The monty hall trap

[Flame]

432

A3

AJ106

6532

 

A65

K876

K987

AK

 

the biding goes 1NT - 2NT - 3NT

west leads the 4 of club explained as 4th best.

you have 5 trucks outside the diamond, and you will make the game if you can hook the diamond q, the question is on which side to look for it.

Now lets take the simple approach Ben took on earlier problem to figure out the odds.

we know west has 4 card clubs and east has only 3, we go to this nice program

distribution calculator

put 4 known card for west, and 3 for east, we put Q in the missing cards, and click GO, we get that the chances for the Q to be on west are 47.368 while with east

52.632. now clearly we finnese east for the queen right ? NO

Lets examine this in a different way, west has 4 card club, we also know that west doesnt have a 4 card heart or spade because he didnt lead any of them, this give him at most 3♥ ,3♠ and 4♣, this leaves atleast 3 cards in ♦

this mean that west is clearly longer in diamond and we must finnese him for the queen.

How did we go wrong ? We fall into a trap, we took the information of west having 4 cards in club and adressed it as an new ifnormation, while this wasnt new but a known info, we knew west has atleast one 4+card suit, and we knew he will lead his longest suit, this just happend to be club, for it could just as well be heart or spade, his having a 4 card suit doesnt put him with less diamonds.

Now to the general question, how to know the odds ? I cant say because its too complex , but in genral its a good idea to take an avarage lead to be out of 4.5 card suit, this mean if the lead was from 4 card suit, there is a lil more chance that the leader will hold more of the suit we check (diamonds in the example)

while a 5 card lead will give the leader lil less chances, and a 6 or 7 changes the odds in more drastical way.

This isnt only valid for leads, lets say your LHO bid a takeout double over your 1h which exlained as showing exactly 4 card spades, this might put you in similar position to the lead problem, you shouldnt approach the 4 spade cards and a new info, because you already knew he will have a 4+ card somewhere.

In the discussion with Ben west bid showed 6 card major, 6 cards in a suit are more then avarage, making thier holder less chance to hold a certain card you are looking for, but how less are the chances ? you cant use the program with a known 6 card on one side and 2 on the other side, you have some new info, but some was already know, i would say that 4.5 cards in the long suit is the know info, so we only have 1.5 "new cards" not 6 new cards.

You can find a chapter about this in granoveter's book "for experts only", with some good examples, unfortunetly i dont have it with me here, but hope i manage to expalin it anyway.

[inquiry]

I know the monte hall problem.. it goes like this...

 

Deal one ace and two duces face down. Have someone pick one of the three cards. Then, dealer, who knows which card is ace, turns up one of the other two cards. It is, clearly a duce. Now you are given the option to keep the card you picked initially or switch to the other card. Is it 50/50? No. Always pick the other card you will come out way ahead.

 

The use of the hand the math calculator on the hand in question I specifically said, In isolation, the "correct" aka percentage play in the ♣ suit can be readily calculated.. That is just taking the club and spade suit and ignoring others. And indeed, what i said remains accurate. Give WEST 6[xp] and east 2♠, and know nothing else about the hand, the chances of EAST having certain club holdings can be readily calculated. This is the "in isolation" part.

 

Next, I showed that you can't consider the suit in isolation. And I went ahead and gave an additional example (but see new post coming in that taking into account luis's comments).

 

As for you problem here. There is an assumption in the hand that WEST would have preferred a ♥ or ♠ lead with four. This is of course, not always the case. There is also the "assumption" that the ♣ small was "honest" card, that is also not always the case. But I am never going to make a decision on which way to hook based upon 4/3 split in a side suit.

 

Ben

[Flame]

I don't understand how you do this math.

you said there :

With WEST having 6♠ to east's two, the odds of dropping the ♣J in three rounds (J, Jx, Jxx with either), is 69.5%. The hook of EAST for the ♣Jack is only 66.5% (and that includes teh 5-0 split which isn't that helpful, and with WEST having 6♠, odds of 5-0 is 5.4%, reducing the ♣ hook to 61.1%). So clearly hooking ♣ as your partner did appears wrong.

How did you avoid the monty all trap here ?

cascade later on the same thread gave his chances, which i suspect have the monty hall problem in them meaning they arent accurate.

About the ex problem here, yes we dont know for sure that west doesnt have a 4 card major, but the chances for him to have it is smaller, and even if it was even chances to lead a major or minor with 4/4 its still a restricted choice here. I'm sure that on this hand the right play is to fineese west for the Q.

About Luis's remark, i dont think someone would bid differently with 6 card major and 4 card side suit, especially if the other suit is a minor, so it need some adjustments.

[Free]

I don't like the hand: we've got 2 ♦K's...

[Fluffy]

First of all, with 2 ♣ losers you are able to loss 2 tricks in the majors to investigate a bit more befor emaking your decision. (yes, it may lead to more uundertricks often, wich scoring method you said you were using?)

 

Next the fact that west didn´t lead a ♦ means he probably doesn´t have 4 (the % depends on the card eastplayed, wich we don´t know), so if someone has 4♦ it is probably east, that makes him favourite for ♦Q, you said west doesnt have 4 card major?, Not having a outside 5 card suit is a solid argument, not having a same lenght major is weak, only in my opinion of course, probably someone here is too sure of peple using the same methods of him, sadly I am starting to beleive its me ;)

[Free]

I have a question for you Fluffy: do you always lead a suit from Q543 or worse INTO a strong NT hand? If you do, good luck (!!!), but I rather let that suit aside and lead something else (unless I have a good reason). So your entire analysis of the ♦s is wrong imo, and would probably be the other way around. Leading a stiff can sometimes win a lot...

 

Anyway, I usually don't start calculating the odds on such hands at the table (I find it a waste of energy, but afterwards we can think about it ofcourse). Most of the time it's still around 50-50. If it's 51.05-48.95, what more do we know?

 

In these 50% games, I always play the same way: I place the Q behind the K, so I'd play ♦K (dropping the J to unblock) and finesse West. ;)

[Flame]

Its ok to analyze the hands, but dont lose the main point of this thread, The example hand i just gave is not something i took hours to think about, its just an example to expalin the idea of the monty all trap, do you understand the point in it ? Do you understand why saying west got 4 clubs and east only 3 therefore there are more chances that east has more diamonds is a wrong conclusion ?

[AceOfHeart]

Actually i read somewhere whether does we take the 4 card clubs into consideration is according to the method of discovery....if you discover the club break yourself,It will be better to finese the person with less clubs, however if the defender tells you so,it will not affect the initial odds. I dont know why just quoting the author,Phil Martins from this book For experts only. The table of contents can be seen here http://www.ny-bridge.com/bt/expert.html

[Flame]

Actually i read somewhere whether does we take the 4 card clubs into consideration is according to the method of discovery....if you discover the club break yourself,It will be better to finese the person with less clubs, however if the defender tells you so,it will not affect the initial odds. I dont know why just quoting the author,Phil Martins from this book For experts only. The table of contents can be seen here http://www.ny-bridge.com/bt/expert.html

You should try to understand it, wather you discover or they tell you is a nice aid for memory but you better understand the principle behind it.

[Trpltrbl]

I play, with no other info available, the Q after the J.

 

Mike B)