Lessons

One spot at a time, with the reasoning shown rather than a verdict.

Game or partscore, after a raise to two hearts

You have opened, partner has raised to two hearts showing 6–9 points and exactly three-card support, and you hold a balanced hand with five hearts and 15–18 points. Pass, or bid the game? Type a hand and see the reasoning. The adjustments for suit structures were modelled from a large set of double dummy solves.

The interesting decisions live between 15 and 18 points for a 5-3-3-2. Anything more, just bid game; anything less and two hearts is plenty.

Where the answer turns over depends on how you are scoring. At matchpoints you want a genuine favourite, because you win or lose the board either way. At IMPs the game bonus outweighs the penalty, so you bid on odds against — and more so vulnerable, where the bonus grows faster than the cost. For this shape it works out at 17.0 points at matchpoints, 16.6 at IMPs not vulnerable and 16.1 vulnerable.

Some hands worth comparing. A good fifteen count is worth more than a poor eighteen.

15
16
17
18
Try the game Ten hands, eleven bubbles. Pop the one that matches.
Where these numbers come from

Thirty-two thousand deals were solved double dummy for this one spot, a thousand for each possible trump holding. Each deal was scored twice, once for the game and once for the partscore, and the difference recorded.

A straight line through point count gets you most of the way: the two calls break even at 16.7 points, and each further point is worth about 1.33 IMPs. The tables above are what is left over — how much each holding is worth beyond what its points already say. Fitted that way, the model agrees with the solver to within a third of an IMP, which is as close as the deals themselves can measure.