Doubling for Penalty

Suppose that you re playing duplicate.  Your opponents have hearts; you and partner have spades.  After a back-and-forth, you end up pushing all the way to Three Spades, but the opponents, after some thought, bid a VERY hesitant Four Hearts, vulnerable.  What happens if you double?

Suppose that there are five tables at play and that only 40% of the field would bid Four Hearts, 60% settling for defending Three Spades.  Assume, also, that Three Spades would fail by one trick, for -100.  What if Four Hearts makes, but you do not double?

-420
-420
-100
-100
-100

You were -420, for a 1/2 on a 4 top.

Suppose you double, instead.  You now get a goose-egg, but this only cost you 1/2 MP.

What if Four Hearts goes set one trick, without the double?

+100
+100
-100
-100
-100

You get a 3 1/2 on the board.  Had you doubled, you would get a top, but that only gains the same 1/2 MP that you lost when 4H made.  So, a wash.

But, what if Three Spades would have made?

Now, both 4H and 3S makes, let us say.  No double, and the scores are as follows:

-420
-420
+140
+140
+140

You get a 1/2 for defending 4H undoubled.  Bad score.

However, if you double, you get a goose-egg again, losing 1/2 MP.

Now, what if the opponents cannot make 4H but you make 3S?

Undoubled, the scores are:

+100
+100
+140
+140
+140

You get a darned 1/2 again!

But, if you double:

+200
+100
+140
+140
+140

A top!  Gaining 3 1/2 MP!

The point should be easy to see.  If you double a minority contract when you were going down anyway, not much is at stake.  In the example, you gain a smidge when the contract fails but lose a smidge when it succeeds.  Nothing to get too excited about.  However, if your contract was making, not doubling costs you a ton on the board. 

So, a few principles seem clear.  When the opponents bid a minority contract, it seems right to double if you think you were making, even if the contract might be close to making.  There is a lot of upside to doubling, and little downside.  However, if you think you were over your head, then double if you think they won't make.

The "odds" might be stated a different way.

If you think you were failing, double if their contract seems 51% to fail.

If you think your contract was making, double if their contract might fail every so often.