Imps, cross-imps, and 23 paradox...

[inquiry]

Hi,

 

In the thread on bidding vulnerable game at imps, the discussion was how much lighter than normal do you need to be to press to game. A lot of discussion occured versus is 1 point lighter than normal ok? Is two points too much?

 

So I decided to use BridgeBrowser to examine statistics from hands played on BBO. First a quick observation. For these comparisons, I used the main room which means each board was played 16 times. In the process I learned something that I had never known before. It seems cross imps had an odd effect on the math of imps. The reason now is clear to me, when you compare to 15 other tables, someone people will bid game for sure and some will not bid game for sure, and a few will end up in bizarre contracts (hopeless slams, wrong strain). This "smooths" out the results. You will neither get a great score for bidding a close game (vul maybe 4 to 5 imps instead of 10) nor punished harshly for staying out of one (losing the same number if you are wrong). The Win 10, lose 6 doesn't seem to hold up on bidding vulnerable game.

 

As a result of this, at cross imps at least, the strategy suggested by a few very insightful people (fluffy in particular) of not really altering your game invites seems closer to the winning strategy than what I have been doing. So you have to separate "IMPS" (two table comparison) from "cross-imps". In cross imps, you still need to bid close games when vul, but 35% chance simply is not good enough. Nor is 40%. You need around 45% for both. This surprised the heck out of me (maybe 42% vul, 45% not vul, but that is a guestimate). The absolute reward for being right is a little higher when vul, but the cutoff for chance to make for being right is very close to the same.

 

I obseved this "fact" (observed statistically in data I analyzed) that cross imps can has dramatic effects on the mathematics of imp play. However, looking at thousands and thousands of cross imp hands in a large field the normal imp math simply does not hold. The reason is both the reward for being right, and the penalty for being wrong has been reduced by the variability found in the field. One could do some math to calculate the odds I guess, but if half the field is bidding game and half is not, even vulnerable, you reward for bidding game is reduced but so is your "punishment" for not bidding game.

 

So the reward is less for being right and the penatly is less for being wrong. As the percentage of who bids and doesn't bid game will also have affect on the score. Does this make sense? I had never thought of this before. At team game (just one comparison), the "known math" still seems to hold. But at cross imps, looks like you need around 44% or so to justify bidding any game... that is Fluffy was right as it relates to cross imps.

 

I arrived at this conculsion by examining 4 of a major contracts (this includes doubled and redoubled contracts as well), vul and not vul, with a combined 24 or 25 hcp, without regard to quality of the fit. You won more imps, in both cases for bidding the game when vul (not a large surprise), but the problem was some of the hands were in 3 card fits!! some in 6, etc.

 

So I switched tactics and compared hands where one partner had five cards in the major and the other had 4 for exactly a nine card fit. Clearly bidding game with 26/25 hcp is no brainer, so I looked at 24 hcp, and 23 hcp. To make it statistically significant, I shot for 1000 hands (each actually a llittle larger than 1000, as I didn't bother to input 1000 as a stop term).

 

A paradox (which isn't one if you really think about it) was that you won more imps bidding game with 23 hcp than with 24 hcp. The reason being, is that less people bid game with 23, so when you make, the reward is richer, this turns out to be true rather you are vulnerable or not. But interesting, as I manipulated teh distritubitons and hcp, the profibility of bidding game both vul and nonvul was lost around 44%. Anytime only 43% of the game contracts were made, it was not profitable to bid them, and i could watch in real time the % contracts making and the average imps by vulnerabilty.

 

What does this mean? I have been much too aggressive when vulnerable by pressing to too many games in tournments and in the main room. Again, this does not seem to affect the odds of team game play at imps.

 

Anyone else have any thoughts? Wayne, you volunteered to show the math for 35% game at "imps" want to give some cross imp math vul a try, whle making some assumptions about what the field will be doing (some will no doubt be in game going down when it should make or making when it should go down too).

 

Anyway, I learned something today.

 

Ben

 

BTW, what is one hcp worth? I did some comparisons looking at 25 and 24 and 23 hcp with and without fixed trump fits. One hcp is worth 0.37 trick without a fixed trump lenght. With a known precise 9 card trump fit, 1 hcp was only worth 0.16 of a trick. I haven't done any notrump calculations.

[Guest Jlall]

The thing that all these statistics and simulations fail to take into account, bad games often make at the table. Sometimes they make the wrong lead. Sometimes they guess the wrong shift. Even at the highest levels this holds true. Bad games make, and when people do their percentages and simulations they never take this into account. In my experience bidding close games at imps has been a big winner.

[Fluffy]

The thing that all these statistics and simulations fail to take into account, bad games often make at the table. Sometimes they make the wrong lead. Sometimes they guess the wrong shift. Even at the highest levels this holds true. Bad games make, and when people do their percentages and simulations they never take this into account. In my experience bidding close games at imps has been a big winner.

