p.s I was just looking at the analyses you did regarding AK vs PP. The idea is that if everyone folds round then AK gains equity because those with a rag ace would have called. Fair point, but say you have a situation that there are multiple limpers who fold at the AI, then the AK's equity is reduced. And this is just one AI scenario. How about AK vs Ax, say, which is a pretty common occurrence, or PP vs PP which is another one. My intuition (which could well be wrong) tells me that 0.5% as a naturally occurring phenomena over all pre and post flop all-ins just isn't credible. But, as you say, it can certainly be tested using a simulator loaded with typical betting patterns.

I'll bet your intuition is wrong.

This sounds interesting and could obviously effect interpretation of the results of the tests - do you have the details of your work so that we can have a look?

Sherman what is your estimate for the underdog effect based on card removal effects?
My estimate is less than 0.1%.

I do actually have a game simulator I got on a cheap poker tutorial CD so if I can get it to run without me constantly having to play myself I will set it running for, say 100K hands and see what comes out. I have to write a prog first which will do the mouse clicks for me and also program the extraction of the HH's from its machine format, so it might take me a while.

You might look into Wilson Turbo Texas Holdem too. It has a powerful simulator and well made bots that are realistic enough for this, but I'm not sure it will record the data you need for this particular statistic.

It's pretty much impossible to figure this out mathematically with any precision because it's too complex. You can make some assumptions and come up with directional predictions that are in the right order of magnitude (and those predictions turn out to be true empirically), but beyond that you need to simulate it.

I don't have an estimate. I don't need to make a point prediction to think that your intuition (as stated previously) is wrong. I know what the data from multiple unrelated poker sites look like. They all point to the same thing. I don't need to create a simulation because the data already exist.

I have found a free simulator which will enable me to run about 700 hands an hour without me having to play myself. It is running as I write. I plan to run a lot smallish simulations (say 1000 all-ins) then plot the results of each as a distribution about the mean.

I find it odd that everything I have read about large scale studies say all the data from multiple sites show no bias from what one would expect. Where are the 100K all-in studies which show a 5 SD bias? Also it has been done to death how any deviation from expected win rates would be immediately obvious when studying HH's. Now it appears any such studies would be meaningless without knowing the magnitude of the card removal effect, which nobody seems to have any idea about.

This is quite an old article (Spadebidder contributed a comment) but the only one I can find that discusses card removal effects and possible favouring of the underdog:

http://www.notedpokerauthority.com/a...et-caught.html

Just a tip - run some simulations using heads up games as a 'control'...

Also - if you're looking to simulate how people play use the analysis tab on PTR. It shows how tight/loose the whole population at a given game is. For example:

http://www.pokertableratings.com/gra...-usd-stars.png

Correct, but it takes a *lot* to get the results to hit expectation to the precision he is looking for and provide a baseline for the natural bias caused by card removal. Underdog hands as a group will have something close to 35% average equity. That means the SD on 1000 all-in hands is 15, and +/- 15 hands when you expect 350 is an 8% range for just 1 standard deviation. 2 SD will have a 16% range. So 1000 all-in hands isn't going to tell you anything at all.

If you do 100,000 all-in hands now the SD will be 150 hands. If we expect 35,000 then that's only +/- 0.4% for 1 SD, or 0.8% for 2SD.

So the bottom line is you need to simulate about half a million all-in hands to get a read on this. And in a full ring simulation with realistic bots that don't shove every hand, that means you will need tens of millions of hands played, perhaps as much as a hundred million.

You need a real high speed simulator that can play 10,000 hands per minute, not 1000 per hour.

Well I will have to see how I get on. One problem I have is that the simulator stops when the SNG finishes. I could use huge chip stacks but you don't get many all-ins then and I want to try to model the types of games which are normally played. How many samples I will need is a function of how big the effect is. I can dedicate an old laptop to churning out the results 24 hours a day. Obviously if someone with supercomputing capability was prepared to get involved it would make matters much easier.

Where I am at just now is completing writing the software which will extract the info I need from the software's HH file. This should be finished this evening.

I am extracting both pre and post flop all-ins together with relevant board cards. I will keep a record of how many players are left on the table for each all-in so will have some samples of HU when the SNG is down to 2 players.

BTW Laughing Assassin I sent you a couple of private messages which you don't seem to have responded too. I was interested in what results you got with your million PS HH's, rather than the limited set you used for your published results.

Been thinking a bit more about this and am wondering if the following proposal sounds reasonable:

I could easily write a program which would deal out a 10 handed table, then just put the top 2 hands all-in preflop against each other, calculating the preflop equity taking into account the removed cards held by the other players. I could compare this to the equity without the removed cards. It would only only take a few hours to generate to generate 100K points which I could plot against each other. If there is an underdog effect it should be apparent when I plot one against the other isn't it?

I am not saying it would necessarily be quantitatively correct compared to actual game play, but it should be of the right order of magnitude at least.

I am still working away generating full synthetic HH's from the other simulator but I am only getting HU all-ins around 3 or 4 per game so I am never going to get up to a big enough sample for this purpose. However I plan to use the data also for seeing what proportion of hands end in quads, fh, fl and str which I can compare to real HH's. I think this could be interesting too.

It should be obvious to you why that won't work - the problem is not that the cards were dealt to other players, it's that those cards weren't good enough for them to play them. If there's no action by the other players who dealt in, then they might as well not have been dealt in - what's the difference between those cards in their hands and the ones in the bottom of the deck.

This. His idea will average out to a heads up game and all-in results will converge to exactly on calculated equity, with no bias.

wykh - if you really want to do this you will need a high speed simulator with realistic bots that make decisions based on hand ranges and opponent actions.

I see what you are saying. Can you just explain the mechanism that the bias should occur over large samples then? In Spadebidders study he looked at 10K HU PFAI and saw a 1 SD swing to the underdog which I thought was meant to possibly have something to do with card removal effects.


I can see how, if you are often getting a situation where say a pp or suited connectors are going AI against Ak and AQ at the same time, then the pp gains in value. If these types of multi-way AI's are occurring more frequently than other types of multiway pots then it could provide a systematic bias.

But the effect I am seeing in actual HH's has only ever covered pre and post flop with a single caller. How can the equities become biased on such situations?