[EricK]

Hannie, on Sep 8 2005, 05:15 PM, said:

cherdano, on Sep 8 2005, 04:59 AM, said:

By the same argument, if I throw coins and decide for 4 out of 5 deals that NS can make 9 tricks, and 10 on the other, this would be a perfect analysis for MP contracts, since the average predicted number of tricks is 9.20.

Arend

Arend,

This is very disturbing to me. Last time I was in Germany they were using Euros, and these coins have only two sides. It seems to me that it is impossible to guarantee a 4/5 chance by throwing coins a finite number of times.

Apologies for an off-subject response.

You generate any probability you like with a coin as follows:

Express the probability as a binary number (eg 4/5 = 0.1100110011001100....) and throw the coin until you get a head. Then count it as a success if the first head appears on a throw number indicated by a 1 in the expansion (eg for 4/5 if the first head appears on throw number 1,2,5,6,9,10 etc), and a failure otherwise.

This doesn't guarantee a finite number of throws, but you would be very unlucky to have to throw the coin an infinite number of times

Eric

[awm]

Why should we be interested in the probabilities of making game?

I think a lot of us count points for shape when we open. For example, other than 10-12 notrumpers, I don't think many of us would open this in first seat:

xxx
xxx
Axx
KQJx

However, I know a lot of people who would open:

xxx
x
Axx
KQJxxx

Now, assuming fairly standard methods, it would be logical to open 1♣ on both hands (if we were going to open). This steals basically no space from opponents. It doesn't particularly direct a lead (in this case the clubs are good, but we have to open 1♣ on three small at times so I don't think partner can bet on good clubs). It doesn't really help us in competitive auctions much, because partner won't know we have six clubs on the second hand and can't really raise the suit very aggressively.

So why is it that people open the second hand and not the first? The reasoning is that the second hand is somehow "better." Suppose that partner has some random thirteen count and we end up in a game. The top hand is likely to be a disappointment, and our chances of making 3NT or 4M are probably not good when partner has a "minimum game force." The bottom hand has a nice source of tricks for any contract, and a possible ruffing value if we find a spade fit. It seems likely that we would have play for a game on most 13-counts partner could produce.

As for majors versus minors, I would happily open this hand playing fairly standard methods:

AQxxx
KJxxx
x
xx

I have six losers, 27 ZAR, rule of 20, blah blah blah. Most players would open this hand. It's likely that we have a fit in one major or the other, and we will often have a good chance at game when partner has a decent hand. On the other hand, switch this to:

x
xx
AQxxx
KJxxx

I'm not nearly so eager to open this hand, and would probably pass. If I open, chances are good that we will end up in 3NT when partner has a decent hand (despite a likely 5-3 or 5-4 minor fit). I don't necessarily like our chances of making 3NT. My weakness in the majors suggests partner will need many cards there.

I should also note that many modern systems require that partner make immediate decisions about whether to force game opposite an opening. This includes the 2/1 game forcing method that is so popular, as well as most strong club or diamond response structures. Most relay systems also have this property, even some of the ones where the relay is not game forcing (since the main information discovered before deciding to game force is frequently whether opener's points are max or min, not opener's detailed shape). Obviously being forced to decide whether to set up a game force early in the auction has its weaknesses. But since we seem to have to do it, it will be good to understand how to evaluate distribution in the absence of detailed knowledge about fit.

So the relevent question would seem to be:

How many points do I need, with various distributions, such that the probability of game becomes roughly equal?

[Blofeld]

EricK, on Sep 8 2005, 01:08 PM, said:

This doesn't guarantee a finite number of throws, but you would be very unlucky to have to throw the coin an infinite number of times

To be overly pedantic, it does guarantee (i.e. probability 1) a finite number of tosses, but the # of possible numbers of tosses is infinite.

[cherdano]

Hannie, on Sep 8 2005, 07:15 PM, said:

cherdano, on Sep 8 2005, 04:59 AM, said:

By the same argument, if I throw coins and decide for 4 out of 5 deals that NS can make 9 tricks, and 10 on the other, this would be a perfect analysis for MP contracts, since the average predicted number of tricks is 9.20.

Arend

Arend,

This is very disturbing to me. Last time I was in Germany they were using Euros, and these coins have only two sides. It seems to me that it is impossible to guarantee a 4/5 chance by throwing coins a finite number of times.

You have a lot of trust in the fairness of our coins in Germany

[awm]

Jlall, on Sep 8 2005, 02:11 PM, said:

I'm not sure how we got from "5521 is more likely to make game than 2155" to "AQxxx KJxxx xx x is an opener and xx x AQxxx KJxxx is a pass." It seems a few steps in the logic chain are missing.

