Posted 2007-February-21, 10:56
This is imps. This is one of the areas in which imps truly is a different game than mps.
Consider the odds: what you stand to win and lose by doubling. In making such a decision, it is wise to assume that partner has a bad hand, in context. When he shows 15-18, statistically he will hold far more 15 counts than 18s. Making tight doubles on the assumption that partner has the top of his range is not a good business plan.
So, if he has 15-16, then the opps have roughly half the deck and more than half the trump: I'd guess they own about 7.4 trump on average: if partner has a stiff, he will sometimes be able to compete either via 2♠ or 3♣, but he may have a motheaten 6 card ♠ suit and 15 hcp or some 5143 with a terrible minimum.
On this scenario, we have little expectation of -2: we are really doubling in the expectation of beating them 1.
Let's make some assumptions and see how double works out:
Let's say that we have a 5% chance of +300, a 60% chance of +100, a 30% chance of -470 and a 5% chance of -570.
+300 wins 5 imps 5% of the time (as opposed to +100, undoubled)
+100 wins 2 imps 60% of the time
-470 loses 8 imps 30% of the time
-570 loses 9 imps 5% of the time
This means that over 100 simulated deals with these odds, doubling loses an average of 1.4 imps per board. And note that we are assuming that we are twice as likely to beat them 1 as opposed to their making precisely 2.
Unless your team is FAR stronger than the opps, spotting a team 1.4 imps a board gives you no realistic chance in a long match.
We can all quibble about the percentages, but the point is that the double has to be a heavy, heavy favourite to be right. Even if we make it 70% -1 and 20% making, we still lose imps on average! If we ignore extra undertricks or overtricks, and simply say that the contract will either make or fail by 1, the odds need to be 4-1 in favour of a set in order to break even... not to make doubling a long-term winner... just to prevent it being a loser.
And this cold analysis leaves out the psychological factors. If my opps make a double like this and beat me 1, I actually get encouraged: I know that my opps are reckless and I expect to beat them handily in a long match. And if we make the contract, I get even more confident, while, usually, the opps are unhappy.
'one of the great markers of the advance of human kindness is the howls you will hear from the Men of God' Johann Hari