percentage question

[Fluffy]

I am playing 4♥ and after some ducking ruffing etc, I come to a 3 card ending with:

 

♠Ax

♦10

 

 

♠KJ9

 

originally I had 4 spades in hand and I can count that RHO had started with 5 spades. LHO with 2 spades. LHO has ♦K and 2 spades left and RHO has 3 spades left

 

I play ♠A then low spade, RHO plays ♠6 and 8.

 

This means LHO has either ♠Q♦K left or ♠10♦K left now.

 

I think ♠10 is irrelevant hence the finese is 5/7 favourite, but is it?

 

if relevant, RHO has played all his spades up the line

[whereagles]

I think 5/7 is about right and you should finesse.

[dake50]

I agree with your assessment.

So I play K - my luck is this bad.

[ArtK78]

Assuming that you need 3 tricks, and assuming that you have nothing else to go on besides the distributional count that you have, the finesse is clearly the right play. The spots played are not relevant.

[han]

The 10 is not relevant against good defenders.

[bluecalm]

Yeah, I don't get it. Why wouldn't it be 5/7 ?

 

if relevant, RHO has played all his spades up the line

 

It's only relevant against an opponent who play up the line with a queen but differently without it :)

[phil_20686]

Yeah, I don't get it. Why wouldn't it be 5/7 ?

 

 

 

It's only relevant against an opponent who play up the line with a queen but differently without it :)

 

I think the point being we should exclude the holdings where rho started with QTxxx which would change the odds. RHO can have only one of the Q and ten if he does not randomise his pips.

 

for 2-5 splits, there are 6 cases where the Q is on your left, and 5 cases where the ten only is on your left. So one could argue that there are only 11 relevant cases, 6 where the finesse loses and 5 where it wins.

 

I do don't know how much one would trust this reasoning against poor players, good players will counter by throwing the ten from holdings like Txxxx or concealing a pip from QTxxx etc. In fact I'm not even sure its a correct way to count cases. Will think about it.

[HighLow21]

The odds haven't changed from the beginning. RHO started the hand with 5 spades, so is a 5/7 favorite to hold Q♠.

[Cascade]

The odds haven't changed from the beginning. RHO started the hand with 5 spades, so is a 5/7 favorite to hold Q♠.

 

This seems correct to me.

 

The player had five spades and came down to three spades. The spot cards he threw gave you no new information. You always knew he could throw two small spot cards whatever his holding.

[Fluffy]

The 10 is not relevant against good defenders.

 

what about bad defenders who pick throw their spots up the line?

[gnasher]

what about bad defenders who pick throw their spots up the line?

 

If RHO has played 2-3-6-8, and you know that he always plays upwards, his only possible holdings are 108632 with Q8632, so it's 50:50.

 

There's another category of player who would always play the 10 at this point if they had it. Against such players, the finesse is 100%.

[phil_20686]

If RHO has played 2-3-6-8, and you know that he always plays upwards, his only possible holdings are 108632 with Q8632, so it's 50:50.

 

There's another category of player who would always play the 10 at this point if they had it. Against such players, the finesse is 100%.

 

This logic is intuitively convincing, but I dont think its correct. Consider, that the missing pip may be the 5, then there are only three possible holdings, the two above and 86532, so you could argue that there are three possible holdings, in two of which the finesse loses.

 

A correct way to argue is to consider that this is a type of restricted choice situation. If they discard randomly from pips less than the T, and happen to have played 2368 from 23568, then you should conclude that xxxxx is less likely than Qxxxx or Txxxx as there were more alternative cases. If they will also randomly discard including the ten, then Qxxxx is more likely than xxxxx/Txxxx because the first had fewer alternative ways to discard.

 

If they are known to play up the line, then there is no alternative to their play, and you should not infer from the alternative discards available. Thus in the case where they play up the line its 50:50. The a priori % are all predicated upon the belief that the opponents will discard randomly from among cards that do not matter.

[gnasher]

This logic is intuitively convincing, but I dont think its correct. Consider, that the missing pip may be the 5,

Why would I consider something that, with the stated conditions, is impossible? Fluffy asked "what about bad defenders who pick throw their spots up the line?", and I began my answer with "If RHO has played 2-3-6-8, and you know that he always plays upwards"

[phil_20686]

Why would I consider something that, with the stated conditions, is impossible? Fluffy asked "what about bad defenders who pick throw their spots up the line?", and I began my answer with "If RHO has played 2-3-6-8, and you know that he always plays upwards"

 

My point being that simply comparing the holdings at the end is not logically consistent. You must consider not only the holdings, but also if they could have played differently with the same holding.