1) There are other variables. Lead direction, saves, preemption. One could argue since you are 2155 THEY are more likely to make a game thus you should open lighter with the minors in hopes that you can find a fit and save. Obviously something is missing from that logic too, but to think that likelihood of game is the only variable in opening seems wrong.

2) Passing does not preclude getting to game. We are more likely to make game with the majors, true, but only if we find a fit. If we pass first and then later find a fit, we can upgrade accordingly. It is not like it's now or never and we have to guess. Maybe we should wait to find a fit before doing our upgrading?

3) Bridge is a partnership game. Partner also knows major suit games are easier than minor suit games (or light HCP 3Ns) and can adjust his aggression according to where we are likely to play. If he has a minor suit fit, for instance, he will be less agressive than if he has a major suit fit.

4) Even if it were only about likelihood of game, the chance may be great enough to open the second hand. Alternatively, it may be so low even with 5-5 in the majors that we should pass the first one. All of this is moot, of course, since there are other things to consider.

Let's not jump to conclusions because of a priori odds that involve only 1 variable and 1 person in the partnership. Perhaps there is more to bridge than that.

(1) Yes, there are other variables. If I could open the 1-2-5-5 hand with 2NT showing 8-11 points and 5-5 in the minors I would happily do so. However, we're considering one-level "constructive" openings in a fairly standard system. I'm not convinced that a 1♦ call has a great lead directional value, or that it's even much help to partner in finding a fit since it doesn't necessarily show five cards.

(2) I agree that passing doesn't preclude getting to game. But if there are fairly "normal" hands which make game good but which partner wouldn't bother to open (i.e. Kxxx Qx Axx xxxx) that's a pretty good argument for bidding isn't it?

(3) Sure, partner knows these things. But partner often has to decide whether to force game pretty early in the bidding (i.e. her first bid over 1M in a 2/1 game forcing system, and her second bid in many other sequences). Partner will generally assume that my hand is "normal" for the bidding so far (minimum but not sub-minimum values, not much more distributional than I have shown). These five-five hands with ten points are likely to be a surprise to partner, who will probably be assuming something along the lines of a (5422) twelve-count when making her decisions. So the question is: will partner usually make the right decision anyway? Or is my hand so far from what she expects in terms of playing strength, that she will often force us to games that go down?

(4) Certainly, we don't have all the data about probabilities of game yet. It could be that 1-2-5-5 hands play incredibly well in 3NT because we can run the five card suits. I suspect that hand evaluation for notrumps and suit contracts are different (i.e. 5431 is better than 5422 for play in a suit, but probably the same or worse for play in notrump). But these are just my suspicions, and that's why I'm asking the question.

[Fluffy]

Hannie, on Sep 8 2005, 05:04 PM, said:

Also, I expect that the more unbalanced we are, the more likely the opponents have game (since they are more likely to have distributional hands too). This could be yet another argument for opening light with highly distributional hands.

I somehow think the opposite, the chances that opponents have game when you get 4333 is quite high, because everything breaks evenly. Maybe this is a weak argument.

[thomaso]

Some notes on my Binky Points research.

(1) I have specifically never made claims about how the research should guide bidding. There are some obvious points and some less-than-obvious points about how to use such 'fine' evaluations. When do you invite? When do you accept invites? These are all non-trivial problems, made even more non-trivial by the fact that the narrower you put the ranges for inviting, accepting, and rejecting, the more opponents know about your hand in these circumstances. I don't want to claim that my results have only purely theoretical value, but they were never meant to be a guide for bidding.

(2) In particular, obviously, you want to open different strength hands differently depending on the shape of the hand (rather than the pattern.) Clearly, a light 5-5-2-1 is a better candidate for opening than a light 2-1-5-5. That's because the number of hands partner can have where game makes is higher, because he needs less for game in a major than in a minor, and if we're gonna play a suit contract, that suit contract is probably gonna be in one of my five-card suits. It's not a flaw in BP (or any other evaluation system) if it gives the same value for equivalent 5521 and 2155 hands, it's a flaw in bidding if you use one value for determining what to open all hands. When to open light is a matter of whether you have any defense, whether you have a safe rebid, whether passing might miss an easy game.

Many moons ago, someone made much of the fact that my data showed that AKxxx xxx Ax xxx actually had lower playing strength than xxxxx Axx Ax Kxx - that is, that honors in your long suit were actually less valuable. It is a surprising result, considering all those expert recommendations over the years.

