At Best vs. At Worst

The Long Beach Regional just concluded this past Sunday. The Sunday Swiss is always a big event at the end of the regional.

In the last round, my team was in first place by five VP’s. My partner, Ed Piken, faced an interesting bidding decision.

Holding ♠AKQJ963  ♥K  ♦A75  ♣Q6, he heard the bidding proceed:

Mark	Opp	Ed	Opp
1N (15-17)	P	4♥ (Transfer)	P
4♠	P	4N (KCB)	P
5♥ (2 KC, no Q♠)	P	5N (Kings?)	P
6♠ (No Side Kings)	P	?

At first glance, this seems like a simple problem. Partner has no side kings, so we should just sign off in six. However, Ed took the time to think deeper about this. Nineteen points in his hand plus fifteen points in my hand is 34. Add in the two side kings that I denied to get to 40 points. So I must hold all the rest of the high cards. Ed envisioned a hand like:

♠42
♥AQJ7
♦QJ86
♣AJ8

With this hand there are seven spade tricks, four heart tricks and the two minor suit aces for thirteen tricks off the top. So now he should just bid 7♠ (or 7NT), right? Well, there is a small issue with that. What if my hand was:

♠42
♥AQJ
♦QJ86
♣AJ87

Now we only have three heart tricks despite holding the four top heart honors. So how do we resolve this? So, let’s review. Ed analyzed that the grand slam may be cold, but that if it wasn’t there was still a chance to make it via a winning finesse (granted that on this hand, I would probably have to guess which finesse to take), which means that a grand slam was at worst on a finesse.

To see why this is important, let’s change the hand and bidding on this just a bit. Suppose that Ed’s hand was this:

♠AQJ9632  ♥K  ♦AK5  ♣Q6

 

Mark	Opp	Ed	Opp
1N (15-17)	P	4♥ (Transfer)	P
4♠	P	4N (KCB)	P
5♥ (2 KC, no Q♠)	P	?

Here, even if I told you that my hand contained the ♣K, you would know that we might be missing an ace, and down in 7♠ off the top. But if we aren’t off an ace, then we could make thirteen tricks via a successful spade finesse. So in this case, we are at best on a finesse. Note the difference between the two – if in the bidding you can identify the best case and worst case scenarios for a bid and put some estimates on the two extremes, that can help you make bids that put the odds in your favor.

So in our first scenario, let’s make some estimates. Given that Ed’s hand only had one heart, that increases the chances that my hand has four hearts (or more). The math gets complicated here, but thanks to some tools from Durango Bill’s Bridge Probabilities and Combinatorics I am able to estimate that those odds are about 56%. For the remaining 44%, the finesse will succeed 50% of the time for an additional 22% where we make thirteen tricks. So in the bidding, we think that the grand slam will succeed 78% of the time. That brings it over the line of 55-69% to make a grand slam worth bidding as suggested by Alan Truscott in a 1981 New York Times bridge column.

In the second case, approximately 50% of the time, the missing key card will be an ace (ignoring the adjustment for the odd of holding 15, 16 or 17 points). And in the 50% of the time where the missing key card is the ♠K, the finesse will be off 50% of the time. So the odds of the grand slam during the bidding are 25%, a distinctly bad proposition.

Ed thought this through (although without the detail mathematics) and decided that the combination of the odds of seven making was enough to justify bidding the grand, and I agree with his decision.

So how did it work out?

♠AKQJ963
♥K
♦A75
♣Q6

♠72
♥AQ6
♦QJ983
♣AJ8

Ugh…another fly in the ointment. This time I upgraded by good fourteen count to a 1N opening because of the five card diamond suit with good spots. Perhaps we needed to account for that in our calculations…

So we fell into the “at worst” part. And unfortunately on this hand, both minor suit finesses were off, so I had no way to guess or squeeze out the thirteenth trick. So, unhappy ending, right?

Well, Ed and I did have a couple of other good results in the round and our partners, Phil Hiestand and Rai Osborne supplied another one of their consistently strong cards during the day for us to win the final match and the event.  So we lost the battle, but won the war.

I hope that if my partner or I were faced with this type of position again that each of us would make the exact same decision – going with the odds is the winning strategy over the long run. You don’t have to remember the calculations involved in this, but if you remember the difference between an “at worst” and an “at best” situation, you will make better decisions.