It's been a while since the last post, but I promised neither frequency nor regularity so won't apologise! I've just not been doing very much simulating recently. Somebody did ask me a question towards the end of last year so I might post on that subject at some point. Anyway, on to today's topic, which isn't even about simulations at all.
Your partner is declaring a game contract and has to tackle a suit of AKJx opposite xxxx. With zero information to go on other than the a priori odds, he plays for the drop and goes down one, -100. At your teammates' table, they take the finesse and make the contract, +620, lose 12 IMPs. Your partner has just carved the contract and cost your team 12 IMPs. What an idiot! And you tell him so.
Now, this isn't a piece about being polite to partner. You'd be better off keeping quiet and moving on to the next board, but some people can't keep schtum and have to say something. It's the magnitude that I'm questioning. You shouldn't tell him off for losing 12 IMPs, you should tell him off for losing 0.8 IMPs.
What am I talking about? He clearly lost 12 IMPs because there's a big 12 written in the minus column and it was all his fault! But this doesn't account for the fact that he might have been successful in his line on a luckier day, or it might have made no difference. He wasn't
always going to lose 12 IMPs when he made this decision.
These are the probabilities of the various opposition holdings, courtesy of
Richard Pavlicek's calculator tool:
East West Ways %
1 Qxxxx — 1 1.96
2 Qxxx x 4 11.30
3 Qxx xx 6 20.35
4 Qx xxx 4 13.57
5 Q xxxx 1 2.83
6 xxxx Q 1 2.83
7 xxx Qx 4 13.57
8 xx Qxx 6 20.35
9 x Qxxx 4 11.30
10 — Qxxxx 1 1.96
It's quite straight-forward. For instance, line 1 shows that there is a 1.96% chance of East having all five missing cards. The blue lines are where it makes no difference which line you take. If the suit is 5-0, for example, both the finesser and the dropper will realise on the first round and make the same number of tricks. The red line is where the dropper will make while the finesser will go off. The green line is where the finesser will make while the dropper will go off. The finesser wins 20.35% of the time and the dropper 13.57% of the time. The ratio between these is why you see in books that the finesse is a 3:2 favourite.
Let's look at it in terms of IMPs. For all the blue cases — about two thirds of the time — it's a flat board. For the green case the finesser wins 12 IMPs. For the red case the dropper wins 12 IMPs. Thus, the finesser will win on average (0.6608 * 0) + (0.2035 * 12) + (0.1357 * -12) = 0.8136 IMPs.
As you can see, the 12 IMPs your partner cost the team is a mirage. He made a 0.8 IMP mistake — the rest of it was just bad luck. If his line had made it would still have been a 0.8 IMP mistake, even if it had gained IMPs. Now, 0.8 IMP mistakes are fairly bad as things go — if you make them on every board of a 32-board match you'll lose by a whole 26 IMPs — but there are far worse crimes at the bridge table.
Here's an example of a far worse crime. You're declaring 3NT and have 10 tricks on top. You merrily cash them away, lose concentration, don't realise you're actually squeezing somebody and your six of clubs is good. You've dropped an overtrick and your team loses 1 IMP. No probability calculations are needed — your play had no upside and you just took a 0% line for 11 tricks when you had a 100% line available. Your mistake was worth precisely 1 IMP, clearly greater than 0.8 IMPs. Next time your partner takes a view and plays for the drop instead of finessing, don't be so hard on him — especially if you dropped an overtrick earlier on!
Now one thing (as you may be shouting out now) which I've ignored here is
variance. Given the choice of which mistake to make you might claim you'd still prefer to lose an overtrick, because if you're 5 IMPs up going into the last board of a knockout match then the overtrick error will never cost anything, whereas the failure to finesse will cost the match 20% of the time. And that might be true but it does require some fairly rigid assumptions. It goes out the window when you play a league match, or a multiple teams event, or it's early on in a sufficiently long knockout match. For the vast majority of situations, all you should need to worry about is maximising your expected number of IMPs.
One lesson you might learn from this is to not let yourself get bogged down in esoteric safety plays and squeeze chances and ignore simple basics like concentration and card counting. Very few of these plays will gain you more than half an IMP of advantage over the 'normal' line. It's all a waste of time as soon as you make a silly mistake and let through a no-play game costing 12 IMPs. Even if you only make one such mistake every 100 boards (and very few of us could say that), you're going to have to find the half-IMP brilliancy every 4 boards in order to compensate. The random deal just doesn't provide that kind of ammunition.
Other lessons you might learn are ones of partnership harmony. Don't be so hard on partner when his mistake appears to cost a game swing. At least consider whether his play had an upside or whether it would usually have made no difference at all. You've almost certainly made lots of marginally negative plays too, but they didn't happen to get highlighted by fate. And try to remember that just the other week you took a finesse to win 10 IMPs when you should have played for a 3-2 break and earned a flat board. It was still an error, despite the outcome, and partner said nothing.
K 2 
-- 
J 2 
A K J 10 6 5 4 3 2
after three passes. My reasoning: on the evidence so far, my expectation would be that we have 8/9 hearts between us, and oppo have 8/9 spades. So by LTT this is likely to be a 17-trick hand. By virtue of the concentration of hearts in my hand, and the absence of a 2