Echognome, on Jun 3 2010, 01:04 PM, said:
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".
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?