
The Worst Hand Always Wins
Been looking further at my preflop allins from one site I play and found some curious results:
I divided the data into 2 groups, those for which I had 50% equity or greater, and those for which I had less than 50% equity.
For the first group (1894 samples) I had average equity of 0.664 but won only 0.634. This has a probability of 0.2%
For the second group (1245 samples) I had average equity of 0.331 but won 0.371. This has a probability of 0.1%.
So in summary when I went allin preflop with the best hand I didn't win as often as I should have, but when I went all in with the worst hand I won far more than I should have.
I repeated the exercise for another site and found the same thing, although the respective probabilities were 1.6%/1.2%. On a 3rd site I was way below for both the >=50% equity and the <50% equity (5%/3%) and on a 4th
also below for both groups (26.7%/3%).
Has anyone else noticed anything similar?


Results
Originally Posted by kalfred Been looking further at my preflop allins from one site I play and found some curious results:
I divided the data into 2 groups, those for which I had 50% equity or greater, and those for which I had less than 50% equity.
For the first group (1894 samples) I had average equity of 0.664 but won only 0.634. This has a probability of 0.2%
For the second group (1245 samples) I had average equity of 0.331 but won 0.371. This has a probability of 0.1%.
So in summary when I went allin preflop with the best hand I didn't win as often as I should have, but when I went all in with the worst hand I won far more than I should have.
I repeated the exercise for another site and found the same thing, although the respective probabilities were 1.6%/1.2%. On a 3rd site I was way below for both the >=50% equity and the <50% equity (5%/3%) and on a 4th
also below for both groups (26.7%/3%).
Has anyone else noticed anything similar? I looked at hands for this year
First group (1010 hands)  average equity = 70.9%, win percentage = 68.18
Second group (1083)  average equity = 28.96, win percentage = 32.2
Not sure if this means anything. But  since you asked  there it is.
I do not think rigging would ever manifest itself in EVs other than if you are comparing when you are losing/winning in Tournies  i.e., I believe that your EV in terms of hands won should not vary when you have $1500 chips vs $15,000 chips. Mine does and that is bothersome. But  ultimately I don't think that is where the real rigging will be found because (a) most hands you are not Allin and therefore there is no equity and (b) it does not show what happen to you to get to  EV. For example, you have a hand where you are 91% fav on the turn, you bet, villian calls  villian hits 3 outer on river and you are 0% on the river when all the chips go in and the All in Equity is calculated at zero or  no one is all in  just a lot of chips in the pot  again  no all in equity calculated.
Long winded way of saying the real analysis is that are your hands progressing/digressing in a statistically acceptable manner. e.g., If your are 90% on the turn  is your hand holding up through the river 9/10 times (again  regardless of whether there is an al in)?
There is no software I am aware of that calculates this so if you are interested you have to do it manually which is a real ass ache. You also don't know hands that were folded. For example  let's look at 20 hands where you had AA. Say 10 of those hands went to showdown and you were an 80% fav in all 10 at the time the turn hit  but you only won 5 (50%).
Assume that the villiian mucked the river in other 10 hands. For these you don't know what your % was on the turn and you can be pretty certain that your villian missed the river. Do you count all of those as instances where you won where you were 80%?  If so  you really won 15/20 (75%). A completely different result from the 50% rate above. The issue is that you can see hand after friggin hand where you went into the toliet far more than you should have and never see what the villlian had when you didn't  all of which points for the need of independent audits of HHs where someone can see all the cards that were held. It is the only way to really validate one way or another and it is why those who argue  if it were rigged  don't you think all of the players would have seen something wrong by now?  are fundmentally wrong. Because they don't have access to all cards and therefore they would have no idea if something were wrong or not.

Thanks for your data Eldave.
I did the binomial calculation on your stats:
For your good hands you are 1.86 sd's left of mean with prob of 2.9%
For your bad hands you are 2.28 sd's right of mean with prob of 1.0%
This is pretty similar to my data.
I wrote my own software do do the calculations of actual/expected equity. I do not work in chips or BB's, just give an equal weighting to each sample.
I am also pretty dubious that rigging or cheating would manifest itself in such an obvious way. If it were indeed true across the board it would mean that donk play (ie calling or shoving allin preflop with a rag hand) was getting disproportionately rewarded compared to solid tight play. This in effect would erode the earnings of the good players in favour of the bad players.
There are indeed many strange things that can occur between Turn and River, which would not be picked up . Anything postflop is also influenced by skill, so you are never going to prove anything. Unfortunately, therefore, you are more or less stuck with working with preflop allins.
I am just interested to know if other players have noticed anything similar with their data sets.

Interesting. how do you get these percentages in pt3?

Pt3
Originally Posted by bizkit Interesting. how do you get these percentages in pt3? You don't  you have to generated a report on PT3 (report section, select all in equity), export the report to Excel and do the calcs there  pretty straight forward to sort the spreadsheet by EV Equity and then split the spreadsheet 50+ and 50 and below. You can use the spreadsheet to calc the average equity for your hands in the two ranges. In terms of tabulating the number of losers I just wrote a macro that if amount won was less than zero assign a value of one  then it's pretty easy to sum that column to get the number of losses. In retrospect, I probably overstated the number of hands one since I think my approach would have counted all ties as wins.

Welcome
Originally Posted by kalfred Thanks for your data Eldave.
I did the binomial calculation on your stats:
For your good hands you are 1.86 sd's left of mean with prob of 2.9%
For your bad hands you are 2.28 sd's right of mean with prob of 1.0%
This is pretty similar to my data.
I wrote my own software do do the calculations of actual/expected equity. I do not work in chips or BB's, just give an equal weighting to each sample.
I am also pretty dubious that rigging or cheating would manifest itself in such an obvious way. If it were indeed true across the board it would mean that donk play (ie calling or shoving allin preflop with a rag hand) was getting disproportionately rewarded compared to solid tight play. This in effect would erode the earnings of the good players in favour of the bad players.
There are indeed many strange things that can occur between Turn and River, which would not be picked up . Anything postflop is also influenced by skill, so you are never going to prove anything. Unfortunately, therefore, you are more or less stuck with working with preflop allins.
I am just interested to know if other players have noticed anything similar with their data sets. Your welcome Kal  I agree that  if one is looking at only their own hands all in is pretty much what you are stuck with  sadly  probably won't tell you much. There are some other tests you can do (e.g., are you dealt PPs within expectations, What percent of time does AA showup when you have KK, what percent of time you flop certain hands, etc). But  can't imagine that any site would be stupid enough to rig it in those areas  what you really need are all the complete hands  alas  the problem.

I go over the thread and I am happy to say that I have learn something useful here. especially in pt3. I though the percentage calculation is a little bit complicated but its not. Pretty cool to share this Ideas guys. Thanks.
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