Has anyone else noticed that when playing a HU Sit & go match (turbo or regular speed) there will, I would say, 90%-95% of the time be a hand played when both players have the same holding of cards (75 vs. 75).

I've noticed this when playing way to often and find it a way above standard in terms of 4 random cards being dealt to 2 players over a course of a match. Of course it can't always be seen if the hand doesn't go to showdown but I've played over thousands of heads up matches and I can say confidently that this scenario comes up almost all of the time once through out the match.

Any one else notice this? Or maybe its just standard and I'm thinking its not. I have not done the math, I wouldn't even know how.

I find it peculiar and don't know what to make of it.

If it were true (which I doubt), the site would be doing so on purpose. If they do so regularly, the games will last longer, which is obv bad for the site. So, basically, no, you're an idiot, etc.

Some quick math, it is not exact, but should be close. odds of 2 players having same hand ~(3/50 * 3/49) = ~.0036

If a match lasts 50 hands, the odds of this scenario, with p=.0036, occurring at least once is about 1/6 (used binomial distribution).

Shouldn't it be: (6/50 * 3/49) ?
Since the first card can be any of the two the opponent got dealt.

This results in a 0.7% chance of getting same cards.

yea and that would raise the odds of seeing this in a 50 hand match to about 30%. The point is that it is not as rare of an occurrence as the OP imagines. I do not know how long the average hu match lasts, if it is 300 hands, then the op may indeed see this situation nearly 90% of the time, as the odds of it happening in such a match would be ~88%

This results in a 0.7% chance of getting same cards.


This means it will happen once in 142 hands if everything runs even. It never runs even. If he's continually seeing it in 90% of his matches this is an anomaly.

Edit: going to explain this better

When something has a low % of failure vs success you actually bury that %. .7% will be more likely to appear less than the desired .7%.

10% chance:

1= Success

2= Failure

12222222222222222221 = 18 misses in a row if you allow the 10% to come off both times

If we "assume" every one of your matches last close to 145 hands it would have to hit at a 90% rate (you are seeing it 90%). Then you would have to "assume" that it will appear in a position where it goes to showdown 100%. Strong likelyhood it's not going to happen.

Computer deals, especially continuous shuffle (Fulltilt), are flawed and your are experiencing an anomaly.

If you do it this way yo have to divide by 2 to get rid of the duplicated hands. Like if I have 72o then you're right, there are 6 ways to select your first card (7 or 2) and 3 to select the 2nd (whichever you didn't select first). But 72=27 so you double count.

No.

OP hasn't even established how often he's seen it, how many matches he's played, what percentage of hands go to showdown, or even indicated that he had any idea how often it SHOULD happen. All he's said is that he thinks it happens "too much"

No, (6/50)*(3/49) is correct. This is (6*3/2)/C(50,2).

The first card can match either card with probability 6/50, and the second must match the remaining card with probability 3/49.

Using fractions is the same as using permutations rather than combinations.

6*3/(50*49).

Ha, ok, you're right.

Lots of numbers being thrown around (especially early on) with very little math actually shown (not that it is always necessary, but if I don't know who the hell you are, I kind of want to see your calculations).

The event occurs with 6*3/2 / C(50,2) or 9/1225 probability.

1 - (9/1225) = .992653, which is the probability of not getting the same cards on the same hand.

If we have 50 hands we get (1-(9/1225))^50 = .691613, which is the probability of not sharing the same hand in 50 hands.

1 - .691631 = .308369, which means there is about a 31% chance of this happening if you play 50 hands. From here, it is easy to adjust the figures based on different numbers of hands played and number of SNGs played (by using the binomial).

I think what you are trying to say is that with a very low occurrence frequency, you will normally need a large sample size to observe the event. Yep! For the 0.7% case, it should occur, on average, about once every 143 trials I would say.

IMO, your statement makes little sense.

BTW that percentage would than have to be further reduced because we are talking about the hands you see.

Anyway - I don't really understand why this "online poker is rigged" thread is in probability?

You have the same problem as me, we are dense and can't understand this stuff.

Like many similar threads, I think OP is probably looking for an explanation. One explanation is "FTP is rigged" and another is "my expectation of how often this should happen is wrong" possibly in conjunction with "I don't carefully keep track of how often it happens to me"

I appreciate everyone's input, I didn't expect this many replies in such detail regarding the math but it does shed some light. Sounds like the consensus is that this should happen around 30% out of every 50 hands. I'll pay closer attention to how many hands I play in a match but matches don't typically last more then 75-80 hands. I do play a style of poker that sees a lot of showdowns though.

My gut is that something weird is going on but I can't provide any backup (I don't use tracking tools) other then my anecdotal experience with playing.

I'll add to this as I continue to play and observe but if anyone wants to experiment with low stakes HUSNGs to see how this plays out for them. Or if a reg who plays HUSNGs wouldn't mind data mining their database that could add to this conversation.

Thanks everyone.

Isn't it less than 6/50 * 3/49? Opponent may have a pair, calculated probability seems to be chance of sharing same cards *given* that opponent holds unpaired cards, was that what the OP wanted?

For the more general problem I get 16/17 * 6/50 * 3/49 + 1/17 * 2/50 * 1/49

= 29/4165

i dont understand why you ever bother posting at all

Why does this even seem weird at all to you?

Incidentally, at a full ring table, there is a 23% chance on EVERY DEAL that two players at the table hold the same rank cards. It happens almost 1 out of 4 hands. So seeing it once or twice in a heads up match shouldn't even raise an eyebrow except in those who are just furiously looking for a pattern they can claim is not random.

Really 23% of the time full ring? I'd have never thought it'd be so high

If we have a decent unpaired hand and we see a flop against one player he is going to have the "same hand" more often that 0.73%. If we see the flop with AK in Full Ring against one player essentially we are looking for the probability that someone else as the table has AK cause AK is not folding.

Even in HU if we play 3/4 of our hands and so does our opponent when we see a flop with a unpaired hand that both players would play the chance will be approximately 1% as our opponent's range is about 3/4 of his preflop cards and there are still 9 hands like ours left.