Bridge, Probability & Information

[Echognome]

I'm reading this book by Robert MacKinnon, titled as the topic above. Only a few chapters in, but I thought this was an interesting problem for the experts (math and bridge).

 

[hv=n=sajhq7daq73ckq986&s=st6hakt9843dkt4c7]133|200|[/hv]

 

South opens 1♥ and the contract ends up being 6♥.

 

The opening lead is the ♠2 (3rd/5th).

 

1. Is the opening lead more likely to be 3rd or 5th best?

 

2. Are diamonds more likely to split 3-3 or 4-2 (either direction)?

 

3. Say you win the ♠A (East plays the 7 -- encouraging) and run all of your hearts but one, coming down to the following end position:

 

[hv=n=sajhq7daq73ckq986&s=st6hakt9843dkt4c7]133|200|[/hv]

 

The order of the discards wasn't given, but the defenders are world class. Hearts were 2-2 and West discarded ♠9, ♣T43 (but not necessarily in that order), while East discarded ♠43 and ♣J2 (but not necessarily in that order).

 

On your last heart, West discards the ♠K, dummy the ♣Q, and East the ♠5.

 

What now?

[Jlall]

Run the DT

[Hanoi5]

Now: ♦T.

 

I thought the spade was more likely from 5 cards, evidently not, is it because of the non-existent overcall?

 

As I thought West had 5 spades my first thought was diamonds were breaking 2-4 and that the finesse was the best play on the second trick.

 

I hope at least I got the diamonds 10 right.

[dburn]

I thought the spade was more likely from 5 cards, evidently not, is it because of the non-existent overcall?

West is more likely to have been dealt five spades than three (by a ratio of roughly 2-1), but on some hands with five spades he might have overcalled. Since he does not appear from the lead to hold ♠KQ, and is only a 50-50 shot to hold ♣A, there are probably not many hands with five spades with which he would have overcalled, but the number is an imponderable (especially since the vulnerability and the form of scoring are unknown).

 

However, if one considers that West would overcall on fewer than half of his possible hands with five spades, the lead is more likely to be from five cards than three. If the answer in the book does not say this, get a refund.

[awm]

I'll lead a club now.

 

Assuming the opening lead was honest, West started with either 3244 or 3235 shape. While a five-card spade holding was initially more likely, the subsequent plays have shown that for West to have five spades he must've started with KQxxx and lead fifth-best. This is a bizarre lead against a slam (and means that East falsecarded his encouraging signal). I think we can discount the possibility.

 

Playing a club now will win if West started with 3244 including the club ace, as he will have to win (he has pitched three clubs) and lead into my diamonds. Assuming the initial 3244 distribution, West's odds of holding the club ace are 4/7.

 

The alternate line of running the diamond ten works if East's initial diamonds are 9x, 8x, or 98. This is 7/15 of the initial 4-2 splits. Running the ten will also work if East started with 9xx or 8xx (but not 98x) from an initial 3-3 division (I assume that if the ten is covered and won in dummy and we play back to the king with east dropping the nine or eight, we are hooking). This is 6/20 of the 3-3 splits.

 

If we assume that 3244 and 3235 are just random, it's about 5:4 in favor of 3244, and adding these up, letting the diamond ten ride is somewhat better. So why do I prefer the club play? A couple reasons:

 

(1) If West was in fact 3235, this means his last six cards were ♠K, ♣A5, and some three card diamond holding. Looking at the ♣KQ behind him in dummy, it seems weird to pitch his winning spade king in this position. In fact there are some layouts where that gives declarer an impossible contract (although West may know this is impossible by now due to count on the spades from East's discards). In any case holding two sure winners and a bunch of meaningless cards against a slam, it is odd to discard a winner even knowing that partner can cover the suit.

 

(2) If West was in fact 3244 without the club ace, he might have discarded his last small club rather than ♠K. It is true that this makes it possible to endplay him, but it is not obvious that declarer will find that play (or play the hand in that manner). In fact discarding the club makes it harder for declarer to get count on the spades, and he might assume spades were 5-4 and play diamonds from the top. Of course, if West started 3244 with the club ace he basically had to pitch as he did, so there is something of a restricted choice situation.

 

Combining these I believe that West holding the club ace when 3244 is substantially more likely than 4/7 (since otherwise he might've pitched his last remaining baby club) and also that West holding 3235 is substantially less likely than the a priori odds (since he would be very likely to pitch a small club or even a worthless diamond from that holding). Combining these, I prefer playing a club and hoping for the endplay.

