[EricK]

Does anybody know what the distribution of par contracts is, or have the software (and time) to calculate (or at least estimate) it?

Well actually I mean to calculate them because there would be a different distribution at each vulnerability (both V, both non-V and non-V v V).

Eric

[hotShot]

Do you mean something like this?

http://forums.bridge...wtopic=6758&hl=

[EricK]

hotShot, on Mar 19 2005, 11:30 AM, said:

Do you mean something like this?

http://forums.bridge...wtopic=6758&hl=

Not really.

That shows the actual results reached by real life players. I am interested in the theoretical par contract (i.e. the lowest contract for which neither side can improve their score by bidding on).

But thanks, anyway!

Eric

[tysen2k]

Here is the distribution of our double-dummy par contracts by vulnerability. Numbers are percentages:

      None   Unfav  Fav    Both
P    2.40   6.33   0.89   2.34
1C   0.86   1.45   0.42   0.83
1D   1.23   1.80   0.61   1.19
1H   1.70   2.23   1.02   1.68
1S   2.29   2.76   1.46   2.20
1N   1.53   1.50   1.61   1.52
2C   2.48   2.63   1.86   2.37
2D   3.23   3.41   2.62   3.11
2H   4.29   4.36   3.74   4.16
2S   5.83   5.88   5.26   5.75
2N   2.64   2.59   2.66   2.64
3C   4.31   4.22   4.05   4.25
3D   5.29   5.10   4.99   5.21
3H   6.23   5.96   6.02   6.16
3S   7.19   6.85   7.07   7.15
3N   3.67   3.64   3.73   3.68
4C   3.59   3.14   3.71   3.54
4D   4.07   3.64   4.28   4.05
4H   5.59   5.01   6.01   5.59
4S   6.41   5.51   7.28   6.39
4N   3.26   3.11   3.37   3.26
5C   1.89   1.49   2.47   1.95
5D   2.28   1.74   2.98   2.29
5H   3.32   2.72   4.07   3.32
5S   3.46   3.06   4.02   3.50
5N   2.16   2.15   2.18   2.16
6C   0.95   0.78   1.28   1.01
6D   1.17   0.98   1.49   1.24
6H   1.34   1.15   1.64   1.41
6S   1.54   1.36   1.95   1.69
6N   1.72   1.72   1.73   1.72
7C   0.32   0.22   0.65   0.45
7D   0.37   0.27   0.81   0.55
7H   0.35   0.26   0.75   0.51
7S   0.35   0.29   0.59   0.44
7N   0.69   0.69   0.70   0.69

Tysen

[EricK]

Thanks Tysen.

I am not entirely clear on what this represents.

I am guessing that for example the initial 2.4 means that on 2.4% of hands at nil vulnerable we would do worse than par if we bid at all (and were doubled). Is that right?

What I was hoping for was the percentage of that contract being the par contract (so that both sides would do worse if they bid on). So for the special case of the hand being passed out the percentage would be the same in each column.

Also I was expecting the table to also include doubled contracts - often the par contract is eg 4SX-1. Are these included in with the undoubled contracts?

Eric

[tysen2k]

Yes, the numbers are the % of the time where we can score no higher. Maybe an example is in order:

No one is vulnerable. If we can take 9 tricks in hearts, and they can take 10 tricks in spades, then our par contract is 5H. From our opponents' point of view, their par contract is 4S.

For Pass to be the best contract for us, it means that any 1-level contract by us doubled would give the opponents a better score than any contract they could make on their own.

I see what numbers you are interested in (the par of the whole hand rather than one side). I don't have those numbers and I don't think I'll have time to generate them anytime soon. Sorry. Hope you can find some use in what I do have.

Tysen

[winkle]

Take a look at:

http://web.mit.edu/m...library.par.txt

[EricK]

winkle, on Mar 22 2005, 09:34 AM, said:

Take a look at:

http://web.mit.edu/m...library.par.txt

That's brilliant!

Thanks for pointing it out.

Eric