Declaring the Odds

Here is one hand that I spent a long time thinking about the percentage play to make the contract, and I tried to calculate it mathematically but I don't trust my combinatorics skills anymore. In an otherwise flat match, I was in 4H - making would mean winning the match (against a team I want to beat more than any other - Emory, Bob Heller, Owen, and Warren Roberts) by 1 and going down would mean losing the match by 10 imps, since 3NT managed to make at the other table (possibly with a low diamond lead from the KQ or blocking diamonds or not leading a diamond - I don't know - perhaps Emory will share how he was allowed to make it)

KTxx
xx
Ax
Axxxx

AQ
AJ9xxx
Jx
Qxx

West led a big diamond and the contract looked unlikely to make but I pondered upon the 2 main options I had:

One line is to play a heart from dummy immediately toward the 9, conceding a diamond loser but allowing myself to finesse trumps. This wins whenever hearts can be picked up for 1 loser and picking up clubs for 1 loser. Basically, needing a 3-2 split with KQ tight or KQT, or HT(x) onside, and the suit combination table says this is 27%. From that 27% we have to subtract the chances of having to lose 2 club tricks. Initially when I did the calculations I thought this was about 50% but it's closer to 10% that you'll have to lose 2 club tricks. Either LHO will lead a club for you after taking the first heart (and may then get to ruff one if he had a stiff) or LHO will lead something else in which case you can pitch a club on the spade K (creating an extra loser when spades are 5-2 and the one that ruffs is not doing so with a natural trump trick. I guess this brings it down to about 24%.

Another line, which is the one I chose, is to take the diamond ace, spade ace and queen, cross to the club ace and play the spade K to pitch the diamond loser. When that held, I led a club toward the queen. Even if LHO ruffs, he is fairly likely to have started with 3 or 4 trumps - it would only cost if a hand with only 1 or 2 hearts gets to ruff in. So, this line makes the contract when: spades are 4-3, the club K is onside, and they don't get to ruff a club with a doubleton or singleton heart. Plus the spade J may drop tripleton and then you can lead the 4th spade to pitch a club so you don't need the club to be onside, hoping again that they have to ruff with the long trumps. My math shows this line to be about 24% as well so I guess it's a play question no one is going to win.

LHO had 2 small clubs and Qx of hearts so I went down when he got to trump a club and RHO still had 2 natural trump tricks with KTx and me having no more entry to finesse.

Overall this sectional in Atlanta was somewhat disappointing at least as far as bridge results are concerned. 5 sessions and less than 5 masterpoints, almost all of which came in the Saturday night single-session Swiss game during which (and for an hour and a half before and afterward) I was drinking copious amounts of the free beer. Sean and I continued our streak of getting blitzed in the first round of Sunday Swisses. But we did not continue our streak of placing overall despite horrendous starts.