getting 3 pocket Aces in a row

[valueplayer]

what's the prob. for that?
1/220 * 1/220 * 1/220 = 1/10,648,000 ?????
Thank you.

[BruceZ]

[Ray Zee]

its really only getting them twice in a row. see why? and actually its really only getting them the next hand. 220 to one. see that. if not think awhile as this concept will help you think about probability in the correct way.

[DanS]

Oh mighty Z,
Yes, I see why this is true. It was obvious to me instantly, so I won't spoil it for those to who(m) it comes across as a trick question.

I have two questions for you: what is the name for this phenomenon (if there is one, and I get the feeling like I learned it in Psych 101), and how do you take advantage (poker wise, not Montana/Deliverance wise [img]/forums/images/icons/tongue.gif[/img] ) of people who think this way without even realizing it?

Dan

[Cyrus]

"What is the name for this phenomenon ?"

All those mistaken beliefs are variations of the Gambler's Fallacy (aka Monte Carlo Fallacy, etc). The gambler sees 5 Blacks in a row in roulette and either believes a Red is "overdue" or that the Black "streak" will continue. (In fact, each result has again the same probability of occuring.)

To the mathematicians the "Red overdue" is a mistaken belief in negative serial autocorrelation of a non-correlated process. The "Black streak" is a mistaken belief in positive serial autocorrelation. (Ask BruceZ for a translation to English.)

In the case of back-to-back, or three times in a row, of a "rare event" such as getting pocket Aces, the gambler confuses the probability before the fact of unrelated events happening in a sequence, with the probability of each event happening separately in the sequence.

"How do you take advantage (poker wise) of people who think this way without even realizing it?"

Here's one : If the other players are allowed to make or see my hand and then, in a round soon after, I have approximately or exactly the same hand in the hole, I can reasonably assume that the average opponent will estimate the probability of me having again something like I had previously, to be smaller than it really is.

A distant variation of that theme is a play immediately after a multiway pot in which a lot of blood was shed. The next round is often an opportunity for someone to steal quietly (but steal early) with relative impunity.

[Mangatang]

It's like the old saying, "Lightning never stikes in the same place twice." Once lightning has stuck a spot, it is just as likely that it will stike that spot again as is any other previously non-stuck spot.

[Ray Zee]

its much more likely to strike the same spot again, then a non previously struck spot. it isnt a random act.

[David Ottosen]

Yes but according to Zeno's paradox, you will never get pocket aces. In fact, you will never even get one ace, as the dealer will never be able to deal it to you.

[FA_man]

I understand that these events are unrelated, and the gamblers fallacy, but I dont agree.

The question isnt what is the chance of being dealt AA again. The question is to be dealt AA 3 times in a row.

Are you telling me you are willing to bet me with 1:1 odds that I will flip a coin to tails 3 times in a row? This is substantially different than waiting for tails to come up twice and then betting on the next flip alone - at which point the bet would be even.

Am I totally bonkers on this?

[Cyrus]

"I understand that these events are unrelated, and the gamblers fallacy, but I dont agree. The question isn't what is the chance of being dealt AA again. The question is [what is the probability of being] dealt AA 3 times in a row."

Yes, this was the original question and the mathematical answer was provided by BruceZ, in this thread.

But Gambler's Fallacy was mentioned in the context that at every round the player has the same chances of getting AA. When a player gets AA two times in a row, the fallacy lies in the belief that getting AA for a third time straight is a different (and smaller) probability than the probability of being dealt AA in any round.

"Are you telling me you are willing to bet me with 1:1 odds that I will flip a coin to tails 3 times in a row?"

Well, depends who gets to take those odds. [img]/forums/images/icons/smirk.gif[/img]

"This is substantially different than waiting for tails to come up twice and then betting on the next flip alone - at which point the bet would be even [i.e. p=0.5]."

Correct about that call. And Mr Z said so, too, in so many words. Needs a little deciphering, is all.