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Most bridge teachers (and books) teach players to draw trumps at the first possible opportunity. The reason is that you don't want your opponents to take tricks with low trumps. (If they have the A, or Kx or Qxx "offside" your ace, their high trumps will take tricks.)

One exception is a cross-ruff. Then you want to take your top card winners in side suits, before cross-ruffing, so that your opponents can't discard those suits and later ruff your high cards with their remaining trumps.

Another example that was given in a bridge write-up was when you want to ruff low cards in one hand with trumps in the other hand (after it runs out of the suit). If you do this, you leave opposing trumps outstanding. On the other hand, is it true that the act of your ruffing (thus playing trumps from one hand), "qualifies" as a trump play so that you don't leave yourself unprotected? Or put another way, does it often make sense to ruff before drawing trumps?

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I don't really get your question: I can't seem to make sense of the second last sentence. Can you please elaborate? Also, what exactly do you mean by "often" (in the last sentence). –  Aryabhata Jul 1 '12 at 5:32
    
@Aryabhata: Today, I might word the question, "if drawing trumps is a good thing, is ruffing an adequate substitute." And my answer was yes. –  Tom Au Jul 1 '12 at 21:34
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2 Answers

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There isn't really a single answer to this; when to draw trumps and when not to is probably the area where most judgement is called for, as opposed to applying rules. You have to balance the probable gain from ruffing early against the possible loss if the opponents ruff your winners later (or, of course, over-ruff). I realize this isn't necessarily helpful, so here's a list (non-exhaustive) of factors that weigh against taking out trumps:

You can use a trump in the short hand (ie one that would be swallowed if you take out trumps).

You have enough high trumps to ruff high without compromising control.

You have a long suit that can be established by a ruff or two (in which case of course you must take out trumps after the ruff).

After one or two rounds, the opponents have the high trumps: they're going to win anyway, no sense in letting them take your trumps as well.

You can see that normal play, such as taking out trumps, will leave you one trick short, so a gamble will give better returns than normal in the score.

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A very good summary of multiple scenarios. –  Tom Au Jun 30 '12 at 20:11
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Like most aphorisms, this has a grain of truth, but also needs to be taken with a grain of salt.

Trump is the most powerful suit on the board. That's a good reason for PLAYING them early, but not necessarily drawing them early.

Suppose you have a singleton in a side suit in dummy, and Axx in your hand. You'll want to take the ace, ruff an x, get back to your hand (possibly with a trump), and ruff the other x. With only four in the suit, your opponents will have nine. And if no one bid the suit at the three level, you can safely assume that they are distributed 6-3 or 5-4. If you have three trumps in dummy, you can't afford to draw more than one (possibly to get back to your hand), because you'd be drawing YOUR OWN trumps.

In other cases, you'll be ruffing longer suits, but may have high trumps in dummy to overruff anything your opponents can play. And if an opponent's trump holding were something like K9, s/he might not want to trump and "unguard" the king against your ace.

So I would re-word the advice by saying PLAY trump early, rather than DRAW trump early. Ruffing counts.

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