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I am being conservative to use 34% for vulnerable game and 42% for non-vulnerable game taking into consideration that once in a while you may get X and go down and lose more imps. A more aggressive % would be 33% and 40% if you assume you seldom get X. Here is where most of the traditional analysis went wrong. They assume you either make the game or you go down one. The fact is most bridge hands have wide distributional results and you have a large % of hands that go down more then one. I am going to use the game invitation of 1NT as an example. The computer simulation of all 15 HCP with 15 HCL point should decline game invitation from partner with 7 to 9 HCP with exactly 9 HCL point. 31.1% of hands make 3NT or better. 36.8% of the hands make exactly 2NT. 32.1% of the hands make less then 2NT. For non-vulnerable bid and make game is +6 imps, bid and down one is -5 imps, bid and down more then one is -2 imps. For vulnerable bid and make game is +10 imps, bid and down one is -6 imps, bid and down more then one is -3 imps. Let’s assume g% make game or better, d% down 1 and dd% down more then one. In order to gain by bidding game:- For non-vulnerable g > ( 5 * d + 2 * dd ) / 6 For vulnerable g > ( 6 * d + 3 * dd ) / 10 With g = 31.1, d = 36.8 and dd=32.1 it is just slightly below and you should not bid game even if you are vulnerable. If you change the % to say g = 34 d = 40 and dd = 26, then it is clearly correct to bid the vulnerable game. If you change the % to 4say g = 42, d = 36, dd = 22, then it is clearly correct to bid the non-vulnerable game.
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