037: Par

thI played a full weekend’s worth of bridge recently at a local sectional tournament, plus a couple of other evenings of bridge, and I have a few topics stored up about which I can write. But the most urgent one seems to be par.

When you play in a tournament with pre-set hands arranged by the ACBL, at the end of the session you receive a piece of paper that contains the boards that you played — the “hand record”. At the bottom of each hand in the hand record is a listing of all the contracts that can be achieved by any player.  Here’s an example that brought the topic up for many players:

Board 18 (Par)You’ll note that no bidding is given; this is deliberate. East deals, and N/S are vulnerable. At the bottom of the hand you’ll see all the possible contracts that are “unstoppable”; that is to say, for instance, North can make 6D against any defense. This is not to say that if N/S stumble into a 6D contract, they’ll make it; there’s always the possibility of misplaying the hand. Similarly, if N/S are in 6D and E/W misdefend, N/S might make all the tricks. (Incidentally, no one is saying that these contracts are sensible, or that anyone would actually bid them and play them. But they’re possible and makable.)

Let’s take a moment and look at the values for all the unstoppable contracts. For the purposes of this discussion, we’ll express them all in terms of the N/S scores. So for 6D N/S, they would score +1370. 4NT by South = +630; 4S by South = 620; 1NT by North = +90; 1H by E/W = -80; 1C N/S = +70.

Note that the highest-value contract that can be guaranteed for E/W is 1H. Therefore, if E/W end up in 2H, they’ll probably be down one; if they’re in 4H, down three, etc.  Similarly, the highest-value contract for N/S is 6D. If they end up in 7D, they’ll be down one.  So from N/S’s point of view, the best contract to be in is 6D, making +1370 if they play it properly. (And as you can see, it’s easy to play; they lose the ace of hearts, ruff South’s spades good, and all remaining losers go on the long diamonds.)

This is where the concept of par comes in. Let’s define par and then explain it in the context of this hand:

Par is the contract and score that are produced by the best efforts of both sides in the bidding, making the best possible decisions. 

If you look at this hand entirely from N/S’s point of view, the best result is +1370 — which results in a score for E/W of -1370. But E/W’s best interests are not served by sitting back quietly and scoring -1370. If E/W find their heart fit, they can play a contract that yields scores ramping up from the excellent 1H making 1, for +80 their way (or, in N/S terms as we’ve been looking at this so far, N/S -80). The higher level E/W reach in hearts, the larger the penalty they will take — but if they end up in 7H, which will be down six if N/S defend properly, and N/S have the sense to double, they’ll be down -1400. -1400 is worse than the best score N/S can legitimately achieve, 1370, so -1400 should yield a zero for E/W. The best score that E/W can achieve is down five doubled for -1100, since they’ve still lost less than N/S’s best score of 1370.

Therefore, the best bidding efforts of N/S should put them in 6D making six, and the best bidding efforts of E/W should put them in 6HX down five.

If N/S decide to bid 7D and get doubled, they’ll be down 1 for -200 and a very probable zero; as above, if E/W go to 7HX they’ll be down 1400 for a very probable zero. Since the highest biddable contract is E/W in 6HX down five, that becomes par.

Now, it’s important to realize that par is not going to happen at every table; in fact, par is not likely to occur at ANY table, since none of us has a knowledge of what the cards will produce. At my table, N/S played in 5D making six for a score of N/S +620.  At another table N/S decided to take the penalty from E/W in 5HX down four, -800, which actually got them a good board — because no E/W pair figured out that 6HX down five was the best contract. The top match point scores were made by N/S pairs who bid and made 6D — no E/W pairs doubled that contract, incorrectly but temptingly. Par on this board was not achieved.

So the next time you see the hand record telling you what “par” is for the board, it’s merely a guide to what could have happened, not what actually did happen. Par is the optimal contract but, as we all know, hindsight is 20/20.




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