Well, the difference between these two hands in Binky Points is actually relatively miniscule. On the other hand, consider what opening 1S does to partner's hand. When you open the second hand 1S and partner has Qxx in spades, he is going to over-value that queen. That means that partner is going to push to game often on precisely the wrong hands, because, from his point of view, you are likely to have honors in the suit. Even though the second hand technically has nearly exactly the same playing strength, it doesn't mean it is just as good an opener.

[tysen2k]

Welcome to these forums, Thomas.

[tysen2k]

For those interested, I have the chance that the opps have a game as well.

Shape   Game?    Error Opps?    Error
2-2=5-4  24%     0.3%   35%     0.3%
3-2=4-4  24%     0.2%   32%     0.2%
3-3=4-3  25%     0.2%   31%     0.2%
4-3=3-3  25%     0.2%   29%     0.2%
3-2=5-3  26%     0.2%   33%     0.2%
4-2=4-3  26%     0.1%   30%     0.1%
3-3=5-2  27%     0.2%   32%     0.2%
4-3=4-2  27%     0.1%   28%     0.1%
2-2=6-3  27%     0.4%   38%     0.4%
4-4=3-2  28%     0.2%   26%     0.2%
3-2=6-2  28%     0.3%   36%     0.3%
4-2=5-2  28%     0.2%   32%     0.2%
5-2=3-3  28%     0.2%   31%     0.2%
5-3=3-2  28%     0.2%   29%     0.2%
5-2=4-2  29%     0.2%   31%     0.2%
3-1=5-4  29%     0.3%   33%     0.3%
2-2=7-2  29%  *  0.7%   41%  *  0.8%
2-1=6-4  30%     0.4%   38%     0.5%
2-1=5-5  30%  *  0.5%   35%  *  0.5%
4-1=4-4  31%     0.3%   30%     0.3%
3-1=6-3  31%     0.4%   36%     0.4%
5-4=2-2  31%     0.3%   27%     0.3%
2-1=7-3  32%  *  0.7%   41%  *  0.7%
4-1=5-3  32%     0.3%   32%     0.3%
3-3=6-1  32%  *  0.5%   31%  *  0.5%
6-2=3-2  32%     0.3%   34%     0.3%
6-3=2-2  33%     0.4%   32%     0.4%
4-3=5-1  33%     0.3%   28%     0.3%
5-1=4-3  34%     0.3%   31%     0.3%
2-2=8-1  34%  *  2.2%   46%  *  2.3%
3-1=7-2  34%  *  0.7%   42%  *  0.7%
4-4=4-1  34%     0.3%   25%     0.3%
5-3=4-1  35%     0.3%   27%     0.3%
3-2=7-1  35%  *  0.7%   37%  *  0.7%
4-2=6-1  35%     0.5%   32%     0.4%
4-1=6-2  35%     0.4%   35%     0.4%
5-4=3-1  37%     0.3%   25%     0.2%
2-1=8-2  37%  *  1.6%   47%  *  1.6%
6-1=3-3  37%  *  0.5%   35%  *  0.5%
6-3=3-1  38%     0.4%   29%     0.4%
5-2=5-1  38%     0.4%   30%     0.4%
7-2=2-2  38%  *  0.8%   37%  *  0.8%
1-1=6-5  38%  *  1.2%   40%  *  1.2%
5-1=5-2  39%     0.4%   33%     0.4%
3-0=5-5  39%  *  1.1%   33%  *  1.0%
6-1=4-2  40%     0.5%   35%     0.5%
1-1=7-4  40%  *  1.7%   40%  *  1.7%
6-2=4-1  41%     0.5%   32%     0.4%