[gnasher]

The alternate line of running the diamond ten works if East's initial diamonds are 9x, 8x, or 98. This is 7/15 of the initial 4-2 splits. Running the ten will also work if East started with 9xx or 8xx (but not 98x) from an initial 3-3 division (I assume that if the ten is covered and won in dummy and we play back to the king with east dropping the nine or eight, we are hooking). This is 6/20 of the 3-3 splits.

Running ♦10 also works when diamonds are J98-xxx, so it would be 7/20 of the 3-3s

[Jlall]

It also works on stiff 9 or stiff 8 with RHO unless I'm missing something can't LHO be 3253?

 

Anyways I agree with a club I was too drunk last night I think :)

[Echognome]

Here are the "book" answers:

 

1. Spade lead is more likely to be from a 5-card suit than a 3-card suit. Others have mentioned that we should consider a lack of overcall (which the book doesn't at this stage). The basic idea was that if we consider the rest of the suits as being most even as possible, we should compare:

 

5=2=3=3 and 4=2=3=4 with

 

3=2=4=4 and 6=2=2=3

 

The author points out that the former pair of hands is twice as likely as the latter.

 

2. Given the above, the author states that diamonds are more likely to split 3-3 than 4-2 or 2-4.

 

3. Tundal lead the ♦T and went three down when there was Jx of diamonds on the right. The author thought this was the right play. (Please note however that the author claims expertise in probability and statistics, not bridge)

 

The club throw in would have worked.

[dburn]

Here are the "book" answers:

 

1. Spade lead is more likely to be from a 5-card suit than a 3-card suit.  Others have mentioned that we should consider a lack of overcall (which the book doesn't at this stage).  The basic idea was that if we consider the rest of the suits as being most even as possible, we should compare:

 

5=2=3=3 and 4=2=3=4 with

 

3=2=4=4 and 6=2=2=3

 

The author points out that the former pair of hands is twice as likely as the latter.

 

2. Given the above, the author states that diamonds are more likely to split 3-3 than 4-2 or 2-4.

Does he, by golly? Take the book back and get a refund in any case.

 

Assume that from the opening lead, it is known that West has five spades or three (we ignore the possibility of one, which might have led to some bidding by East).

 

Now, if West has five spades and East four (and nothing else is known about the distribution) we calculate

 

Chance that West has three diamonds: 38.01%;

Chance that West has four diamonds: 20.36%;

Chance that West has two diamonds: 28.51%.

 

The chance of a 3-3 diamond break has increased slightly (because of the even spade division), but the chance of a [4-2 or 2-4] break (which has not changed very much at all) still comfortably outweighs it.

 

If West has three spades and East six (and nothing else is known about the distribution) we calculate

 

Chance that West has three diamonds: 33.94%;

Chance that West has four diamonds: 35.63%;

Chance that West has two diamonds: 12.73%.

 

The chance of a 3-3 break has decreased slightly (because of the uneven spade division), and West has become more likely to hold four diamonds than three. But again the chance of a [4-2 or 2-4] break has not changed very much, and now outweighs the chance of 3-3 by a greater margin.

 

Perhaps Mr (Professor? Doctor?) MacKinnon does not have to tear his book up altogether. He just needs to add to the title the letters "Mis" before the word "information".

[Siegmund]

I may be misremembering the passage in the book; I thought this was the hand where there was a big discussion about how 3-3 is less likely than [4-2 or 2-4], but 4-2 one way is shown to be an irrelevant case, and it turns into a comparison of 3-3 against 2-4, and we decide based on vacant places.

 

It is an interesting but rather turgid book. Lots of examples and thought-provoking material, but I shudder to think of what would happen if an intermediate player bought it hoping to learn some basic information about bridge probability. I am tempted to compare it with another book with a yellow cover by Max Hardy.

[Jlall]

I might just play a diamond to the ten immediately.

[dburn]

I might just play a diamond to the ten immediately.

Was wondering about that on the bus home from work. Came to the conclusion that although I could easily convince myself that it was right, I could not so easily convince team-mates should it prove wrong. Probably better to cash ♥Q first, though - after all, if West shows out on that, you might not (should not?) play a diamond to the ten next.

[Jlall]

I might just play a diamond to the ten immediately.

Was wondering about that on the bus home from work. Came to the conclusion that although I could easily convince myself that it was right, I could not so easily convince team-mates should it prove wrong.

Why not? It is the percentage play in the suit in a vacuum when you have no entry to the long hand (ie you cannot unblock when its Jx anywhere). The only question is do the squeeze/endplay/whatever chances make up for the loss in the suit enough, and I would guess probably not since 3-3 diamonds is like 15 % less than a diamond to the ten.

