Two Plus Two Older Archives  

Go Back   Two Plus Two Older Archives > General Gambling > Probability

Reply
 
Thread Tools Display Modes
  #1  
Old 12-31-2004, 04:25 AM
therockofgibraltar therockofgibraltar is offline
Senior Member
 
Join Date: Jul 2004
Location: Finland
Posts: 107
Default AA?

I raise preflop. Everybody folds to a player who reraises me. I cap with my AK.

Me and one opponent see the flop.
A-6-4 rainbow
I bet-he raises-I reraise-he caps.

turn is 8.
i bet - he raises - i went into calling mode and finally won the pot, he had A9s.

BUT the question ain't related to my "bad" play. It is a probability question. If I have AK and the flop contains one A, what is the chances that my opponent has AA??
Reply With Quote
  #2  
Old 12-31-2004, 05:22 AM
Stallion714 Stallion714 is offline
Junior Member
 
Join Date: Dec 2004
Posts: 3
Default Re: AA?

1 in 220 hands. Regardless of what you hold.
Reply With Quote
  #3  
Old 12-31-2004, 05:42 AM
niin niin is offline
Member
 
Join Date: Sep 2004
Posts: 94
Default Re: AA?

I know that's the chance he has AA before the flop, but can't you go back and recalc, given the fact that you know 2 aces are gone? He'd have to have 2 specific cards (and not just 2 out of 4 specific cards). Since we have more information, you should be able to get a better chance.

Just like people say "well, there's 2 jacks on the board, so the chances of him having a jack is reduced". Since 2 aces are accounted for, the chances of them having an ace is reduced?

So, given that 5 cards are known, would the chance be 2/(47*46)?
Reply With Quote
  #4  
Old 12-31-2004, 06:21 AM
maddo maddo is offline
Member
 
Join Date: Jun 2004
Posts: 36
Default Re: AA?

Looks correct to me.

The 1/220 comes from having 4 aces available from 52 cards:

4/52 * 3/51 = 1/221

But now there are 2 aces available from 47 cards:

2/47 * 1/46 = 1/1081

I believe this is correct.
Reply With Quote
  #5  
Old 12-31-2004, 07:38 AM
BruceZ BruceZ is offline
Senior Member
 
Join Date: Sep 2002
Posts: 1,636
Default Re: AA?

Correct, assuming he holds any 2 random cards with equal probability.
Reply With Quote
  #6  
Old 12-31-2004, 07:42 AM
gaming_mouse gaming_mouse is offline
Senior Member
 
Join Date: Oct 2004
Location: my hero is sfer
Posts: 2,480
Default Re: AA?

[ QUOTE ]
1 in 220 hands. Regardless of what you hold.

[/ QUOTE ]

This is not true. You cannot ignore known information. The easiest way to see this is to imagine that you hold AA yourself. Do you still think your opponent's odds have not changed?

However, to calculate the probability we need to assume that your opponent's hand is a random hand from the unseen cards in the deck -- and this assumption is false given his PF three bet, which limits his range of hands unless he's a total maniac. So the calculation is more of an exercise. Nonetheless....

There are 47 unseen cards in the deck. There are two aces left. So the chance that your oppo holds them is:

1/(47 choose 2) = 1 in 1081.

By the way, I don't think you played this poorly given an unknown opponent. An aggressive oppo might have played pocket eights this way, and a true LAG might even play pocket fours or sixes this way. Make a note, though, and next time keep playing back.

HTH,
gm
Reply With Quote
Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump


All times are GMT -4. The time now is 09:53 AM.


Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2024, vBulletin Solutions Inc.