grand?

[pclayton]

Against a weak team, gnome and I mused about missing a grand with Txxxx, Qxx, AQ, Qxx opposite void, Akxx, Kxx, AKxxxx.

 

Lose 13? No, the other team played in 3N.

 

Here's the question. On this hand if the other table rates to play game and you are looking at small vs grand, what percentage do you need for the grand to be right?

 

Also, on the given hand, what frequency do you need the opponents to bid slam for you to bid the grand?

[jdonn]

I really wish you'd post the hands this way Phil.

 

[hv=n=stxxxxhqxxdaqcqxx&s=shakxxdkxxcakxxxx]133|200|[/hv]

Much easier reading.

 

As for the question, heck, if they bid 3NT they could even go down there! I will let someone else calculate it, but I would want a pretty substantial positive expectation to bid a grand under the given conditions (those of expecting the other team to be in game), maybe 80% chance of it making or better. I think against a weak team I would (barely) not want to be in this grand. 4-0 clubs, 5-1 hearts, or maybe 6-2 diamonds can beat it. Add the jack of hearts and I want to be there for sure, add the jack of clubs instead and I just don't know.

[benlessard]

This seem like a bit short for a grand . You need clubs 2-2 or clubs 3-1 & heart 3-3 or very unlikely squeeze. Wich is quite under 70%

[skjaeran]

This seem like a bit short for a grand . You need clubs 2-2 or clubs 3-1 & heart 3-3 or very unlikely squeeze. Wich is quite under 70%

That's not quite true. You can throw a heart on the ♦K and ruff the 3rd heart in dummy, and will win with 3 clubs and 4 hearts in the same hand too.

 

Which still means that you should not bid the grand under the given conditions.

 

Under normal conditions this is a very good grand however.

[pclayton]

This was posted from my handheld so the hand diagrams dont function well.

[gwnn]

This would be quite complicated cause u don't know how often they actually make 3NT/how often slam doesnt make one. However, just for theoretical interest, let's assume the other table always plays 3NT= and we'll play 6♣ or 7♣, making 12 or 13 tricks. In that case elementary calculations (win 11 all the time vs lose 10/ win 14) yield a percentage of 87.5%.

 

The other thing is too complicated to me sry :rolleyes: The odds are easily calculated if we multiply them and all but that's just wrong.

[benlessard]

Under normal conditions this is a very good grand however.

 

disagree

 

22 trumps 40%

 

3-1 trumps & H 3-3 50 % x 35% = 17.5 %

 

3-1 trumps & hearts 4-2 with 4H in the same hands as the 3 trumps= 50%x20% = 10%

 

40+17.5+10% = 68%

 

borderline grand slam =70%

 

good grand slam = 80%

 

Of course ur right about ruffing a H if trumps are 3-1 and the long trumps has 4H. It was in my calculation but I forgot to post it.

 

These number are approx. so exact calculation is needed. But I think its under 70% and im sure this doesnt qualify as a good grand (Imps scoring )

 

edited (if youre not sure they will bid slam at the other table if you are 100% sure they bid a slam on the other side then bidding 7 is good)

[skjaeran]

Under normal conditions this is a very good grand however.

 

disagree

 

22 trumps 40%

 

3-1 trumps & H 3-3 50 % x 35% = 17.5 %

 

3-1 trumps & hearts 4-2 with 4H in the same hands as the 3 trumps= 50%x20% = 10%

 

40+17.5+10% = 68%

 

borderline grand slam =70%

 

good grand slam = 80%

 

Of course ur right about ruffing a H if trumps are 3-1 and the long trumps has 4H. It was in my calculation but I forgot to post it.

 

These number are approx. so exact calculation is needed. But I think its under 70% and im sure this doesnt qualify as a good grand (Imps scoring )

 

edited (if youre not sure they will bid slam at the other table if you are 100% sure they bid a slam on the other side then bidding 7 is good)

If you're sure the opponents will reach slam at the other table the break even odds for bidding a grand is 57%. Thus anything over 57% is "good" in that context. And I'd be unhappy to stay out of a 60% grand against a strong team.

 

If you can't count on opps to reach slam, the picture changes of course.

 

The wellknown treshold of 70% for bidding a grand is old - not sure whether this was a rule for the Dallas Aces or the Italian Blue Team. Anyway, it's from an era where slam bidding in general was far less accurate than in todays expert community, thus only bidding a grand with 70+% odds made sense.

[lexlogan]

To answer the first question, if they can be counted on to stop at 3NT, and both 3NT and 6C are 100%, we need 7C to be 85% to bid it not vulnerable.

 

Let x = probability 7C makes

Let A = expected gain from bidding 7C if it makes

Let B = expected loss from bidding 7C if it fails

Let C = expected gain from bidding 6C (assumed to be a 100% contract)

 

Then Ax - B(1-x) = C will give us the break-even point for x

Re-arranging, (A+B)x = B+C, so x = (B+C)/(A+B)

 

Not vulnerable, A = 14 imps (+1440 vs. +440) , B = 11 imps (-470), C = 11 imps (+920 or + 940 vs. +420 or +440).