[dburn]

I might just play a diamond to the ten immediately.

Was wondering about that on the bus home from work. Came to the conclusion that although I could easily convince myself that it was right, I could not so easily convince team-mates should it prove wrong.

Why not? It is the percentage play in the suit in a vacuum when you have no entry to the long hand (ie you cannot unblock when its Jx anywhere).

Surely it is.

 

Sorry to be editing my own posts and making nonsense of the thread, but this is a difficult hand. The 4-0 heart break with East having four - a solid 5% shot - has (no doubt for reasons of simplicity) been omitted from initial consideration, but...

[han]

Here are the "book" answers:

 

1. Spade lead is more likely to be from a 5-card suit than a 3-card suit. Others have mentioned that we should consider a lack of overcall (which the book doesn't at this stage). The basic idea was that if we consider the rest of the suits as being most even as possible, we should compare:

 

5=2=3=3 and 4=2=3=4 with

 

3=2=4=4 and 6=2=2=3

 

The author points out that the former pair of hands is twice as likely as the latter.

 

Apart from ignoring the bidding, this argument seems needlessly complicated. If we are going to estimate which distribution of the spades is more likely while ignoring the bidding then we can just consider the suit in isolation. A 5-4 split is more likely than a 3-6 split, period. There is no need to assume that the other suits are split evenly. Although this does lead to the same qualitative answer (5-4 is more likely than 3-6, which anybody reading this knows), the method is more complicated. Moreover, if you want to know how much more likely the 5-4 split is compared to the 3-6 split, the above method gives the wrong answer. The 5-2-3-3/4-2-3-4 split is exactly twice as likely as the 3-2-4-4/6-2-2-3 split. However (as dburn hinted) the 5-4 split is not exactly twice as likely as the 3-6, but a bit less than that (about 1.87 times as likely).

 

So not only does the method ignore the bidding and is it more difficult than the straight computation, it also gives the wrong answer.

 

2. Given the above, the author states that diamonds are more likely to split 3-3 than 4-2 or 2-4.

 

Since the question was poorly phrased and no argument is given, it's hard to know what is meant here. And what does "given the above" mean, is the author just assuming that spades split 5-4 and calculating the diamond split from there? That's not a good method at all.

 

3. Tundal lead the ♦T and went three down when there was Jx of diamonds on the right. The author thought this was the right play. (Please note however that the author claims expertise in probability and statistics, not bridge)

 

The author is a retired mathematician says a website that sells the book. I found 9 mathematics publications by a Robert F. MacKinnon so it seems likely that this is the same person. I suspect that Siegmund hit the nail on the head when he described the book as "thought-provoking", although perhaps not in the way Siegmund intended it.

[han]

The bridge hand is indeed interesting. Against most defenders I think that running the hearts will be best. Against very good defenders who would be hard for me to read and who would overcall 1S on many hands I would hook the diamond after cashing the heart queen.

[whereagles]

thread digging of the year? bored at work, han? :P

[nige1]

[hv=n=sajhq7daq73ckq986&s=st6hakt9843dkt4c7]133|200|

Echognome informs us

I'm reading this book by Robert MacKinnon, titled as the topic above. Only a few chapters in, but I thought this was an interesting problem for the experts (math and bridge). South opens 1♥ and the contract ends up being 6♥. The opening lead is the ♠2 (3rd/5th).

1. Is the opening lead more likely to be 3rd or 5th best?

2. Are diamonds more likely to split 3-3 or 4-2 (either direction)?

3. Say you win the ♠A (East plays the 7 -- encouraging) and run all of your hearts but one, coming down to the following end position:

The order of the discards wasn't given, but the defenders are world class. Hearts were 2-2 and West discarded ♠9, ♣T43 (but not necessarily in that order), while East discarded ♠43 and ♣J2 (but not necessarily in that order). On your last heart, West discards the ♠K, dummy the ♣Q, and East the ♠5.

What now?[/hv][hv=w=sKhdJ9cA&n=shda2ckq&e=Sq7hdc54&s=sth3d3c7]300|400|

 

Thank you Echognome. Some here have a low opinion of the book and It has a damning review on Amazon. But few seem to have read it all. What did you, Echognome, think of the book, as a whole?

 

I've just noticed that the book is also reviewed here on BBO

 

Adopting AWM's cunning line, If LHO has four diamonds and black tops, then LHO is triple-squeezed (no matter who has the ten of diamonds). When declarer cashes the last heart and LHO discards a spade honour, if declarer reads the position, he can just discard a diamond from dummy. It is better to keep diamonds intact, however, in case RHO has four diamonds. And tough if diamonds are 3-3.

