Delving Deeper

So in our hypothetical club night of 24 boards, trying for a heart game beats bidding 3NT by a whopping 1.68 IMPs. How significant is this? Is it just random variance or is it proof that bidding Stayman is absolutely right on this hand? Let's try and find out.

The first thing to notice about that ranking table is that passing 1NT did incredibly badly. The three leaders would have spent the whole evening bashing that one pair and most of their IMPs would have been won off of them (of course, I'm talking figuratively — our hypothetical tournament is a Mitchell where each of our seven pairs sits North/South against 7 pairs of slightly passive clones). Any IMPs which the leaders gain against each other might be significant, but they're just lost in the torrent of IMPs they're getting from the crap pair.

So let's narrow down the field. Our tournament was just a qualifier for a final and the top three pairs progressed. Over those same 25,000 hands we now get these values:

1. Bid 3NT:          -0.045
4. Minor try/GF:     -0.029
5. Heart try/GF:     +0.074

or, over 24 boards:

1st  Heart try/GF    +1.78
2nd  Minor try/GF    -0.70
3rd  Bid 3NT         -1.08

Still not much in it. So we ask ourselves, again, how significant is it? Think back to our definition of the strategies here. Strategy 4, trying for a minor game, will end up in 3NT whenever North has no four-card minor — a little over half the time. Strategy 5, trying for hearts, will end up in 3NT a full two-thirds of the time! These are just approximate and based on, you guessed it, simulation results. The point is that on the majority of deals we're comparing exactly the same score. This has the effect of substantially diminishing the strength of the signal.

Another, different, question we could ask is: if I know that partner has four or more hearts, would I rather play in 3NT or 4? So we eliminate all deals where partner has 2-3 hearts and get back to our simulatin'. Over 10,000 deals:

1. Bid 3NT:          -0.27
5. Heart try/GF:     +0.27

Similarly, we can eliminate all deals where partner has no four-card minor and again run 10,000 deals:

1. Bid 3NT:          -0.10
4. Minor try/GF:     +0.10

And now we're getting somewhere. What we're saying is that if partner has a four card heart suit then playing in 4 will do about a quarter of an IMP per board better than playing in 3NT. If partner has a four-card minor then playing in 5 or 5 is marginally better than 3NT. If partner has both, incidentally, then you'll do way better in a suit contract as partner now will have shorter spades.