 

So, 21/24 = 85%.

 

If the opps might bid 6C, this will reduce A (from 14 toward 11 imps), increase B (from 11 toward 14 imps), and reduce C (from 11 toward 0 imps.)

 

For example, if it's 50-50 whether they'll bid 3NT or 6C, then A = 12.5, B = 12.5, C = 5.5, so x = 18/25 = 72% . If it's 100% they'll bid 6C, A = 11, B = 14, C = 0, so x = 14/25 = 56% .

[gwnn]

To answer the first question, if they can be counted on to stop at 3NT, and both 3NT and 6C are 100%, we need 7C to be 85% to bid it not vulnerable.

 

Let x = probability 7C makes

Let A = expected gain from bidding 7C if it makes

Let B = expected loss from bidding 7C if it fails

Let C = expected gain from bidding 6C (assumed to be a 100% contract)

 

Then Ax - B(1-x) = C will give us the break-even point for x

Re-arranging, (A+B)x = B+C, so x = (B+C)/(A+:rolleyes:

 

Not vulnerable, A = 14 imps (+1440 vs. +440) , B = 11 imps (-470), C = 11 imps (+920 or + 940 vs. +420 or +440).

 

So, 21/24 = 85%.

 

If the opps might bid 6C, this will reduce A (from 14 toward 11 imps), increase B (from 11 toward 14 imps), and reduce C (from 11 toward 0 imps.)

 

For example, if it's 50-50 whether they'll bid 3NT or 6C, then A = 12.5, B = 12.5, C = 5.5, so x = 18/25 = 72% . If it's 100% they'll bid 6C, A = 11, B = 14, C = 0, so x = 14/25 = 56% .

21/24 is 87.5%

[lexlogan]

To answer the first question, if they can be counted on to stop at 3NT, and both 3NT and 6C are 100%, we need 7C to be 85% to bid it not vulnerable.

 

Let x = probability 7C makes

Let A = expected gain from bidding 7C if it makes

Let B = expected loss from bidding 7C if it fails

Let C = expected gain from bidding 6C (assumed to be a 100% contract)

 

Then Ax - B(1-x) = C will give us the break-even point for x

Re-arranging, (A+B)x = B+C, so x = (B+C)/(A+B)

 

Not vulnerable, A = 14 imps (+1440 vs. +440) , B = 11 imps (-470), C = 11 imps (+920 or + 940 vs. +420 or +440).

 

So, 21/24 = 85%.

 

If the opps might bid 6C, this will reduce A (from 14 toward 11 imps), increase B (from 11 toward 14 imps), and reduce C (from 11 toward 0 imps.)

 

For example, if it's 50-50 whether they'll bid 3NT or 6C, then A = 12.5, B = 12.5, C = 5.5, so x = 18/25 = 72% . If it's 100% they'll bid 6C, A = 11, B = 14, C = 0, so x = 14/25 = 56% .

21/24 is 87.5%

I got the loss wrong: -470 is -10 imps, not -11.

But the 21/24 was correct (10+11 divided by 10+14), and you are correct that 21/24 is 87.5%.

[lexlogan]

To take things a bit further, what we really care about is winning the match, and how much we win by. Suppose this slam hand is one of 7 boards in a Swiss match, scored on the 30 point VP scale.

 

If we're already ahead in the match, the VP scale will compress our gain. For example, if this is the last board in a dead-even match, bidding and making the grand vs. a small slam at the other table will gain us 11 imps (not vul), which will translate into +10 VP's (25-5 instead of 15-15.) Going down costs us 11 VP's (4-26 instead of 15-15.) But if we're up 6 imps at this point, the grand rates to gain us only 6 VP's (28-2 instead of 22-8), while going down costs 15 (7-23 instead of 22-8.)

[foo]

Against a weak team, gnome and I mused about missing a grand with

Txxxx, Qxx, AQ, Qxx

opposite

void, AKxx, Kxx, AKxxxx.

 

Lose 13? No, the other team played in 3N.

 

Here's the question. On this hand if the other table rates to play game and you are looking at small vs grand, what percentage do you need for the grand to be right?

 

Also, on the given hand, what frequency do you need the opponents to bid slam for you to bid the grand?

1C-1S;2H-3D!;4C-4D;4H-etc

 

I don't know it I'll get to 7C, but I'll certainly get to 6C.

[Fluffy]

I am awful at calculating these odds, it depends on the field, for example Dad told me he scored 11% by bidding and making 7 Spades against heavy peemting at the european open pairs final last year. At MP its even harder to calculate.

[ArtK78]

It is not too difficult to calculate the IMP odds of bidding a small vs. bidding a grand when your opponents bid game if you make certain assumptions:

 

1) The small is 100%.

2) The game (in a different strain) is 100%.

3) The vulnerability.

 

Assume that you are vulnerable and the game (3NT) makes +690 all the time. If you bid 6♣ you will make +1370 or +1390 for a win of 12 IMPs. If you bid 7♣ you will make -100 or +2140 for a loss of 13 IMPs or a gain of 16 IMPs. So, you are risking 25 IMPs to gain 4 IMPs. The break even point for this venture is 86.21%.

