[drinbrasil]

Hi all,

Was playing 7♣ in this hand:

♠Ax
♥x
♦AJx
♣AKQ10987

and dummy

♠Kxx
♥AJ10xxx
♦Qx
♣J2

The guy lead was clubs, won in hand, so i cross to A of hearts, ruff in hand, both guys playing twice small hearts. Now i have to go to dummy in K of spades and decide, if i play for hearts fall 1-1 or to make diamond finesse.

Can anyone calculate here what is better play in moment? Dont forget in my left playing against 7 guy dont have KQxx or he would split honors without problems (but dont need take this in consideration for maths). Also hearts distrbuiton is -2 or 3-3 from start as we know now.

[FrancesHinden]

There are two maths problems, depending on who, if anyone, played a heart honour on the second round of the suit.

[jchiu]

Edited: see my post below, we should test to ensure hearts are 4-2, and fall back on the diamond finesse they are not.

Neither. Playing as such would require 2-2 trumps to be able to enjoy the long hearts. I would just take a straight up diamond finesse after winning the first trump in hand and crossing to the ♥A. This line works slightly less than half the time. The alternate line seems to be: preserve the ♠K entry to dummy to enable a squeeze position. This line would be, win ♣A in hand, ♥A, ruff a heart, ♣J, run off all trumps, ♠A, ♠K. It works whenever hearts break, and whenever the opponents mispitch. However, even given that hearts are no worse than 4-2, I would estimate this line at slightly less than 45%.

[drinbrasil]

jchiu, right, correct, need 2-2 trumphs, but whats your maths in the situation i published. whats the chance for finesse x chance for hearts 3-3?

with Qxx in my right ple good play of Q in 2nd would catch me. but i have entry in A of diamonds if trumps no 2-2.

[drinbrasil]

FrancesHinden, on Apr 24 2007, 04:59 PM, said:

There are two maths problems, depending on who, if anyone, played a heart honour on the second round of the suit.

both played xx frmo hands

[drinbrasil]

Jlall, on Apr 24 2007, 05:17 PM, said:

drinbrasil, on Apr 24 2007, 12:13 PM, said:

jchiu, right, correct, need 2-2 trumphs, but whats your maths in the situation i published. whats the chance for finesse x chance for hearts 3-3?

dude you only need 2-2 trumps if you play a spade to the king...

Basically I think its KQxx/xx vs Hxx/Hxx. In theory this is not true as you have restricted choice stuff on the Hxx's but in practice they just always play low, so I think going for Hxx/Hxx is the best shot. (plus if it doesnt work out you have the admittedly remote squeeze chances that ch00 pointed out as a fallback)>

yes, i have to decide to play trumph to jack and hearts 3-3, or spade to K, diamond finesse.

[cherdano]

Jlall, on Apr 24 2007, 11:10 AM, said:

Good problem though, I'm bad at these, but my gut is that when no heart honor drops they are more likely to be 3-3 because no one drops Q from Qxx or K from Kxx.

Assuming that (and that noone splits from KQxx of course), the odds are 11:10 that the heart honors are split now.

[jchiu]

Sorry for the misinterpretation. I now believe that it's a tossup between playing a club to the jack, and ruffing a heart to cater to 3-3 hearts; and playing a spade to the king, and taking the diamond finesse.

Since hardly anyone drops honours from most holdings unless forced to, I think it is a tossup between playing for a 2-0 split with 11 spaces, and a 1-1 split with 11 spaces. In particular, what are the odds between KQxx/xx vs Kxx/Qxx? The executive summary says that the latter occurs 52.38% of the time and should be slightly favoured over the straight-up diamond finesse.

The maths behind it: The odds of a 1-1 break now is (2 choose 1) (2 choose 1)(20 choose 10) / (22 choose 12) = 52.38%. Therefore the odds of a 2-0 break are 47.62%. Alternately, of the specific 4-2 breaks, only 6 of the 15 contain KQxx and are possible now. This is 40% of the 48.45% for a 4-2 break, or 19.38%. Similarly, of the 3-3 breaks, only 8 of the 20 are contain KQx and are now impossible. This leaves 60% of the 35.53% for a 3-2 break, or 21.32%. Note that these probabilities are in the exact 11:10 ratio as above.

[drinbrasil]

i made some maths, dont know if is correct, you can correct me pls, maybe i am wrong way (all values aprox).

the finesse i work with 50%, so i need 3-3 be better than this to work in this line.

so chances for 4-2 suit was 48%
chances for 3-3 suit was 36%


as we dont have other possibilities for suit we have (isnt 6-0 or 5-1)

chances for 4-2 suit was 57% (48/84)
chances for 3-3 suit was 43% (36/84)

so my cases are of success x down are
2 in 30 in the 57% no sucess 57/30*2 = 3,8%
2 in 20 in the 43% sucess = 43/20*2 = 4,3%

then i have 4,3+3,8=8,1 and this means around 53% for suit 3-3 now....better than finesse

but i dont know if i am missing something.....or is totally wrong way to calculate this....