3-0=6-4  41%  *  0.9%   36%  *  0.9%
4-0=5-4  42%  *  0.6%   31%  *  0.6%
6-4=2-1  43%     0.5%   28%     0.4%
4-0=6-3  43%  *  0.9%   33%  *  0.8%
3-0=7-3  43%  *  1.4%   38%  *  1.4%
7-2=3-1  43%  *  0.7%   37%  *  0.7%
7-1=3-2  43%  *  0.7%   38%  *  0.7%
5-5=2-1  43%  *  0.6%   26%     0.5%
7-3=2-1  44%  *  0.8%   34%  *  0.7%
5-0=4-4  44%  *  0.9%   31%  *  0.8%
4-1=7-1  44%  *  1.2%   36%  *  1.1%
3-3=7-0  44%  *  2.0%   29%  *  1.8%
4-4=5-0  45%  *  0.9%   24%  *  0.8%
3-1=8-1  45%  *  2.1%   44%  *  2.1%
2-0=7-4  45%  *  1.7%   38%  *  1.7%
2-0=6-5  45%  *  1.3%   36%  *  1.2%
4-3=6-0  45%  *  0.9%   28%  *  0.8%
5-0=5-3  46%  *  0.8%   32%  *  0.7%
1-1=8-3  46%  *  2.9%   44%  *  2.9%
3-0=8-2  47%  *  3.1%   46%  *  3.1%
5-3=5-0  48%  *  0.8%   26%  *  0.7%
5-1=6-1  48%  *  0.9%   35%  *  0.8%
5-4=4-0  49%  *  0.7%   23%  *  0.5%
2-0=8-3  50%  *  3.1%   42%  *  3.1%
6-0=4-3  50%  *  0.9%   31%  *  0.8%
6-3=4-0  51%  *  0.9%   26%  *  0.8%
4-2=7-0  51%  *  1.7%   32%  *  1.6%
3-2=8-0  51%  *  3.2%   36%  *  3.1%
6-1=5-1  51%  *  0.9%   35%  *  0.8%
8-1=2-2  52%  *  2.2%   45%  *  2.2%
4-0=7-2  52%  *  1.7%   35%  *  1.6%
5-5=3-0  52%  *  1.1%   22%  *  0.9%
6-4=3-0  52%  *  0.9%   25%  *  0.8%
8-2=2-1  53%  *  1.7%   42%  *  1.7%
5-2=6-0  53%  *  1.3%   31%  *  1.2%
7-0=3-3  54%  *  1.9%   38%  *  1.9%
5-0=6-2  55%  *  1.3%   36%  *  1.2%
1-0=7-5  55%  *  3.0%   41%  *  3.0%
6-2=5-0  56%  *  1.3%   27%  *  1.1%
7-3=3-0  57%  *  1.4%   29%  *  1.3%
6-0=5-2  57%  *  1.3%   35%  *  1.2%
7-1=4-1  57%  *  1.2%   35%  *  1.1%
4-1=8-0  57%  *  4.6%   43%  *  4.6%
1-0=6-6  58%  *  3.7%   44%  *  3.7%
6-5=1-1  58%  *  1.2%   27%  *  1.1%
7-4=1-1  59%  *  1.6%   30%  *  1.5%
4-0=8-1  59%  *  4.7%   36%  *  4.6%
7-0=4-2  60%  *  1.7%   34%  *  1.6%
7-2=4-0  60%  *  1.7%   31%  *  1.6%
8-0=3-2  60%  *  3.1%   43%  *  3.1%
8-1=3-1  61%  *  2.1%   41%  *  2.1%
6-5=2-0  61%  *  1.2%   25%  *  1.1%
1-0=8-4  63%  *  4.7%   48%  *  4.9%
7-4=2-0  63%  *  1.6%   27%  *  1.5%
8-2=3-0  63%  *  3.0%   35%  *  3.0%
5-0=7-1  64%  *  2.8%   42%  *  2.9%
8-3=1-1  65%  *  2.7%   32%  *  2.6%
5-1=7-0  65%  *  3.0%   33%  *  3.0%
8-3=2-0  67%  *  2.9%   36%  *  3.0%
6-1=6-0  70%  *  2.5%   35%  *  2.5%
7-0=5-1  70%  *  2.8%   37%  *  3.0%
6-0=6-1  71%  *  2.4%   38%  *  2.6%
7-5=1-0  72%  *  2.9%   30%  *  3.0%
8-0=4-1  73%  *  4.3%   41%  *  4.8%
7-1=5-0  73%  *  2.8%   35%  *  3.0%
8-1=4-0  74%  *  4.0%   44%  *  4.5%
8-4=1-0  75%  *  4.3%   28%  *  4.4%
6-6=1-0  83%  *  3.1%   24%  *  3.5%

