I was at Grant's lesson last week. He mentioned that I am a mathematician and maybe I could say a few words about probability. This can be tricky. The fact is I rarely really compute the exact odds of a line of play, it would drive everyone nuts waiting. But I will try to put something together, something fairy short and incomplete, but perhaps having some use. In this note, I will give one example and then I am open to suggestions. The example is from the robots.
http://tinyurl.com/y8uu2jd9You might or might not like the auction, I held the South cards during the auction, I was switched for the play. Anyway, it's what I did. Now I am playing 6
and I have to make it. The opening lead is a club, a lead that leaves it all up to me.
If W holds
KQ3 I am going down. No point in worrying about what cannot be dealt with. If E holds
KQ3 I can hold my spade losses to 1 by winning the
in hand and then playing the
J and letting it ride if it is not covered. This would guarantee the loss of only one
on any hand except the one where the KQ3 are with W. That one we ignore. So maybe that's right? Hold on! We still have a heart loser to deal with.
Let's consider the alternate play of laying down the
A. If W shows out I will regret this play since now I am going down for sure, while I would still have a chance if I had run the J. Otoh, if everyone follows suit when I lay down the A, then I am, with practical certainty, making this hand.
Let's think it through:
I lay down the A, we suppose everyone follows. I play another club and presumably everyone follows. I can now claim 12 tricks. I start in on diamonds. As it happens, everyone follows to three rounds but I don't care. After cashing two diamonds and ruffing the third, I lead a trump. Whoever holds the last trump has a choice that is really no choice at all: Lead a heart, eliminating any heart guess, or lead a side suit, clubs or diamonds, in which case I toss a heart from the South hand and, ruff in the North hand, and claim.
So there are 2 possible lines:
1. Take the safety play of running the
J, holding my spade losers to one whenever they can be held to one, and then later taking the heart finesse or
2. Lay down the spade A, possibly losing a spade that need not be lost.
Did I compute the odds? No. The hear finesse is surely about 50-50 and a 2-1 split in spades is surely better than 50-50. That's enough so I took line 2. It worked.
Further: If you go to the main page and click on learning and then on articles, you find Ellen Pomer. Click on her name, scroll down category to Miscellaneous and click on it, then go over to Article Title and click on Cards out.
You will find that the probability of a 2-1 split is 78%. Great, this slam had a 78% chance of making. But I did not need to know that before selecting Line 2 over line 1, I only had to know that Line 2 had a better chance than Line 1.
I told Grant I would try to say something about probability but that I might need some guidance. A short story from 20+ years ago: I had moved and was trying out a new barber. He was good but also chatty, as barbers often are. He got around to asking me what I did for a living and I said I was a mathematician. "Oh, I really love math" he said. Not what I usually hear. The he tried to say a few words more. He acknowledged that he did not like algebra and he did not like geometry. But he really liked, and now he paused for thought to try to think of something he really liked, he really liked addition. It was ok, he was a good barber and I really do not expect mathematics to be a favorite topic at social gatherings.
So guidance would be welcome. I will see if I can say something useful.
Added: These things can quickly get complicated. Suppose the lead had been a heart. This eliminates the need for a heart finesse. So now it seems that we should take the safety play in spades. Win the heart, run the !s J. But wait. It is at least possible that the j will lose to the singleton K or Q and a heart will be returned, ruffed. This gets tough to evaluate. Cards Out tells us that the probability of a 5-1 split is 15%. That means a 5-1 split either way so the probability of a 5-1 split with E holding the 1 is half that. Similarly, the probability of a 3-0 split in spades is 22% and the chance that E holds the 3 is half that. So it might seem that the 11 % chance of E holding all three spades is a bigger changer than the 7.5% chance of E holding a singleton heart. But not really. If E had held, say, 2 or 3 hearts he might have led something else. Mathematics really cannot answer the question as to just how much weight you should put on this. Surely one answer to "Why did he lead a heart?" could be "because it's stiff, if he had 2 or 3 hearts he might well have led something else". I would call this uncertain. I think I would run the
J but it could go wrong. In the case we need to worry about, E has exactly one heart and two spades, giving him 10 minor suit cards. Possibly he would have acted over `1
with that, but with say six diamonds to the Q and four small clubs I would not bet heavily that he would come in. So without being certain that it is right I would win the heart and run the
J.
