[jdeegan]

A recent hand from the JEC bridge salon. The contract is 6♠. There are no losers outside the trump suit. The ♠ holding is:

♠10632 (dummy)

♠KJ854 (your hand)

Alas, you are really good bidders, but your system just didn't get the ♠9 in the auction.

So, how now, grasshopper?

On the surface, you have two, apparently equal, cases to consider. The difference: Play one: RHO can have ♠ AQ97 opposite void. Play two: ♠Q opposite A97. Superficially, both seem equally likely. Richard Pavilcek and the 'law of vacant spaces' say no because 4-0 splits are less likely than 3-1 splits. But, fear not. Google 'Pavlicek'. Click on 'Bridge Calculators'. Next on 'Card Combination Analysis'. Figure it out. Now you too can divine the subtle differences (and, normally, they are very minor) in these probability situations. With play one, you start with the ♠10 off the dummy. With play two, lead small.

It turns out that, absent any other info, there is only a very minor 1.5% difference between the chance of ♠AQ97 opposite void, and ♠Q opposite A97. You don't have to remember much more than that a 4-0 split is less likely than a 3-1 split and adjust the odds (very) slightly. If you have more info from the bidding or play, then you might be able to adjust the odds a fair amount. For example, if RHO overcalled a suit showing 5 or 6, then it reduces the odds of him/her having ♠AQ97. The odds of ♠Q opposite A97 increases. The spread of 1.5% goes up from to 4%. So, starting with the ten looks not so good in this situation.

It is still not safe to come in out of the rain. JEC's partner on this hand is a fearsome rubber bridge player. In his world, players sometimes cover an honor with an honor when they should not. You should only do so only when covering builds a trick, either in your hand or partners. In the opponent's trump suit, this sort of trick promotion happens rarely.

So, how do you play this card combination?

Turns out, JEC's partner led the ♠10, the ♠ seven showed, so he floated it to the ♠ace. It worked as ♠ were Q7 onside versus A9 offside. What fun. At the other table in this high level game? The contract was also 6♠. For whatever reason, declarer played a small ♠ to the king. Down one.

[Fluffy]

Playing the 10 loses to BOTH stiff queens not only 1, and there are other positions to consider. But you are talking about JEC match were intrafinesses are succesful.

[johnu]

Running the 10 picks up singleton 7, 9, or A (have to guess if 10 is covered) offside, AQ97 onside, or Q9/Q7 onside.

Low to J picks up onside singleton Q, offside singleton 7, 9, but loses to singleton A, loses to AQ97 onside, picks up Q9/Q7 onside.

I think that makes running the 10 the favorite.

Interestingly, you hope RHO doesn't cover the 10 with Q97 since you can't go wrong when the 10 forces the ace. Covering is the right play with this combination because it gives declarer a guess.

[rhm]

johnu, on 2013-September-26, 23:02, said:

Running the 10 picks up singleton 7, 9, or A (have to guess if 10 is covered) offside, AQ97 onside, or Q9/Q7 onside.

Low to J picks up onside singleton Q, offside singleton 7, 9, but loses to singleton A, loses to AQ97 onside, picks up Q9/Q7 onside.

I think that makes running the 10 the favorite.

No it does not.
Running the 10,which of course gets covered from either Q7 or Q97, you can not claim to make the contract against both singleton ace and A9 offside
Suitplay offers only low to the jack.
I am pretty sure that is your best chance for 4 tricks, admittedly by a small margin, a 39% chance.

I also think that trick promotion by covering happens rarely is nonsense.
Average player cover too frequently, because it is more likely to be right than wrong if you do not analyze the specific situation.

Rainer Herrmann

[Lorne50]

jdeegan, on 2013-September-26, 18:52, said:

On the surface, you have two, apparently equal, cases to consider. The difference: Play one: RHO can have ♠ AQ97 opposite void. Play two: ♠Q opposite A97. Superficially, both seem equally likely. Richard Pavilcek and the 'law of vacant spaces' say no because 4-0 splits are less likely than 3-1 splits.