 

If you are not vulnerable, the numbers are +490 for the opps, +920 or +940 in 6♣ (a win of 10 IMPs) and -50 or +1440 in 7♣ (a loss of 11 IMPs or a gain of 14 IMPs). So, you are risking 21 IMPs to gain 4 IMPs. The odds are slightly better - the break even point is only 84%.

 

When you translate this into winning or losing the match, the analysis becomes more difficult. If you are playing a weak team, I would guess that the win/loss odds would have to be about 99% or more, since you will probably win the match well over 90% of the time if you bid game on this hand. By bidding the small slam and winning 10 or 12 IMPs, you probably increase your chances of winning the match to 96% or more. However, if you take the chance on the grand and are successful, you might improve your chances of winning the match from 96% to 99%, but if you go down in the grand your chances of winning the match probably go down to 50% or less. Under these circumstances, the chances of making the grand must be close to 100% to warrant the bid.

 

Against a better team, one that you estimate that you will beat about 60% of the time, bidding and making the grand might improve your overall winning chances to 80% or better, but going down might reduce your overall winning chances to 40% or less. However, if you know that they will be in game, bidding the small slam might improve your chances of winning to over 75%. Under these circumstances, the grand slam must be a prohibitive favorite to justify the bid, but not quite as much of a certainty as against the weak team.

 

The analysis at VP scoring is similar to the win/loss analysis, since most of the VPs are won by winning the match. But even if winning the match is no longer in doubt, there are still some VPs to be won at the top end of the VP scale. Without going into an arithmetic analysis, suffice it to say that there is more justification for bidding the grand at VP match scoring than at pure win/loss scoring, but the odds are still very long.

[ArtK78]

If you change the question to how good does the grand slam have to be to bid it if you assume the opponents will always be in the small slam, the analysis is as follows:

 

VULNERABLE:

 

Opps will score +1370 or +1390 vs. your -100 (Loss of 16 IMPs) or +2140 (gain of 13 IMPs). The break even point is 55.17%

 

NOT VULNERABLE:

 

Opps will score +920 or +940 vs. your -50 (Loss of 14 IMPs) or +1440 (gain of 11 IMPs). The break even point is 56%.

 

Again, these are the IMP odds. How this particular result will affect the overall chances of your winning the match or your overall VP score for the match depends on your assessment of your chances of beating this team prior to playing this hand.

 

Usually, one uses 68% or so as the break even point for deciding whether to bid a grand slam if one assumes that the small slam is 100%. The reason why my IMP odds calculations are lower than 68% is that the assumption is that the opponents will always bid the small slam. The 68% figure takes into account that the opponents will not always bid the small slam. Sometimes they will be in a partial! I have mentioned in a post some time ago that my partner and I had a mixup on a reverse sequence once when he thought that my bid was a weak bid and I thought it was forcing. We played in 3♦ when 13 tricks were cold unless the trump broke 4-0 offside, which they did. Our opps bid 7♦ and went down 1 opposite our +170. Strange things do happen.

[gwnn]

Art, there are less than 12 tricks in NT after they lead spades

[pclayton]

It is not too difficult to calculate the IMP odds of bidding a small vs. bidding a grand when your opponents bid game if you make certain assumptions:

 

1) The small is 100%.

2) The game (in a different strain) is 100%.

3) The vulnerability.

 

Assume that you are vulnerable and the game (3NT) makes +690 all the time. If you bid 6♣ you will make +1370 or +1390 for a win of 12 IMPs. If you bid 7♣ you will make -100 or +2140 for a loss of 13 IMPs or a gain of 16 IMPs. So, you are risking 25 IMPs to gain 4 IMPs. The break even point for this venture is 86.21%.

 

If you are not vulnerable, the numbers are +490 for the opps, +920 or +940 in 6♣ (a win of 10 IMPs) and -50 or +1440 in 7♣ (a loss of 11 IMPs or a gain of 14 IMPs). So, you are risking 21 IMPs to gain 4 IMPs. The odds are slightly better - the break even point is only 84%.

This is how I calced it.

[ArtK78]

Art, there are less than 12 tricks in NT after they lead spades

I did not care how many tricks there were in notrump. It was just an assumption for the purpose of the analysis. If you want to assign +460 or +430 to the opposition's 3NT contract and then redo the calculations, feel free. I suspect it makes little, if any, difference.

[Rossoneri]

I personally wouldn't bid a grand under such circumstances unless it is near cast iron. (probably >90% or 95%)

 

I think the slam should be better than the break even point calculated, because if you want to play differing points against strong/weak opponents, you probably have to factor in the fact that you only play 8/12/16/24 boards against them. (Statisticians correct me if I am wrong?)

[pclayton]

I personally wouldn't bid a grand under such circumstances unless it is near cast iron. (probably >90% or 95%)

 

I think the slam should be better than the break even point calculated, because if you want to play differing points against strong/weak opponents, you probably have to factor in the fact that you only play 8/12/16/24 boards against them. (Statisticians correct me if I am wrong?)

12 Board match FWIW.