shyams, on 2020-August-10, 20:04, said:
The above line is obviously very good at IMPs; it improves the odds of bringing in 10 tricks.
My issue was that it was MPs. Can I (or should I) play for a different layout where the upside of scoring +1 is higher than the downside of being defeated in a "cold" game? For example, is ♦A followed by both trumps in dummy, then top ♦ better given that an additional chance of ♦ 4-2 but the doubleton holder also has ♥xx and is unable to ruff?
Al's line is better, and it's pretty easy to analyze. When do the lines differ in their results?
1. If the third diamond is ruffed, then Al's line is better unless West has both club honors (in which case both lines go -1).
2. If the third diamond honor lives, your line is better only if West has both club honors.
In #2, the lines are equal if the club honors are split, because Al gets to take two C hooks, but you only get one (so you lose two C tricks and a spade; Al loses one C trick and 2 spades). Likewise, the lines are equal if East has both C honors, because Al will get a second chance to throw a spade on the third diamond (he wins when East splits his C honors, goes back with a trump, and plays a D honor since he doesn't need the second C hook any more).
Considering just the diamonds, I think case 2 is ever so slightly more likely than case 1. BUT - case 2 only wins if West has both club honors, whereas case 1 wins UNLESS West has both club honors.
West is not at all likely to have both club honors, because on the bidding, a lead from KQ(xxx) is a lot more attractive than one from 2-4 of dummy's suit.
Thus, 1 will gain almost all the time when the third diamond is ruffed. 2 generally won't gain vs. 1 even if the third diamond lives.
Go with Al's line -- #1.
Cheers,
Mike
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My greedy guess. ♦A ♥ ♦s.
- If both opponents follow to 3 rounds discard 2 ♠s and take the ♣ finesse.
- If a defender ruffs the 3rd ♦, then over-ruff if possible. Anyway cross to dummy's ♥Q, and finesse ♣s, hoping RHO has ♣KQ.
Arithmetic is not my long suit but
- Two rounds of ♦ then 2 ♣ finesses = (48% + 36%) X 75% = 63%
- Three rounds of ♦ then a ♣ finesse = 36% + (48% X 25%) = 48%
- But 36% of the time you have a 75% of an overtrick = 27%
If most players reach game that might swing the the odds in favour of the greedy line.
Oh dear, I overlooked the fact that if both clubs are right, then a declarer, who takes 1 diamond discard and finesses clubs, also makes an overtrick when diamonds are 3-3