[Apollo81]

TimG, on Feb 21 2008, 01:49 PM, said:

cardsharp, on Feb 21 2008, 07:45 AM, said:

Of these, 11 (37%) made 11 tricks of which one (3%) made 12 tricks.

How often can the opponents make 4♠?

What are the passers going to do after 4♠ on their left, passed back to them?

Double and lead the ♦A, and if I knew they were going to balance I'd definitely pass. The problem is that you could easily be cold for 5 (or even 6) clubs or the opps could give it to you on a minor suit lead even if it's not cold

[rbforster]

jdonn, on Feb 21 2008, 01:23 PM, said:

Don't forget all the times the opponents lead a diamond and you get to discard a loser. Not to mention some might underlead the ace of hearts from time to time on this auction...

I did some basic calculations for the opening lead, under standard leading (spade from AK or KQ but not Ax or AQ, no heart away from the A, otherwise all non-club suits equally likely). My estimates are:

P(♠ lead)=53%
P(♥ lead)=13%
P(♦ lead)=34%

The expected gain against the above shapes and relative probabilities was about 1/5 of a trick (0.19). This came from either pitching a quick major loser on a diamond lead opposite a singleton or void, or from guaranteeing the ruffing finesse in hearts when they lead into our void and set up fast pitches.

               Perfect   Real lead
Prob(4♣) 56.5% 41.1%
Prob(5♣) 36.3% 48.3%
Prob(6♣) 7.2% 10.6%

The first column is the "perfect lead" outcome, while the second reflects the realistic leads that may cost. Game becomes a reasonable proposition at both MPs and IMPs, even discounting advance sacrifices.

I will again caution against raising opposite 7♣(321) hands, where even with the lead the majority cannot make game.

               Perfect   Real lead
Prob(4♣) 72.4% 64.5%
Prob(5♣) 26.7% 34.1%
Prob(6♣) 0.9% 1.3%

I did not include the 0.08 or so of a club loser in any of these results (which reduces the total tricks slightly but not qualitatively).

[bid_em_up]

Rob F, on Feb 21 2008, 01:16 PM, said:

I think the earlier simulations were just small statistics and agree with later posts that game is relatively unlikely. Ignoring the off chance of a club loser (partner often has the K or it drops), the most likely shapes and their number of losers are given below:

Shape    Rel Prob    Non-Club Losers
2-2-1-8    16.3%    3
2-1-2-8    16.3%    3
1-2-2-8    13%    2
3-1-1-8    12.2%    3
1-3-1-8    7.6%    2
1-1-3-8    7.6%    2
3-0-2-8    5.4%    2
3-2-0-8    5.4%    3
2-0-3-8    4.2%    2.5
2-3-0-8    4.2%    3
0-2-3-8    2.8%    1
0-3-2-8    2.8%    1
1-0-4-8    1.3%    1.5
0-1-4-8    1%    1

The above probabilities are calculated just based on the known hand's suits, and assumes no useful honor cards except in clubs. In addition, the losers only count top tricks and assume we will take a ruffing finesse if necessary to dispose of diamond losers. It doesn't count the possibility of defensive ruffs, etc. The chances for a club loser are quite small - something like 8% of the time we'll lose a club (missing the K or it doesn't drop), given that all hands with 8 clubs and 2+ of KQJ are equally likely and conditioned on our club holding.

This leads to these outcomes (again ignoring the club suit):

Prob(4♣) 56.5%
Prob(5♣) 36.3%
Prob(6♣) 7.2%

I will add that if your partner makes undisciplined 4♣ preempts on 7♣(321) shape you are much worse off. Now you are very likely to have both 2 spades and a heart loser and the contract probabilities drop to:

Prob(4♣) 72.4%
Prob(5♣) 26.7%
Prob(6♣) 0.9%

Now game is quite poor.

Ok, what am I missing?

If I add the probabilities of all hands that have 2 or fewer non-club losers together, I infer than 5C makes 59.1% of tjme and that you have estimated losers of between 2.5/3 54.4% of the time.

Clearly this is not possible and even it it was, it appears to favor bidding 5C, not that game is unlikely.

[helene_t]

jdonn, on Feb 21 2008, 07:23 PM, said:

Don't forget all the times the opponents lead a diamond and you get to discard a loser. Not to mention some might underlead the ace of hearts from time to time on this auction...

Don't think many would underlead an ace after that auction (surely it could work if dummy has ♥KJx and declarer xx), but what could happen is the lead of heart and p is void.

[rbforster]

bid_em_up, on Feb 21 2008, 02:50 PM, said:

Ok, what am I missing?

If I add the probabilities of all hands that have 2 or fewer non-club losers together, I infer than 5C makes 59.1% of tjme and that you have estimated losers of between 2.5/3 54.4% of the time.

I think you might need to check your math.

Rob F, on Feb 21 2008, 01:16 PM, said:

Shape    Rel Prob    Non-Club Losers
2-2-1-8    16.3%    3
2-1-2-8    16.3%    3
3-1-1-8    12.2%    3
3-2-0-8    5.4%    3
2-3-0-8    4.2%    3

2-0-3-8    4.2%    2.5

For 3 loser hands, I see 16+16+12+5+4=53% without counting the 2.5's at half or something.

[hrothgar]

bid_em_up, on Feb 21 2008, 10:50 PM, said:

Ok, what am I missing?

If I add the probabilities of all hands that have 2 or fewer non-club losers together, I infer than 5C makes 59.1% of tjme and that you have estimated losers of between 2.5/3 54.4% of the time.

Clearly this is not possible and even it it was, it appears to favor bidding 5C, not that game is unlikely.

Check your math.

I ended up with 41.7%

[bid_em_up]

Rob F, on Feb 21 2008, 03:10 PM, said:

I think you might need to check your math.

Possibly.