Suit combi % calculation

[kgr]

Working on suit combinations. Can you verify below logic, Is it 100% correct and complete?:

 

AK9x

vs

Qx

 

You first play the Q and East drops the J.

Following relevant possibilities:

East has:

1) J     0.48%

2) JT   0,73% => Divide by 2 because of restricted choice: 0,365%

3) JTx 4,44% (Falsecard) => Divide by 2 because of restricted choice: 2,22%

 

==> 0,48% for finesse vs 2,585% for Drop.

...But if East is not a strong player and will never falsecard then:

==> 0,48% for finesse vs 0,365% for Drop

...But if East is not a strong player and will never falsecard with JTx but always play the J from JT then:

==> 0,48% for finesse vs 0,73% for Drop

 

Thanks,

Koen

[se12sam]

I may be wrong (it's been a while since I was in college) but I think the division by 2 on 3) is incorrect. Restricted choice principle applies ONLY when there is no choice. A false-card from JTx etc is a choice and the "sighting" of the J does not reduce the probabilities from 4.44% to 2.22%.

[kgr]

I may be wrong (it's been a while since I was in college) but I think the division by 2 on 3) is incorrect. Restricted choice principle applies ONLY when there is no choice. A false-card from JTx etc is a choice and the "sighting" of the J does not reduce the probabilities from 4.44% to 2.22%.

I thought that if East has JTx and wants to falsecard he will 50% of the time play the J and 50% the T. Therefor 4.44/2

[benlessard]

your initial calculation are correct. If East is a robot that never falsecard from JTx finesse. If he always play the J from JT its slightly better to play for the drop.

 

 

If he know you have Qx the hes got a mandatory falsecard with JTx. Therefore playing for the drop is way better. If its possible you got Qxx then its still possible for him to play the J from Jx or from JTx but both are dangerous. If the position is

 

[hv=n=sak9xhdc&s=sqxxhxdc]133|200|[/hv]

 

Not only you would usually cash the A or K first but he still can play the J or T (from JTx or Hx) with a small risk. the 2nd round he will play the low card and you will have a guess. (Should finesse) and lose.