It's not just that 3-1 is more common than 4-0 as you are looking at specifically 1 out of 2 possible 4-0 breaks against 1 out of 8 possible 3-1 breaks.

The odds or 4-0 are 13/26 * 12/25 * 11/24 * 10/23 = 4.78%, the top line of each division being the vacant spaces in the hand you want the card to go and the bottom line the spaces in both hands at the time each is dealt.

For 3-1 if you assume the Q dealt first it is 13/26 to go in the right place, then the next 3 cards are 13/25, 12/24, & 11/23 which comes to 6.22% (and you get the same number if you repeat it for the Q dealt 2nd, 3rd or 4th).

so the relevant 3-1 break is 30% more likely than the relevant 4-0 break in the cases where one of these two breaks occur.

[PhilKing]

These maths threads are generally pretty lol, and this one is no exception. Forget all these micro-advantages and get to grips with the big picture.

Running the ten is way better as long as the defence do not know your exact hand. It's not clear to cover with Q97, since you mak have AJ854 and need to play the trumps for no losers, and Qx is not a clear cover if you may have AJ to six. And even if they can work out it is best to cover, in practice they may not.

Also, no account has been made for the correct mixed strategy dictating how often East should cover, to protect himself from us rising king when he does not (which Suitplay will have accounted for).

It's worth knowing a lot of suit combinations, but do not let them dictate you line on hands where the defence may err.

[jdeegan]

It is really quite simple. Small to the jack wins whenever the queen is onside except for AQ97 - a percentage success rate of 45.2%. Ten off the dummy wins whenever the queen is onside unless it is stiff - a percentage success rate of 43.8%. The interesting part is that Q opposite A97 is more likely by 1.5% than AQ97 opposite void due to the law of vacant spaces.

On this this particular hand, declarer is known to have 9 or ten spades in the trump suit. Anyone who covers a lead of the ten with his/her queen by choice is a really weak player.

[jdeegan]

Lorne50, on 2013-September-27, 07:51, said:

It's not just that 3-1 is more common than 4-0 as you are looking at specifically 1 out of 2 possible 4-0 breaks against 1 out of 8 possible 3-1 breaks.

The odds or 4-0 are 13/26 * 12/25 * 11/24 * 10/23 = 4.78%, the top line of each division being the vacant spaces in the hand you want the card to go and the bottom line the spaces in both hands at the time each is dealt.

For 3-1 if you assume the Q dealt first it is 13/26 to go in the right place, then the next 3 cards are 13/25, 12/24, & 11/23 which comes to 6.22% (and you get the same number if you repeat it for the Q dealt 2nd, 3rd or 4th).

so the relevant 3-1 break is 30% more likely than the relevant 4-0 break in the cases where one of these two breaks occur.

These are exactly the numbers you get from Pavlicek's little computer gizmo.

[johnu]

rhm, on 2013-September-27, 01:43, said:

No it does not.
Running the 10,which of course gets covered from either Q7 or Q97, you can not claim to make the contract against both singleton ace and A9 offside

I didn't claim 100%, that's why I wrote "have to guess if 10 is covered" but wasn't as clear as I should have been.

[benlessard]

Quote

Running the ten is way better as long as the defence do not know your exact hand. It's not clear to cover with Q97

I agree with the first statement but covering with Q97 is really a sucker play.

Txxx

AKJxx

[PhilKing]

benlessard, on 2013-October-03, 00:31, said:

I agree with the first statement but covering with Q97 is really a sucker play.

Txxx

AKJxx

It ain't necessarily so. Obviously it's a sucker play in general, but this is one of the reasons why it is ridiculous not to give the whole hand. It's entirely possible that, by the time trumps are played, the defender knows he needs two trump tricks.

Say you knew from keycard that declarer had only one spade honour in a five-card suit, it is somewhat more likely to be the king than the ace given the play, so covering may well be necessary (as it is from Qx).