[Fluffy]

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Play 6 clubs on a ♦Q lead.


the math problem, if we could assume ♦Q leader has ♦QJ regardless or ♦10 position, IE, we have 2 known diamond cards in one hand, no diamond cards in the other, what are the chances or the suit being 3-2 or 4-1 or 5-0?

next problem is when ♦Q can also be singleton.

[gnasher]

Fluffy, on 2012-July-28, 04:04, said:

the math problem, if we could assume ♦Q leader has ♦QJ regardless or ♦10 position, IE, we have 2 known diamond cards in one hand, no diamond cards in the other, what are the chances or the suit being 3-2 or 4-1 or 5-0?

I'll do the easy bit first. Given that ♦QJ are on the left, these are the chances of each break:
QJ-xxx: 13/24 * 12/23 * 11/22 = 14.1%
QJx-xx: 11/24 * 13/23 * 12/22 * 3 = 42.4%
QJxx-x: 11/24 * 10/23 * 13/22 * 3 = 35.3%
QJxxx-void: 11/24 * 10/23 * 9/22 = 8.2%

So the chance of any 3-2 break is 56.5%

[dave_w]

I like ♣K, Club to the Jack. If it loses then I'm backing diamonds to be no worse than 3-2. If it wins then ruff a Spade, Cross to the ♥Ace, draw the trump and claim. If Clubs are 4-0 (either way) then I think I'm struggling a lot. If RHO shows out on the second club then I'll lead a diamond towards dummy, take the Heart hook, ruff a Diamond, ruff a Spade, play a good Diamond pitching my Heart.

This seems to fail when LHO is 1-3 in Diamonds and Clubs and I can't pick up Hearts for no loser or when RHO has 10 cards in the Majors and I can't pick up Hearts for no loser. Seems like pretty good odds to me - especially as in the failing cases of needing to pick up Hearts I'll know whether to play for Kx of Hearts or Tx of Hearts.