villain calls then there is not much fold equity in his range as he would not continue with total air. So this is when you use your turn folding stats to determine whether to bluff more often then not. The max time you should bluff is based on the your bet size if the guys stats are neutral (example is his turn fold is 50% or less). So if you make a psb on the turn you cannot bluff more then 33% of the time in that spot.

Why don't you bluff dry pots also?

I do bluff dry boards but obviously not as often as my range is very narrow. Any decent player would just call or rebluff. Without getting into the math based on the bet size your generally going to have to bet 33% as bluffs regardless of board types anyway so its not much of an issue. What I mean by that is you would have to bet the turn as a bluff 33% of the time if your leading the action on a dry board anyway. Not leading and IP and the villain checks you would bet as a bluff 33% of time as well to keep him honest unless you have some kind of showdown equity.

What is interesting is the bluff percentage is also the percentage that you should be calling as a minimum..even with zero equity otherwise its a leak. So in any given situation you really have two options..you either have enough equity to call or your forced to call/bluff raise due to the fold equity he needs from you. Because if you dont then he is going to win on fold equity alone as he is always getting value from you on his bluffs.

Balancing all this is not easy!

I actually thing I am using the wrong formula above. I think it might have to be 2*BetSize instead of 1x. Everybody seems to have a different opinion on this one so I am not sure which is right

I just realized I can use this same routine for repping a bluff when I have value. So assume the board is dry and I have a strong hand. I cannot really rep many value hands but I can rep a bluff very easily. This would be a good time to overbet or even shove as it does not make any sense.

After a few months I finally found the correct formula for figuring out the max amount of time you should be bluffing based on the betsize. I was confused after seeing several variants:

MaxBluff = (BetSize/(PotSize+BetSize)))*10

Also..the old formula I was using:

MaxBluff = (BetSize/(PotSize+BetSize*2)

is actually the minimum river calling frequency..or how often we are going to have to be ahead in order to make a call. This is just the minimum equity that is needed.

makes no sense. if you bet pot you should be bluffing 500% of the time? (???)

the old one was correct though. you want to make the opponent indifferent between calling and folding.

this of course given the oversimplified case of nut/air vs bluff catcher scenario.

Explain this to me please. I really have seen a ton of different ways that this is done and all of them return different results.

I studied this a bit further and asked a few GTO guys. One thing I hadn't considered was the optimal bet size to make him indifferent

So I take my perceived range which only includes hands I could actually bet for value and total air OTR:



Example: Lets say I have 36% bluff combos and 64% value combos. So in this case I actually rep quite a bit of value. So the optimal betsize in this case would be 1.3 pot which would make him indifferent to calling or folding. If I was bluffing in this spot it would look pretty weak to bet 1.3 pot however...but my range looks so strong that it looks like it could be an act. So I guess it all balances outs which is why its optimal for a baseline bet...I think..

This GTO stuff can get confusing.

EDIT. One thing about this formula is that it assumes your range construction is nearly GTO correct which I believe is 2:1 value to bluff combos.