Percentage games and slams

When should we bid close games and slams?
What percentage game is a good proposition?
What percentage slam is a good bet ?

We will compare the scores for a part game vs a game, and a game vs slam in hearts.
We will take into account the contract making and going one down; overtricks will cancel out,
and in close games and slams there will usually be no more than 1 undertrick.
Since these are "close" games and slams, let us assume that they will be undoubled.

Bid	Non vul 10 tricks	Non vul 9 tricks	Vul 10 tricks	Vul 9 tricks

3H	170	140	170	140
4H	420	-50	620	-100

Gain/(Loss)	250	(190)	450	(240)
Breakeven	43%	100 - 43 = 57%	35%	100 - 35 = 65%
Confirmation	43% x 250 =	57% x 190	35% x 450 =	65% x 240	approximately

So, a non-vulnerable game should be bid if the chances of success are more than 43%.
A vulnerable game should be bid if chances of success are more than 35%.
For example, a non-vulnerable game on a finesse should be bid.
Also, a vulnerable game requiring two out of three finesses should be bid.

On to small slams ....

Bid	Non vul 12 tricks	Non vul 11 tricks	Vul 12 tricks	Vul 11 tricks

4H	480	450	680	650
6H	980	-50	1430	-100

Gain/(Loss)	500	(500)	750	(750)
Breakeven	50%	100 - 50= 50%	50%	100 - 50= 50%
Confirmation	50% x 500 =	50% x 500	50% x 750 =	50% x 750

Hence, a 50% or better small slam should be bid.

On to grands.... When we bid a grand slam we risk a lot more - the points for a small slam.
Let us see what the figures say

Bid	Non vul 13 tricks	Non vul 12 tricks	Vul 13 tricks	Vul 12 tricks

6H	1010	980	1460	1430
7H	1510	-50	2210	-100

Gain/(Loss)	510	(1030)	750	(1530)
Breakeven	67%	100 - 67 = 33%	67%	100 - 67 = 33%
Confirmation	67% x 510 =	33% x 1030	67% x 750 =	33% x 1530	approximately

It seems that we should bid grand slams which are more than 67%.
A thumb rule for bidding grand slams - you can virtually count 13 tricks or you can
count 12 tricks and see at least two posibilities for one more.

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