Friday, November 27, 2009

What's NOT a good pruning strategy in Bridge - Part 2

In the previous post I have presented a counter-example to the following heuristic for selecting a move:
Among all cards that are impossible to win the current winning card, only the one with smallest rank is selected. [1]
My counter example only applied to the trick to be taken by partner. Last night I let Gnubridge look for counter examples when the trick was being taken by the opponent, and fairly quickly it came back with the following (Hearts are trump):

If East applies the strategy in question, he will play 5H, and arrive at the following position, after North plays 2H on the next trick:

East will take the next trick with 9H, but the last trick will be captured by South.

The correct play to North's JH in the first example would have been 9H, leading to the last two tricks being captured by East/West. Therefore, the above strategy is flawed, and should not be used in reducing the number of positions to analyze by double-dummy solvers.

As I understand this strategy is often taught to beginning bridge players, and it is still quite relevant in single dummy bridge, it's just that it is not always optimal. If a player possesses knowledge of distribution of all the cards remaining in play, he should avoid this mental shortcut in his analysis.

[1] Building a Fast Double-Dummy Bridge Solver – Ming-Sheng Chang, Ming-sheng Chang Phd Student - 1996


  1. While you're correct in that this isn't a good pruning strategy it is a vital move ordering strategy. You should always try the the lowest card first when you cannot win a trick. It will result in a significantly reduced tree size.

  2. It has been awhile, but I have a vague recollection that I tried this out and it did not lead to substantial improvements in practice (no more than 20%). I'll rerun the experiment some time this week and post the results - or maybe you can beat me to it.