[Hanoi5]

Games are supposed to be declared, IIRC, at teams at 40% if Vul. or 60% if not. I don't want to ask (though it would be wonderful if you could tell me) how to calculate this percentage when bidding, I just want to know why is it 60% and 40%, what's the math behind it.

Thanks in advance.

[rogerclee]

An IMP table and a working knowledge of arithmetic will help you figure this out very easily, if you assume that the only possible results are making game or down 1. In practice some other things can happen, such as down 2 (good for you), or getting doubled and going down 2+ (bad for you).

By the way, I don't know where you got that NV number from :/.

[gwnn]

<random randomness deleted>

[rogerclee]

baleeted

[awm]

The odds are computed as follows.

You assume that the other table makes the opposite decision of you (if the same decision is made obviously there is no swing). Typically it is also assumed that the only possibilities are making or down one. The calculation is:

At vulnerable, if you bid 4♠ you stand to win 10 when it makes (620-170=450 is ten imps). When it fails, you stand to lose 6 (-100 - 140 = -240 is six imps). So the break even point is when the game makes with probability p, so 10p = 6(1-p) means p = 3/8. This is 37.5% for a vulnerable game.

At nonvulnerable, if you bid 4♠ you stand to win 6 when it makes (420-170=250 is six imps). When it fails, you stand to lose 5 (-50-140=-190 is five imps). So the break even point is when the game makes with probability p and 6p = 5(1-p) means p=5/11. This is about 45% for a non-vuln game.

Of course, when going down multiple tricks becomes a possibility the odds change somewhat, especially if opponents sometimes double you when suits break badly and you go down multiple tricks. It's hard to calculate these percentages at the table (especially without seeing both your hand and partner's); I go by the general rule of "bid games about a point lighter at IMPs than MP."

[pclayton]

Vul:

+620 and -170 = +450 or 10 IMPs. -100 and -140 = -240 or 6 IMPs. Game needs to be 6/16 or better to make or 37.5%

NV:

+420 and -170 = +250 or 6 IMPs. -50 and -140 = -190 or 5 IMPs. Game needs to be 5/11's or better to make or 45.4%.

[jdonn]

awm, on Apr 23 2008, 06:34 PM, said:

Of course, when going down multiple tricks becomes a possibility the odds change somewhat, especially if opponents sometimes double you when suits break badly and you go down multiple tricks. It's hard to calculate these percentages at the table (especially without seeing both your hand and partner's); I go by the general rule of "bid games about a point lighter at IMPs than MP."

The possibility of going down extra can be looked at as a reason to bid game even more, not less, especially if your opponents aren't likely to double.

Lets say you are in 3♠ deciding whether to bid 4 or not, vul at imps. Say you will make 4 35%, 3 35%, and 2 30%, and assume your opponents are in 3♠.

Win 10 x .35 + Lose 6 x .35 + Lose 3 x .3 = 3.5 - 2.1 - .9 = gain of .5 imps per board by bidding your 35% game. The reasoning is you lose less by going even farther if you were minus anyway.

[han]

Unless you can stop in 1NT/2M. And if you are playing against aggressive doublers it's again different.

Bridge is complicated.

[jdonn]

han, on Apr 23 2008, 08:09 PM, said:

Unless you can stop in 1NT/2M. And if you are playing against aggressive doublers it's again different.

Bridge is complicated.

You're telling me. We didn't even talk about how some hands are safe for 9 tricks but in game you have to take a play that is 10 or 8. Or 10, 9, or 8. Or how you give them less information than on an invitational auction and perhaps induce a poor lead. Or how bidding more confidently can keep you from getting doubled when you should be.

I saw someone in a vul 3NT yesterday that was on a 3-2 and a finesse, but on correct defense (which they got) if the finesse was off they were down 7, yes 7, and that's exactly what happened for -700. Their partscore of 3♣ was almost totally safe though.

Pass the tylenol.

By the way I have to credit Justin for teaching me that it often pays to bid game even more aggressively if you think it might be down more then 1. There are certain auctions where he said Hamman believes you need to be making game about 1 time in 5 for bidding it to be right, and I have no reason to doubt it. Rather than try to calculate odds at the table, I say if you think game might make and won't usually be down a ton, bid it. At all vuls and forms of scoring.

[cherdano]

I am sure your 1 out of 5 figure is wrong, I would put it at 30 or 35 % (and I am sure Hamman has a much more precise estimate...).

Btw, another situation where it pays to bid games very aggressively is when you are very shapely - when you go down one in 4M and you have a 5-5 hand opposite partner's single raise, then maybe opponents were making 4m all along, and your -100 translates into +1 IMP.

[kenrexford]

cherdano, on Apr 23 2008, 09:19 PM, said:

I am sure your 1 out of 5 figure is wrong, I would put it at 30 or 35 % (and I am sure Hamman has a much more precise estimate...).

Btw, another situation where it pays to bid games very aggressively is when you are very shapely - when you go down one in 4M and you have a 5-5 hand opposite partner's single raise, then maybe opponents were making 4m all along, and your -100 translates into +1 IMP.

You may have just offered proof of when a 20% game bid makes sense.

[effervesce]

kenrexford, on Apr 23 2008, 09:32 PM, said:

cherdano, on Apr 23 2008, 09:19 PM, said:

I am sure your 1 out of 5 figure is wrong, I would put it at 30 or 35 % (and I am sure Hamman has a much more precise estimate...).

Btw, another situation where it pays to bid games very aggressively is when you are very shapely - when you go down one in 4M and you have a 5-5 hand opposite partner's single raise, then maybe opponents were making 4m all along, and your -100 translates into +1 IMP.

You may have just offered proof of when a 20% game bid makes sense.

Heck, in that example if they're always going to make 4m, and not double you when in game it makes sense to be there on a 0% game.

[jdonn]

cherdano, on Apr 23 2008, 09:19 PM, said:

I am sure your 1 out of 5 figure is wrong, I would put it at 30 or 35 % (and I am sure Hamman has a much more precise estimate...).

I think it supposedly incorporates everything. When it's a save, when they let you make a game they shouldn't, etc. Anyway it's not my figure, just what I was told, and the fact that anyone good even thinks it's true should be an eye opener.

[xcurt]

jdonn, on Apr 23 2008, 09:48 PM, said:

cherdano, on Apr 23 2008, 09:19 PM, said:

I am sure your 1 out of 5 figure is wrong, I would put it at 30 or 35 % (and I am sure Hamman has a much more precise estimate...).

I think it supposedly incorporates everything. When it's a save, when they let you make a game they shouldn't, etc. Anyway it's not my figure, just what I was told, and the fact that anyone good even thinks it's true should be an eye opener.

The odds cited also assume an infinintely long match. Contrast this with Swiss scored at W/L after 6 totally flat boards. Discounting the possibility of a silly result from the other table, now you need 50% odds to bid the game.

Re the 1 in 5 comment -- There is also the possibility of bluffing and how it shifts the odds for some later hand where you can come over the top when the opponents double your game. I think the similarities between bridge and poker are deeper than is generally found in the literature.