Two Plus Two Newer Archives Razz - paired cards
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#1
11-12-2007, 10:44 PM
 *TT* Senior Member Join Date: Apr 2004 Location: Vehicle Chooser For Life! Posts: 17,198
Razz - paired cards

Lets assume that the villain has precisely a 3-card bike hand (three unduplicated cards 5 or lower) on third street. On 4th street the villain catches a 5. What is the probability that the 5 paired the villain assuming that there are 12 bike cards unaccounted for remaining in the deck including the three remaining 5's? Please include the formula, that would help me bunches because I think i calculated this incorrectly. Thanks in advance!
#2
11-13-2007, 12:33 AM
 pococurante Senior Member Join Date: Jul 2007 Location: VA Posts: 138
Re: Razz - paired cards

Villain's possible hands, + whether the 5 paired him:

234 - no
235 - yes
245 - yes
345 - yes

There's a 75% chance the 5 paired him.

(I don't know just what a bike card is, but since you said there are 12 left after 4 were dealt, I assume it means 2, 3, 4, 5)
#3
11-13-2007, 01:15 AM
 *TT* Senior Member Join Date: Apr 2004 Location: Vehicle Chooser For Life! Posts: 17,198
Re: Razz - paired cards

a bike is A2345. Theer are 12 bike cards unaccounted for in the deck, 3 of them are 5's. I assumed it would be just 3/12=25% but I dont know if we have to factor in both cards. This comes from a thread in the Stud forum if you want to read it, Betgo's "Big Pot" right at the top of the forum.
#4
11-13-2007, 01:33 AM
 pococurante Senior Member Join Date: Jul 2007 Location: VA Posts: 138
Re: Razz - paired cards

Hmm.... possibly the best way is just to count all the possible combinations including suits.

We know he holds the 2 of diamonds. The other potential cards he could hold: three 5s, four 4s, three 3s, two As.

A3 x6 - no
A4 x8 - no
A5 x6 - yes
34 x12 - no
35 x9 - yes
45 x12 - yes

That's 27 hands where the 5 pairs him, and 26 hands where it doesn't. 27/53 = there's a 50.94% chance he got paired on 4th street.
#5
11-13-2007, 03:02 AM
 BruceZ Senior Member Join Date: Sep 2002 Posts: 4,078
Re: Razz - paired cards

[ QUOTE ]
Hmm.... possibly the best way is just to count all the possible combinations including suits.

We know he holds the 2 of diamonds. The other potential cards he could hold: three 5s, four 4s, three 3s, two As.

A3 x6 - no
A4 x8 - no
A5 x6 - yes
34 x12 - no
35 x9 - yes
45 x12 - yes

That's 27 hands where the 5 pairs him, and 26 hands where it doesn't. 27/53 = there's a 50.94% chance he got paired on 4th street.

[/ QUOTE ]

Right except that there is only 1 ace unaccounted for. The possibilities then become:

A3 x3 - no
A4 x4 - no
A5 x3 - yes
34 x12 - no
35 x9 - yes
45 x12 - yes

This gives a probability of pairing the five of 24/43 =~ 55.8%.
#6
11-13-2007, 03:53 AM
 *TT* Senior Member Join Date: Apr 2004 Location: Vehicle Chooser For Life! Posts: 17,198
Re: Razz - paired cards

Bruce - pococurante got it right, there are two A's unaccounted for. By using combinations the probability of the villain pairing his 5 is 50.9%.

But now comes the second part of my question, is there a shortcut for calculating this probability on the fly rather than typing out the combinations by hand?
#7
11-13-2007, 04:08 AM
 BruceZ Senior Member Join Date: Sep 2002 Posts: 4,078
Re: Razz - paired cards

[ QUOTE ]
Bruce - pococurante got it right, there are two A's unaccounted for. By using combinations the probability of the villain pairing his 5 is 50.9%.

[/ QUOTE ]

Look at the post you mentioned on the Stud forum. Player 1 has the A [img]/images/graemlins/spade.gif[/img], player 6 has the A [img]/images/graemlins/heart.gif[/img], and hero has the A [img]/images/graemlins/diamond.gif[/img]. Only the A [img]/images/graemlins/club.gif[/img] is unaccounted for.

Your statement that there are 12 bicycle cards unaccounted for is incorrect. There are 6 exposed, and since we are told that opponent's first 3 cards are different, we know that he doesn't hold another 2, which leaves 20 - 6 - 3 = 11 bicycle cards.

[ QUOTE ]
But now comes the second part of my question, is there a shortcut for calculating this probability on the fly rather than typing out the combinations by hand?

[/ QUOTE ]

Not if you want to take into account the exact cards that are unaccounted for.
#8
11-13-2007, 04:48 AM
 pococurante Senior Member Join Date: Jul 2007 Location: VA Posts: 138
Re: Razz - paired cards

[ QUOTE ]
Only the A [img]/images/graemlins/club.gif[/img] is unaccounted for.

[/ QUOTE ]

ahh... good eye there
#9
11-13-2007, 05:19 AM
 *TT* Senior Member Join Date: Apr 2004 Location: Vehicle Chooser For Life! Posts: 17,198
Re: Razz - paired cards

Thanks Bruce, your right there is only one A unaccounted for, I must have made an typo when I tallied up the cards which I carried over here.

so using combinations I have learned that the villain pairs the board 56% of the time assuming he holds any 3-card bike. If we remove the roughest bike hand of (45)2 from his capping range to more accurately represent his likely holdings if he is slightly loose then there is a 39% chance he paired. In the event we open the villain's range to include all but the roughest sixes then there is a 28% chance the villain paired the 5.

thanks a bunch for your help!
#10
11-13-2007, 10:03 AM
 Lottery Larry Senior Member Join Date: Jun 2003 Location: Home Poker in da HOOWWSSS! Posts: 6,198
Re: Razz - paired cards

Does it make sense to call with bike cards WIHTOUT the Ace, if we see 2 Aces?

I'll have to go read that hand in the Stud forum

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