[John Paul]

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Before you write something nasty about me because of the subject of this post, please hear me out and keep an open mind.

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Mojobluesman,
Folks have been a little harsher on this thread than you deserve. I did try to keep an open mind, but I think there are some mathematical errors in your post that make this seem less likely than it really is.

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I just played a relatively short session (about 1 hour)where I played 5 hands past the flop. I lost all 5 hands and wound up losing 30BBs for the session. It wasn't fun, but it was no big deal.

The big deal was this.

I had the best hand going to the river in 4 of the 5 hands and lost to 2 outs once, 3 outs twice, and 4 outs once.

The probabilities of losing with "x" outs on the river is:

2 outs - approx. - 4%
3 outs - approx. - 6%
4 outs - approx. - 8.5%

Individually, no big deal.

However, losing this way in what was essentially 4 of 5 hands taken to the river is a mind boggling statistical oddity. It's about 1 out 100K for 4 consecutive hands. Probably a little less for 4 of 5, but not all that much if you consider that the 5th was pocket TTs that lost heads up.

Now I know you are going to say we've all been through tough beats. 1 out of 100K means it's going to happen and it just happened to happen to you. However, the problem is that this is the 3rd time it has happened to me in about 7K total hands of play.

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Lets look at that more closely.

Based on the % you give above, the proportion of times you will lose these 4 hands is a row is
.04*.06*.06*.085=0.00001224
Dividing 1 by this gives you a 1:81,698 odds, not 1:100k which is a lot less - but still pretty unlikely.

However, these odds aren't right. I assume what you are dong is dividng the number of outs by the number of cards you dont know so 2/46, 3/46, 4/46 - since you know the 4 up-cards and your 2 hole cards. However, you rounded them, the real numbers here are:
2 outs = .0435
3 outs = .0652
4 outs = .0870
In every case your numbers were a little low. So if you redo the calculation with these numbers, you now have a 1:62156 event. More likely still.

But, that is still wrong. You see, in order to have a 2 or 3 or 4 outer, you have to specify the villian's hole cards. Without the hole cards the outs against you don't make any sense. So it should be 2/44 or 3/44 or 4/44. When you do this you get:
2 outs = .0455
3 outs = .0682
4 outs = .0909

Redoing the numbers again gives you 1:51981 which is a lot less then 1:100k.

You stated in the thread that all the hands were heads up at the river and that you counted the outs right, and I don't have any reason to doubt you. But, there could have been folks on the turn that were drawing to runner-runners that did not hit, which ideally should be worked in.

So - how likely is it to happen in 7k hands. You haven't been keeping track, so I will have to estimate. Based on the stats in the FAQ, in 7000 hands you will have seen the flop about 23% of the time = 1610 hands. Of those around 30% will have gone to showdown = 483. I will guess that you are ahead about 50% of the time on the river = 291 hands.

At this point I'm not positive how to proceed. There are 288 4 hand runs in here where you are ahead at the river. Dividing 288 by 51982 gives us 1 in 180 = again unlikely but hardly proof of rigging. However, the 288 runs of four hands are not independet, so I may be doing this wrong.

Also there are lots of other factors not included here. I looked for exactly four hands that loose to a 2,3,3 and 4 outer. But if you had lost to run of 1,2,2,4 outers that would seem bad too, so the odds of that happening should have been included, etc. And, as DBMFan23 pointed out, even if it was really unlikly that most poker sites have so many runs of 7k hands that all sorts of stuff happens.

Finally, how likely is this to happen 3 times - unlikely but hard to calcuate exactly without knowing:
1) what were the situations the other 2 times
2) how unliklely a beat do you need to notice it
3) how many villians were in the hands on the other runs as well.

So,
I do think you had an unlucky session and 7k run, but I don't think the odds against this are quite as bad as they seem if the cards are being dealt fairly.



John Paul
(who's biggest losing hand at 1/2 is KK over 4.5k hands)