They are no simualtions Justin, they are statistics from real hands played from real players, so hopeless games will sometimes make, and cold games will sometimes fail, its true that the average field of BBO cannot be considered expert, but I think it is a good statistic excecpt for the fact that 9 trumps are a bit (0.3 or so) too many for average 4 in a major games.

 

Also talking about cross-imps on BBO is not the same as talking about cross-imps on an homogenean field.

 

Someone suggested vulnerable at IMPs 35% game is good enough to be played?, I really have my doubts there, but if you are right I'll learn something really helpfull B).

[hotShot]

First of all, if we discuss how much weaker one should try game vul at imps, we should say what we normaly do.

 

Openings got lighter, eg. NT shrinked from 16-18 down to 12-14. and i even see 11-13 sometimes. Opening a suit with 11 hcp is not rare, some do it even with 4card suits.

 

If you play an agressive system, you probably should not take more rist when vul.

 

Even non vul at IMPs there is a small advantage for bidding game.

So people playing @IMPs bid a little more agressive.

 

Finally I object to using boards from the main bridge club to do the evalation.

The thing that pickup partnerships lack most, is a good playing defence.

You can do your bidding ok, by using "safty belts". If you are declarer, your play does not depend on your partner (at least it should not :) ).

 

It is my BBO experiance, that you win lots of IMPs with a good defence.

 

Now a little Math:

 

Each board is played 16 times, one result is yours making 15 references.

 

Asume you made 620 the others did 0 * 620 and 15* 170 leading to:

(0*0 IMPs + 15* 10 IMPs) /15 = 150/15 = 10 IMPs

that is what we planned. But for each result that is equal to ours, we loose 10/15 IMPs.

 

(1* 0 IMPs + 14* 10 IMPs)/15 = 140/15 = 9,3333 IMPs

 

If 8 pairs bid game an 8 did not we get:

 

(7 * 0 IMPs + 8 * 10 IMPs)/15 = 80/15 = 5,3333 IMPs

 

Cross-Imps shrink the win you can make, depending on the number of shared results. Since you cannot predict the number of shared results, it is hard to calculate the chances.

 

But a good rule of thumb would be, if half the field is with you in this decicion, you get half the reward you get at IMPs. If your result is unshared, you get the full result.

[DrTodd13]

Fluffy,

 

Let X be the likelihood that the vul game will make. Make the simplying assumption that the contract either makes or is down 1.

 

Expected points if you bid game = (620 * X) + (-100 * (1-X))

 

There is an X chance of getting 620 points and a (1-X) chance of getting -100.

 

Expected points if you don't bid game = (170 * X) + (140 * (1-X))

 

There is an X chance of getting 170 points and a (1-X) chance of getting 140.

 

Set these equal to each other and solve for X.

 

620X - 100 +100X = 170X + 140 - 140X

720X - 100 = 30X + 140

720X - 30X = 140 + 100

690X = 240

X = 34.78%

 

DrTodd

[hotShot]

Well the IMP-Scale is not linear and i think it is a litte easyer:

 

If we make it, we gain 10 IMPs (620 vs 170).

If we loose (-100 vs 140), we loose 6 IMPs.

I want to get at least even, means sum has to be larger than 0.

 

10x + ( -6 * (1-x) ) >= 0

16x -6 >= 0

x>= 6/16 = 37.5%

 

Not vul:

 

If we make it, we gain 6 IMPs (420 vs 170).

If we loose (-50 vs 140), we loose 5 IMPs.

 

6x + ( -5 * (1-x) )>=0

11x -5 >=0

x>= 5/11 = 45.45%

[Cascade]

There is a fallacy in your arguement Ben.

 

The fact that you only get 6.4 Imps for bidding and making your game does not mean that you gained on 6.4 Imps for bidding and making it compared with what you would have score had you not bid it.

 

Here is an example to illustrate:

 

This is the scores from a typical sheet on BBO

 

1100

630

630

600

600

600

210

170

140

140

120

100

-100

-100

-100

-100

 

If I have the opportunity to bid a game that might or might not make then lets analyse the scores.

For simplicity lets assume we will be in NTs and we will either make 8 or 9 tricks.

 

First lets compare bidding 3NT and it making to not bidding 3NT and it making.

 

We will get the following IMP scores

 

-11  -14
-1    -10
-1    -10
0     -10
0     -10
0     -10
9     -2
10   -1
10    0
10    0
10    1
11    2
12    6
12    6
12    6
12    6
== ==
95  -40

We gain 135 IMPs (135/15 = 9 or 135/16 = 8.4 depending on how the calculation is done)

 

On the other hand if our 3NT would fail for us then the numbers are

 

-15     -14
-12     -11
-12     -11
-12     -10
-12     -10
-12     -10
-7       -3
-7       -2
-6       -1
-6       -1
-6        0
-5        1
0         6
0         6
0         6
0         6
===  ===
-112  -48

We would have gained -48- - 112 = 64 IMPs by staying out of game.

 

Now the odds that we would need for our game to make on this score-card are:

 

64/(64+135) = 32%

 

I re-did the calculations based on us being not vul (but kept the penalty scores for the opponent's defeated contracts the same).