There is less of a dependence on overall shape, but still a major factor if we have major cards or not.

Is this a case against some assumed-fit preempts that show both majors? The opps are much less likely to have a game that we need to sacrifice against.

[han]

Very nice, once again. It also deals with Fluffy's conjecture that 4333's make it more likely that the oponents have game. I celebrate this as a personal victory, WINE!

However, it doesn't look like my prediction [more distributional -> more likely opponents have game] is true either, look for instance at 6-6-1-0, just 24%. However, it does show that the more cards we have in the minors, the more likely it is that they have game. Is this an argument for opening light with cards in the minors, or at least for preempting a lot with cards in the minors? I think so.

Perhaps Jlall is right and bridge really is more complicated, sigh.

[Echognome]

Yes Tysen. Very nice work indeed.

To test the assumed fit theory, it would be great to have a common range in as well (since we are only preempting on weak hands). Thus limiting our table to hands that are 4-4=3-2, 5-4=3-1, 5-4=2-2 in the 5-9 range. (4-4=4-1, 5-5=2-1, and 5-5=3-0 are also commonly included) Maybe one with only the first hands and one with all of them?

Along those lines, it would be really interesting to see the "is a weak 2♥ really preemptive?" debate have some light shed on it. Having some 2♠ and 2♥ openings done with limited ranges would also be interesting.

Would be nice to know how 'effective' preempts are and how much uncertainty we are putting our opponents under. The next step would be to vary the ranges of the preempts until we made their game prospects low enough that they had difficulty. For example, I used to play an intermediate 2♥/2♠ and really felt they were IMP winners when they came up, but dropped them due to frequency.

[tysen2k]

This line of study has also made me to start thinking about what hands make the best preempts. Here's something I was thinking about and let me know if you think it's the right track.

If you look at the par contract for a DD deal, there is some chance that the par contract is a sacrifice for us. I'll try if I can find some characteristics that would predict the chance that par is going to be a sacrifice for us. Would that be a good indication of whether it is likely to be a good preempting hand? I think it would combine all the needed elements:

• Enough trick taking ability for a sac to be profitable
  
• Our opponents having a good enough hand on their own that we need to sac
  
• Not having a majority of the strength since otherwise they would have the sac against us

Is it clear what I'm proposing?

Note that it would entail not only the estimated offensive and deffensive strengths of our hand, but the exact hand pattern as well, not just majors vs. minors. So it would get pretty complicated. I don't know if anything meaningful would come out of it. What do you think?

[tysen2k]

Jlall, on Sep 8 2005, 09:27 PM, said:

I consider 2 things, honor location and spots in your suits, to be of EXTREME importance in deciding whether to preempt. Much more than high cards even. Make sure you try to factor those in. My .02

Naturally they are very important in determining both the offensive and defensive potential of our hand.

[tysen2k]

Okay...

I've plugged and chugged and got some results that I think are somewhat reasonable. The only problem is that it's way too complicated to explain in detail. So I'll give you all some take-away thoughts that I gathered from looking over the results. Remember, what I was trying to do was come up with a way that by looking at our hand we estimate the chance that the par contract is going to be us sacrificing. So if you buy that this is a good indication of whether you should preempt, here is the computer's advice about which hands make the best preempts.

• Diamond preempts rock. Be more prone to preempt with diamonds even if the suit quality isn't there or if you've got some outside strength
  
• 55+ hands make very good preempts unless it's both majors. Both minors are the best and 54 minor hands can be good too.
  
• Heart preempts are okay
  
• Spade preempts without heart shortness or minor voids might not be as good as you think. KQxxxx Qxx xx xx is not that good.
  
• Also beware of club preempts with diamond shortness. They might not have a game as often as you think.
  
• Lack of outside strength is more important than playing tricks/suit quality. xxx - Qxxxxxx xxx is great.
  
• Any void makes it likely that you will sacrifice as long as your total strength is not too high. If you have more than ~6-7HCP with a void you are probably too strong to preempt. An exception seems to be 5440 hands with honors in all 3 suits. Even pretty strong hands like Axxx - Kxxxx Qxxx or - KQxx Qxxx Qxxxx were deemed pretty good.

Let the discussion begin.

[Echognome]

Again Tysen, thanks for all your work. This definitely gives me something to think about on the other topic of designing a preempt structure.

I have one additional question along these lines. How do the results you gave vary (if at all) if the par spot is sacrificing in a part-score? This I believe is where a lot of our preempting lies, when the opponents might have a difficult decision whether to come in and when they do we can smack them.

I like the "summary style" you used for presenting these last results. Very useful for understanding the results and implications.

[tysen2k]

Echognome, on Sep 10 2005, 12:43 AM, said:

I have one additional question along these lines.  How do the results you gave vary (if at all) if the par spot is sacrificing in a part-score?  This I believe is where a lot of our preempting lies, when the opponents might have a difficult decision whether to come in and when they do we can smack them.

Partscore sacs are considered just as much as game or higher, all based on frequency. Basically I just considered the question, "What is the chance that the best spot is a sacrifice?"

I'm sure it varies by vulnerability, but for favorable (which is the condition I tested) when we have a sacrifice it is against a:

Partscore 40%
Game 49%
Slam 9%
Grand 2%

[Blofeld]

Can I just check: your guidelines for the suitability of preempting are based on the probability that our par score is a sacrifice?

If so, I imagine that 5440 hands rank highly because it's likely that there are big fits all over the place. But your preemptive methods need to be able to locate the right fit. Unless you're checking the probability that we have a sacrifice in our longest suit?

It's interesting data, but if you have enough time, I'd really like to know precisely what it represents.