Can anyone tell me what the probability is of being dealt the same two starting cards, in the exact same order (i.e. 6h 9s twice) in back to back hands in a 9 person game of hold 'em?

The reason I'm curious is this has happened to me 3 times in the past 300 to 350 hands I've played on full tilt. And, this isn't the first time I've noticed this happening. Though I don't think it has ever happened to me this frequently before.

Thanks

(1/52)(1/51) = about 1 in 2500, assuming you only play 2 hands.

If you play enough, 100%.

Considering specific order as you mentioned, the chance to see this 3 or more times within your NEXT 350 hands is ~1/1036 using the binomial distribution. However, the 350 hands is obviously cherry-picked because that's just when it happened. We don't know how many hands you have played overall, but here are a few examples.

If you have played 20k hands, the chance to have seen this happen within any series of 350 consecutive hands is very close to 100%. If you have played 10K hands it's about 99.5%. 5K hands, about 80%. So it isn't something unusual at all. The chance goes over 50% about 3200 hands played.

This illustrates the fallacy of looking at an ex post facto cherry-picked sample to tell us anything.

Thanks for the in depth answer. Its good to know that this isn't all that uncommon. Though I do still find it strange that nearly every time (at least 90% I'd say) I play on full tilt I have this happen sometime during the session. I've been playing different forms of poker since I was a child and I've never experienced this type of thing with the frequency that I do on that site. Maybe its just the percentages catching up with me, but it still seems fishy.

Or maybe it is that Full Tilt deals cards way way faster than the cards you are used to playing a child. Or maybe your getting old and your memory isn't as good as it used to be. But seriously, this is a common complaint and it is almost uniformly the fact that people play so many more hands online that biases their judgment. When you play more hands, "freaky" events "seem" to happen more often than they should. But they don't.

I thought about that thoroughly before I even made my original post. I can see it being a factor to a degree, but not to the extent it seems take place. You see probably about 20-30 hands an hour in a live game and about 75-100 in a typical non-turbo online game, so that is about 3 to 4 times more hands. This "same cards dealt two hands in a row" thing seem to happen to me much more than 3 to 4 times more often than I have ever experienced before playing online poker on full tilt, and it has been uniform for the 2+ years I've played there. I also never noticed anything like this when I used to play on poker stars. But, as I said before, maybe its the percentages catching up with me.

I really should have taken more classes in math. Given your 20,000 hand sample example, on average, how many times in those 20k hands should I expect to see this phenomenon happen (2 hands in a row, exact same cards, exact same order)?

Every hand has a 1/2652 chance to exactly match the hand that came before it, including order. So 20K/2652 gives us the average number of times it should happen, or about 8 times. About 35% of the time it will happen more than 8 times, and about 14% of the time more than 10 times.

These numbers come from using the binomial distribution.

Well, don't just speculate. Post the actual data. Memory biases are well documented whereas "online poker is rigged" theories are much more well speculated and much less well documented.

I never said online poker is rigged. I would say that, in my experience, the randomly generated hands don't seem to necessarily produce the same results as hands dealt in a brick and mortar scenario.

As for posting actual data, I might just start trying to compile some. Though, considering I'm spending nearly all my poker time playing at the new Rivers casino (Pittsburgh) which is a 5 minute drive from my house, it may take me considerably more time to do so than it would have a month ago. Do you know of any studies that have been done concerning this type of thing? I would be very interested to read them, whether they support my opinion or not.

http://www.spadebidder.com/

This site has some very good articles that demonstrate quite convincingly that every aspect of texas hold'em poker online lines up almost perfectly (and deviations are well within normal ranges) with what one would expect based on the nature of a 52 card deck.

Thanks again spadebidder. This gives me a good gauge as to whether I'm seeing this more often than I should, and it seems to me that I am. I will have to keep track of the number of times I see this vs. the number of hand I'm being dealt. Maybe my memory is exaggerating, but 10 times per 20,000 hands seems really, really low compared to what I think i consistently see.

Cool, thanks, I'll check it out