 

You say that there are only two relevant holdings, Qxxxx or Txxxx, but suppose these defenders discard randomly from pips lower than the ten, and just happened to discard up the line in this cases. In both cases RHO can still only hold the two possible holdings, but it is not right to compare these holdings. Instead you must ask "In how many alternate ways could the defender have played these cards", and choose the holdings where he has the fewest number of alternatives. The keypoint here is that if they play up the line there are no alternatives. If rho discards randomly from pips smaller than the ten, it is something between 5:2 and 1:1, if he discards randomly you get back to 5:2.

 

If they discard randomly including the ten, there are 4! ways to discard from Qxxxx, and two from xx, where as there are 5! ways to discard from Txxxx, so the correct odds is is teh ratio of these two numbers which is 2:5.

 

If they discard randomly excluding the ten, there are 4! ways to discard from Qxxxx, and one from Tx, and the same for Txxxx and Qx, for 1:1.

 

If they play up the line, there is only one possible way for them to discard and its 1:1.

 

Thus we see that requiring them to discard up the line is too strong a condition. All we require for the finesse not to obey vacant spaces at this point is that they guard the ten.

[gnasher]

Phil, I understand your point, I just don't see what it has to do with my response to Fluffy's question, which was specifically about the situation where you *know* that the defenders always play upwards. That is, I don't understand why we seem to have had this conversation:

 

Me: "If RHO has played 2-3-6-8, and you know that he always plays upwards, his only possible holdings are 108632 with Q8632, so it's 50:50."

 

You: "This logic is intuitively convincing, but I dont think its correct."

 

You: "If they play up the line, there is only one possible way for them to discard and its 1:1."

[daveharty]

EDIT: nonsense deleted.

[gwnn]

Because ♥ are trumps and the ♦K is still outside.

[phil_20686]

Phil, I understand your point, I just don't see what it has to do with my response to Fluffy's question, which was specifically about the situation where you *know* that the defenders always play upwards. That is, I don't understand why we seem to have had this conversation:

 

Me: "If RHO has played 2-3-6-8, and you know that he always plays upwards, his only possible holdings are 108632 with Q8632, so it's 50:50."

 

You: "This logic is intuitively convincing, but I dont think its correct."

 

You: "If they play up the line, there is only one possible way for them to discard and its 1:1."

 

Oh, I was questioning your argument, not your conclusion. You seemed to be just comparing the holdings they could have, but those are the same holdings they could have if they played randomly. I just wanted to make clear that it is not the holdings that matter per se.

[daveharty]

Because ♥ are trumps and the ♦K is still outside.

LOL well I would have gone down a long time ago in my imaginary 4S contract.

[omarsh10]

Interesting ?: how did you infer that RHO had 5 spades?

[CSGibson]

Interesting ?: how did you infer that RHO had 5 spades?

 

 

I can count that RHO had started with 5 spades.

 

I hope that there's no need to actually explain the counting process, and that you just missed what the Flufster typed.

[gwnn]

Interesting ?: how did you infer that RHO had 5 spades?

By counting hearts (when he pulled trump), clubs (by this point, he had seen the position of all 13 clubs) and diamonds (RHO showed out at one point). This is the direct way of counting someone's hand. Sometimes you can draw inferences from their leads or signals from during the hand, apply those at your own risk but in practice, most experts counted out most hands by trick ~8, and usually before.

[gszes]

Everyone ast the table should have a pretty

good idea what everyone else has at this point.

 

The 7/5 concept is ok for starters but restricted

choice needs to play a part in this equation.

Both opps know decarers problem and that the

% action is to play rho for the spade Q. Sitting

idly by and doing nothing will result in declarer

getting the problem right most of the time. The

defense needs to steer declarer away from the

proper LOP and they can at least give declarer

a viable option to go wrong by using reasonable

carding.

 

If RHO started with Qxxxx (no T) there is nothing

they can do to dissuade declarer from finessing them

but their p might be able to help. On the play of

the spade A LHO can drop the T (from Tx) to at least

give declarer pause that they have QT.

 

If LHO started with Qx (rho should try very hard to

convince declarer they started with QTxxx and they

should play the T at trick 12.

 

The abscence of these plays would seem to indicate

the opps were unable to create anything special with

their actual holdings. I would draw the conclusion

that lho did not have the spade T and their small

card was forced from Qx. If the spade Q is with RHO

the failure of LHO to play the T under the A would

border on criminal.

 

RHO might have just a bit careless knowing the % play

was to finesse them for the Q and they were so confident

the finesse was going to lose they carelessly played

small vs the T and thus failed to continue the illusion

that the finesse was destined to succeed.

 

IMO I would play to drop the Q if playing readers of this

forum but finessing rho for the Q would be better

overall in most regular games:))))))))))))))))))))))))

 

To me, a more interesting problem would have been what to

do if the spade T dropped from LHO on the A:)))))))))))