[/hv]

Edited July 4, 2011 by nige1

[inquiry]

 

Some here have a low opinion of the book and It has a damning review on Amazon. But few seem to have read it all. What did you, Echognome, think of the book, as a whole? I've just noticed that the book is also reviewed here on BBO

 

Actually, there seems to be two reviews on amazon, one gives it five stars out of five, the other four out of five. I have both this one and Ruben's Expert Bridge Simplified. Let me say that Jeff Ruben's book is by far superior. Bridge, Probability & Information has some interesting ways to approach certain problems, and some different ways to explain a priori verus a posteriori calculations as it relates to a bridge hand, it was difficult for me to follow, and of course, bridge issues that should get in the way of the statistical calculations are either ignored or glossed over frequently. This does not greatly distract from the enjoyment of working out the problems even if you sometimes or frequently disagree. However, I would guide anyone serious about this topic to Ruben's book first.

 

As an admistration, I considered moving this thread to the book review section, but the OP was about the solution to a problem from the book so I did not. If the discuss branches off too much of a general review of the book, I might need to revisit this position, advise on its location welcome. I suspect han found this thread due to link in it from the new review of this book.

[blackshoe]

I have Rubens' book. I started reading it, and while I don't admit this very often, it was a bit - perhaps quite a bit - over my head, so I put it aside. I'll pick it up again in a while, and see how it goes. Eventually, I'll get through it.

 

In fact, my first impression of this book reminded me of my experience with Misner, Thorne, and Wheeler's Gravitation. I never did get through that one. B-)

 

Actually, any physicists out there that can recommend a good text on General Relativity? Gravitation was a good one, at least for the "geometric" approach, or so I understood when I bought it back in the 70's, shortly after it was published. I was a graduate student in Nuclear Engineering, though, not theoretical physics, so perhaps I didn't push it as hard as I might have. I no longer have the book, unfortunately. IAC, it seems likely, or at least possible, that better texts have been written in the past 40 years. :unsure:

 

BTW, I have a BS in physics, and as I recall I had no trouble with Special Relativity, at least as taught at the undergraduate level. I probably remember most of it, once I get back into it, too.

 

We now return you to your regularly scheduled thread. :P

[BunnyGo]

I have Rubens' book. I started reading it, and while I don't admit this very often, it was a bit - perhaps quite a bit - over my head, so I put it aside. I'll pick it up again in a while, and see how it goes. Eventually, I'll get through it.

 

In fact, my first impression of this book reminded me of my experience with Misner, Thorne, and Wheeler's Gravitation. I never did get through that one. B-)

 

Actually, any physicists out there that can recommend a good text on General Relativity? Gravitation was a good one, at least for the "geometric" approach, or so I understood when I bought it back in the 70's, shortly after it was published. I was a graduate student in Nuclear Engineering, though, not theoretical physics, so perhaps I didn't push it as hard as I might have. I no longer have the book, unfortunately. IAC, it seems likely, or at least possible, that better texts have been written in the past 40 years. :unsure:

 

BTW, I have a BS in physics, and as I recall I had no trouble with Special Relativity, at least as taught at the undergraduate level. I probably remember most of it, once I get back into it, too.

 

We now return you to your regularly scheduled thread. :P

 

Einstein's "Relativity" was a really good read. Dense, but very well written (and short).

[blackshoe]

Hm. I read that, or parts of it, back in the day. Maybe my long term memory is in worse shape than I thought. :P

[whereagles]

Try Weinberg's book:

 

http://www.amazon.com/Gravitation-Cosmology-Principles-Applications-Relativity/dp/0471925675

[Mbodell]

Actually, there seems to be two reviews on amazon, one gives it five stars out of five, the other four out of five. I have both this one and Ruben's Expert Bridge Simplified. Let me say that Jeff Ruben's book is by far superior. Bridge, Probability & Information has some interesting ways to approach certain problems, and some different ways to explain a priori verus a posteriori calculations as it relates to a bridge hand, it was difficult for me to follow, and of course, bridge issues that should get in the way of the statistical calculations are either ignored or glossed over frequently. This does not greatly distract from the enjoyment of working out the problems even if you sometimes or frequently disagree. However, I would guide anyone serious about this topic to Ruben's book first.

 

I think different people learn differently so some people might well find BP&I much easier to follow and learn from than EBS. I enjoyed both books (I bought these and the updated Love at the same national and enjoyed greatly all 3).

[blackshoe]

Thanks, Whereagles, I'll add it to my wish list. B-)