[drinbrasil]

jchiu, on Apr 24 2007, 05:27 PM, said:

Sorry for the misinterpretation.  I now believe that it's a tossup between playing a club to the jack, and ruffing a heart to cater to 3-3 hearts; and playing a spade to the king, and taking the diamond finesse.

Since hardly anyone drops honours from most holdings unless forced to, I think it is a tossup between playing for a 2-0 split with 11 spaces, and a 1-1 split with 11 spaces.  In particular, what are the odds between KQxx/xx vs Kxx/Qxx?  The executive summary says that the latter occurs 52.38% of the time and should be slightly favoured over the straight-up diamond finesse.

The maths behind it: The odds of a 1-1 break now is (2 choose 1) (2 choose 1)(20 choose 10) / (22 choose 12) = 52.38%.  Therefore the odds of a 2-0 break are 47.62%.  Alternately, of the specific 4-2 breaks, only 6 of the 15 contain KQxx and are possible now.  This is 40% of the 48.45% for a 4-2 break, or 19.38%.  Similarly, of the 3-3 breaks, only 8 of the 20 are contain KQx and are now impossible.  This leaves 60% of the 35.53% for a 3-2 break, or 21.32%.  Note that these probabilities are in the exact 11:10 ratio as above.

thanks, i was making my post when you already posted,,,,(i had my maths in head and just now put in paper...).

in the table i could not evaluate corectly % from head and though was aprox equal. bad tits shouting me i played 48% x 36% what i ignored. in real life as % was near equal for me, i had some inferences from how tit was angry playing hearts and from not 4-2 in my left (against 7 i have 100% sure he with KQxx would split hearts for sure), so i played for hearts 3-3.....and won

in other table guy did automatic finesse and lost.

thanks all for thinkings in this thread.

[Fluffy]

you can also try to ruff ♥ and if LHO has 4 and ♦K is still onside, maybe there is still a double squeeze, but I am not very sure about it.


EDIT: no, there is no squeeze, because you would need to cash 2 ♦ FROM YOUR HAND for it to work (if you cashed your last winner from dummy it would be all right), then LHO has a scape discarding all his diamonds while RHO discards spades.

[cherdano]

The math is really simpler than you guys are making it. Both opponents have 11 vacant spaces, so you can just arbitrarily give one of them the queen, then the chance that he also gets the king is 10/21, or 10:11.

[Fluffy]

cherdano, on Apr 25 2007, 08:03 AM, said:

The math is really simpler than you guys are making it. Both opponents have 11 vacant spaces, so you can just arbitrarily give one of them the queen, then the chance that he also gets the king is 10/21, or 10:11.

Its not that easy, there is a chance someone would drop a honnor from KQxx on first or second trick (even if it is a mistake). Wich favours the 3-3 split.

[drinbrasil]

cherdano, on Apr 25 2007, 08:03 AM, said:

The math is really simpler than you guys are making it. Both opponents have 11 vacant spaces, so you can just arbitrarily give one of them the queen, then the chance that he also gets the king is 10/21, or 10:11.

So in really as he lead ♣ and played 2 hearts, we have both with 10 cards, and the chance for K + arbitrary Q is then 9/19, or 9:10, so 52,6% for try suit 3-3.

I think the maths i make 3 posts above is near way of thinking but i dont had in mind played cards to do that...but diference is very small.

[drinbrasil]

If the situation was similar, lets say, you have in dummy:

AKQxxx

and in hand

x

you play AK of ♠ and both play small cards, now you have to decide to play Q (and play your last loser out or to run finesse in other suit (no more entries in dummy), does the math is exact same? Like this deal playing 7♣

lead was ♠

---

how is the maths now?

[awm]

Well there are 64 ways spades can break on your last example. This includes:

20 3-3 breaks
30 4-2 breaks (including 15 each way)
12 5-1 breaks (6 singletons each side)
2 6-0 breaks

The even breaks tend to be very slightly more frequent than the skewed breaks.

So in general your two lines are: spades no worse than 4-2 (50/64) and a finesse (total 25/64). Or spades 3-3 (20/64). Alternately you can say that once both opponents have followed two rounds, spades will break about 40% of the time.

The initial problem was different for several reasons. Basically you are assuming that: (1) Neither opponent will play an honor if he doesn't have to (2) LHO would split from KQxx on the original lead up to the board. Of course, neither of these is necessarily obvious (especially the second) but if you do assume those things it substantially increases your odds of the suit breaking. Basically the possible heart holdings in that example were:

LHO Hxx and RHO Hxx: 12 ways (6 to pick LHO's small cards, then 2 honor allocations)
LHO xx and RHO HHxx: 6 ways (have to pick the small cards)

So basically you are 2/3 likely for the suit to break, instead of 2/5.

[Halo]

These calculations are completely determined.

You cannot include incomplete outside suits. You can make assumptions. Includes you can make assumptions about opponents play, eg honour splitting.

Once you do make a set of assumptions the numbers follow. You can like them or lump them. In this case 3-3 is noticeably better than 50%.

[Fluffy]

you can try and deduce soemthing from the opening lead, it will change the math, it always happens, there are no pure math problems