Overcalling 4-Card Suits

Mike Lawrence says in his book, Overcalls, that it is okay to overcall a weak 4-card suit when holding 4-5 of RHO's suit because that holding increases the odds that overcaller's partner will have support for overcaller's suit since he is very likely short in RHO's suit.

On the rec.games.bridge newsgroup, two fellows disputed Lawrence's claim and backed it up with analysis.

Mike Bell did the following calculations by hand:

Heart length of
overcaller

0
1
2
3
4
5
6
Expected heart length
of opener

5.60
5.49
5.40
5.31
5.23
5.16
5.10

Expected spade length
of overcaller's partner

3.22
3.25
3.28
3.31
3.34
3.36
3.39

And Eddie Grove came up with very similar results by computer simulation in which 109,525,519 deals were made of which 2,097,152 had hands where overcaller had 4 Spades and his RHO was able to open 1H.

Heart length of
overcaller

0
1
2
3
4
5
6
Number of
matching deals

72,294
367,558
693,269
616,422
276,170
64,097
7,017
Overcaller's partner's
actual Spade length

3.26
3.28
3.31
3.33
3.35
3.39
3.40

The gist of the above is that the amount of support overcaller can expect from partner, on average, does not vary enough to matter, whether overcaller has 0 or 6 of RHO's suit, so this analysis apparently refutes Lawrence's claim that it is okay to overcall with a poor 4-card suit when holding length in RHO's suit with an expectation of more support for overcaller's suit by partner.

And another way of looking at this is that if you are 4=5=2=2 and RHO opens 1H, partner is more likely to be shorter in Hearts than if you were 4=2=5=2, but he is correspondingly more likely to be longer in Diamonds, not Spades.

Another argument against overcalling 1S over 1H with 4-5 majors is that the most Hearts LHO can have is 3 (assuming RHO's opening 1H shows 5+), and his expected average number of Hearts is only 1.5. Now if overcaller's partner has an expected average number of Spades of 3, then your side has a 7-card fit and it is likely that the opponents don't have an 8-card fit either, making a 2-level contract contrary to the Law Of Total Tricks.

4-Card Overcalls And
The Law Of Total Tricks

It is my opinion that Larry Cohen's book, The Law Of Total Tricks, is the most important book on bidding there is beyond learning the basics. While top experts routinely disagree about various aspects of bidding, one thing they do agree on more than any other aspect (with the notable exception of Mike Lawrence) is the basic validity of the LOTT, particularly in competing for part scores.

When RHO opens and you have 10 or so HCPs, on average you will be competing for part scores, which brings LOTT strongly into play. The simplest aspect of LOTT is that you are generally safe competing to a number of tricks equal to the number of trumps you and pard have between you. If you go set, even doubled, the penalty will be less than the opponents could have made if they had taken the bid.

So after (1H)-1S-(3H), if you have 4 Spades, you can bid for 9 tricks (3S) if you know pard has at least 5 Spades. Let's say that opponents double and you go down 1, non-vulnerable, for -100. If the opponents had played and made 3H, they would have made 170, so you get a top at matchpoints.

But if overcaller has only 4 Spades and you go down 2 doubled, you get a bottom at matchpoints

Perhaps a more common sequence would be (1H)-1S-(2H) and you hold 3 Spades. Playing 4-card overcalls, you either bid 2S and risk an anti-LOTT bottom if overcaller only has 4, or you pass and risk a bottom if the opponents make 2H when overcaller has 5+ Spades and could have made 2S.

Some argue that even if your side only has a 4-3 fit, you are okay on the 2-level as long as the opponents have an 8-card fit. Even ignoring that this concept is not part of LOTT, another problem with it is that in 2nd seat, you don't know if they have an 8-card fit or not. In fact, if you overcall with 5 of RHO's suit, as ML suggests, the odds of them (or you) having an 8-card fit are reduced.

Despite this, we have left the 4-card overcalls on very good suits activated in the bidding database because the LOTT risk MAY be offset by gains made by making the overcall and obstructing the opponents or happening upon a good fit.

Another possible rationale for overcalling with a good 4 card suit when holding 5+ of RHO's suit is that with only 3 (or less) of the suit left for LHO and partner, dummy will be in position to overruff LHO in RHO's suit, and LHO is likely to make and opening lead of the suit, helping to set up the ruffs.

If you wish to be more conservative, deactivate all 4-card suit overcall entries.