How to Avoid a Strategic Illusion
I want to make an observation about a strategic inference that we often overlook, sometimes paying a heavy penalty. The inference is easy to state: when considering if A is consistent with B, no matter how convincing the story ends up being, always check whether (not A) is consistent with B.
It doesn't matter how convincing you think the story about A being consistent with B is: always check the reverse implication, and then look for facts which will distinguish the two stories. It is too easy to be tied to one story, if you have not considered the alternatives.
Here is a really nice example of this thinking, from a bridge tip from the famous Zia Mahmood. Consider the following layout and problem.
The contract is six clubs by South, and there are no clues from the bidding as to the location of the missing honours.
Here is the layout of the hand.
North South
S Q2 S AJ10 H 53 H K2 D 1094 D AKQ3 C AK10972 C Q653
Let's suppose that you know that diamonds are going to break. To make the contract then, you can only lose trick between hearts and spades.
There are four finesses that you could take:
1. the backward finesse of leading a small heart from the board and playing the K if the A is not played,
2. the backward finesse of playing the spade 10 from the hand and playing the spade Q if the K is not played.,
3. the straightforward finesse of playing the spade Q from the board and letting it ride if the K is not played, and
4. finally, a ruffing finesse in spades by discarding the 2 of spades on the extra diamond, playing the spade A and J, letting it ride if not covered by the spade K.
The spade suit looks promising because one of the finesses must work, either the straightforward finesse, leading the Q, or the ruffing finesse, leading the J.
Decide what you would do and why.
Now, suppose you are watching this match on television, but with a twist. You cannot see the play by East or West, but can bet or gamble on what cards were played given the play by North and South. Suppose you see the board playing the spade Q, and some spade card from East, and then the spade A from the closed hand, and some other spade card by West.
What are the chances that East, a competent player, covered the Q with the K? If you had to bet on which was more likely, East covered or East did not cover, what would you bet on? How confident are you of your bet?
Most people will reason that that if the closed hand played the A it was to capture the King played by East. The lead of the spade Q from the board is the beginning of a straightforward finesse and if the spade K is not played from East, then the closed hand will let the Queen ride to finesse East. Therefore, it is much more likely given the play of the spade A that East covered with the spade K. Right?
Make your bet, then. Again, how confident are you of your bet? Because I am going to bet that the play of the King basically tracked the underlying distribution, a 50/50 proposition. Are you going to take this bet? Confident about that?
Not so fast. Most people don't have the bridge acumen of Zia Mahmood. He reasoned differently. If East doesn't cover, then East's play reveals that he doesn't have the spade King, and so the straightforward finesse is going to lose. (East will not gamble on South holding something like AJx of spades, and so must cover if he has the King.) When East doesn't cover, then West has the spade K and the ruffing finesse is going to work. Although we started with the straightforward finesse, the play has revealed it as a loser, we have time and can now stop: play the spade A, play our diamond, discard the board's last spade, and then take the "proven" ruffing finesse by leading the spade J through West.
Thus, South was going to play the spade A, whether or not East covered! The play of the spade A is consistent with both East covering and not covering, and since the underlying distribution of the spade K is equal, you just lost your bet.
Although the story of the Queen being covered by the King jumps to mind first, possibly as the result of the Queen causing the King to cover, the other harder story, that the ruffing finesse is working, has to be considered. If you were very confident about your bet, then you do really need to explicitly perform this check on your strategic inference. If A is consistent with B, no matter how compelling that story is, check for an equally compelling story about (not A) being consistent with B.
I will discuss this further in relationship with a purported whistleblower, stay tuned.
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