I just played in an online Texas Hold’em tournament. An extraordinary event happened. In the space of four consecutive hands, I got pocket aces three times. What are the odds against this?
What are the odds of this happening on any single run of four hands?
Assuming that finalists play about 100 hands in a tournament, and I make the final, what are the odds of it happening to me during a given tournament?
If there are 45 players in the tournament, and each play an average of 40 hands, what is the chance that it will happen to someone? (even if they then get knocked out early)
I didn’t win many chips. Everyone folded all three times. I did, however, finish second out of 45.
This is actually the second time something like this happened to me in a tournament. A couple of years ago I got aces, kings, and aces in four hands.
[Warning: My probability calculations are rusty, so I may have screwed up the numbers somewhere]
The odds of getting specifically pocket aces is 4/52 * 3/51 = 0.0045, or 0.45%.
So you would expect to get an ace pair roughly 1 in 220 hands.
The odds of getting specifically pocket aces 3 out of 4 times (if you only play 4 hands) is 0.00000037, or 0.000037% of the time, so the probability is about 1 in 2.7 million.
However (as you intimate), the chance of it happening in 4 consecutive hands goes up the more hands you play. If you play 100 hands, you’re essentially giving yourself 97 chances to try for the ‘success’, instead of just one. Which makes the probability about 1 in 28,000.
Assuming all players play at least 4 hands, the probability of pocket aces occurring in 3 out of 4 consecutive hands for one player is approximately … 1 in 1,630.
[quote=“Peter_Morris, post:1, topic:921106, full:true”]…I didn’t win many chips. Everyone folded all three times. I did, however, finish second out of 45.
This is actually the second time something like this happened to me in a tournament. A couple of years ago I got aces, kings, and aces in four hands.
[/quote]
Thanks for the answers and the math, everyone.
Peter, then you weren’t raising frequently enough. Or you had a table of rocks. Or, and this is what would happen to me, you were on the bubble. Which positions were you in, and how big was the table, when you had your run?
There are a lot of random things that can happen. The odds of going a long time without something that is very statistically unusual happening is itself very statistically unlikely. If Peter had “called his shot” before the tournament then that would have been very strange.
I once rolled 9 7s in a row playing Craps, over 10 million to 1, but there are a lot of other weird things that could have happened but didn’t, something like that is bound to happen eventually.
It was early in the tournament. 9 players at the table. Nowhere near the bubble. I was in late to middle position. Most people had folded before I bet.
I doubt it. The software is tightly regulated. If they had a faulty random number generator they’d be shut down.
And it isn’t as unlikely as all that. If Smudge777’s calculations are correct, it would happen once every 1630 tournaments. Given that this type of tournament starts about once every 2 or 3 minutes, that means somebody will have the same experience about once every 2 to 3 days. And that doesn’t even include the various other types of tournament running on the site.
Its a bit more complicated than this, because streaks are not independent, if you get a run of four in hands 1 through4, then the chance that you also get a streak of four in hands 2 through 5 go up to 1/220. But your numbers are approximately correct, certainly to the point of indicating the magnitude of the likelihood.