 

On that score-card we would have needed a 41% chance to make it worthwhile bidding a not-vul game.

[nikos59]

Some time ago I had tried to collect data on the factors

that generate a big swing in my BBO games. I have

arbitrarily set the limit for a big swing to 7 imps after

observing that at crossimps (16 tables) 7 imps

more or less correspond to a double-digit swing of a

team match.

 

Nikos

 

PS To Ben: Does BrBrowser contain recent BBO data?

[Fluffy]

Fluffy,

 

Let X be the likelihood that the vul game will make. Make the simplying assumption that the contract either makes or is down 1.

And here is where I wanted to land.

 

You are bypassing 200 vs 100, and much very important 100 vs 500 and 200 vs 800.

[hotShot]

Fluffy,

 

  Let X be the likelihood that the vul game will make.  Make the simplying assumption that the contract either makes or is down 1.

And here is where I wanted to land.

 

You are bypassing 200 vs 100, and much very important 100 vs 500 and 200 vs 800.

You don't need to take these into account, because:

• What we say is, that you should bid game with 9.4 tricks in the majors. If you can fall twice you did not have those.
  
• If opponents double, you will gain 12 IMPs or loose 8 IMPs, you break even with 40% games here.
  
• Ben's analysis did not contain those hands, where opps defended against your game.
  

[MickyB]

Fluffy,

 

  Let X be the likelihood that the vul game will make.  Make the simplying assumption that the contract either makes or is down 1.

And here is where I wanted to land.

 

You are bypassing 200 vs 100, and much very important 100 vs 500 and 200 vs 800.

Including 200 vs 100 actually reduces the required odds for bidding game. Instead of losing 6 IMPs for bidding game going down, you only lose 3 IMPs in this situation. 200 vs 800, of course, is a different matter, but based on frequency I suspect the required odds for game should be less than 37.5%, not more.

[inquiry]

Some time ago I had tried to collect data on the factors

that generate a big swing in my BBO games. I have

arbitrarily set the limit for a big swing to 7 imps after

observing that at crossimps (16 tables) 7 imps

more or less correspond to a double-digit swing of a

team match.

 

Nikos

 

PS To Ben: Does BrBrowser contain recent BBO data?

The most recent data in Bridgebrowser is hands played during november 2004. Generally the data is one month out of date for the online version (at most). It is a little behind now for the holidays.

 

As for what I analyzed.

 

I set partnerhip trumps and hcp and vul. Then searched for game contracts. So the assumption is all hands found game was bid (no one stopped in part-score). But the imp results for these hands take into account (obviously) how sucessful the contract was (it would be plus or minus some number of imps). When you do this, you get two sets of data (three if you want individual number of tricks). One is the average imps for the pair bidding the game, another (with the constraint) is the percentage of hands that got either 0 or a positive imp score and what the average imp score was for this subset of hands.

 

For example, below is the data for the following conditions:

1) Four spade contract

2) The pair has a 4-4 spade fit

3) The combined hcp value for pair bidding game is 22.

 

When you look at this data, keep in mind that this represents not one hand where the decision is to bid game or not, but hundreds of hands. The only similarities between the hands is the 4-4 fit, the same number of hcp, and that 4S was bid.The original goal was to see how many hcp less (based upon quality of fit), should you push to game vul.

 

The data looks like this...

 

number of hands looked at 1010

Detailed trick stats

Tricks Freq All Av IMP Freq Undbl Av IMP Freq X/XX Av IMP

Total 1010 843 83.46% 167 16.73%

0

1

2

3

4 1 0.09% -11.07 1 0.09% -11.07

5 1 0.09% -16.4 1 0.09% -16.4

6 9 0.89% -9.97 6 0.59% -7.07 3 0.29% -15.75

7 78 7.72% -6.99 61 6.03% -5.83 17 1.68% -11.11

8 223 22.07% -5.87 171 16.93% -4.93 52 5.14% -8.94

9 345 34.15% -4.02 290 28.71% -3.68 55 5.44% -5.79

10 267 26.43% 8.14 238 23.56% 7.9 29 2.87% 10.09

11 79 7.82% 7.24 69 6.83% 6.74 10 0.99% 10.7

12 7 0.69% 8.58 7 0.69% 8.58

13

 

 

I hope that makes senses, but here is the key part.

 

1010 hands, average tricks = 9.03 plus/minus 0.03, average score -0.54

 

Of these hands, 378 made (37%) on these 378 hanss,

average tricks = 10.16 plus/minus 0.03, for an average score of 7.54 imps. For the record, the average imp score of the guys going down under these conditions was -5.37 imps. So, bidding and making won 7.54, but going down cost 5.37. So it comes out that about 42% is the place where you might want to bid the vul game.

 

Not sure what this means, but when the percent who makes (add points, change trump fit) approaches 42% vul, the average imp score becomes zero and sligthly postive.

[ack_hh]

PS To Ben: Does BrBrowser contain recent BBO data?

Latest data: 30-November-2004