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Is this a psyche or cheating?

#41 User is offline   PeterAlan 

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Posted 2020-September-30, 14:41

View Postpilowsky, on 2020-September-30, 14:12, said:

Now I can't tell if you are being childish or delusional. You are saying that not only can you project thoughts into my brain, but also into Gordon's brain. Using invisible technology.

There are a lot of people in the world with the surname 'Pilowsky' that care for people who believe that they know what other people think when they don't. Two of them (my father and sister) were world-famous at it.
I'm not one of those Pilowsky's, but I do have a medical degree. If you come to Australia I can give you a referral. Or I can recommend someone for you.

This is nonsense: the problem lies with your comprehension skills. mike said no such thing.

Nor did Gordon claim to "know what other people 'think'" when he said (my emphasis) "I don't think it is what you said".

All that Gordon and Mike have done is to remark on what your statements appear to them (and to me as well) to be saying. If this is at odds with what you intend to convey, then I suggest that the problem lies with how you are expressing yourself.
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#42 User is online   hrothgar 

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Posted 2020-September-30, 15:00

View PostPeterAlan, on 2020-September-30, 14:41, said:

This is nonsense: the problem lies with your comprehension skills.


Peter, your problem is that you're engaging with Pilowsky as if he were anything but a useless troll
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#43 User is offline   pilowsky 

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Posted 2020-September-30, 16:25

View PostPeterAlan, on 2020-September-30, 14:41, said:

This is nonsense: the problem lies with your comprehension skills. mike said no such thing.

Nor did Gordon claim to "know what other people 'think'" when he said (my emphasis) "I don't think it is what you said".

All that Gordon and Mike have done is to remark on what your statements appear to them (and to me as well) to be saying. If this is at odds with what you intend to convey, then I suggest that the problem lies with how you are expressing yourself.


Now we have three people engaged in a folie a trois.

Along with the infamous troll Hrothgar.
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#44 User is offline   nige1 

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Posted 2020-September-30, 16:50

View PostAL78, on 2020-September-28, 10:38, said:

My bridge partner has just told me a situation which cropped up on BBO where she got a bottom because they were diverted from the killing lead by one of the opponents doing what sounded to me like a psyche, but she is adamant they were cheating. She asked one or two senior players at the club (who are very experienced directors) who sided with her saying it was out of order, and there seems to be a view that psyches should be illegal.

View Posthrothgar, on 2020-September-28, 10:58, said:

The two senior players in your club are idiots,

View Postpilowsky, on 2020-September-30, 14:12, said:

Now I can't tell if you are being childish or delusional.
[

View Posthrothgar, on 2020-September-30, 15:00, said:

Peter, your problem is that you're engaging with Pilowsky as if he were anything but a useless troll

View Postpilowsky, on 2020-September-30, 16:25, said:

Now we have three people engaged in a folie a trois. Along with the infamous troll Hrothgar.

Misbids and psyches are not cheating. Bridge laws specifically allow them. Other views are mistaken :( but imply neither lunacy nor idiocy :)
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#45 User is offline   thepossum 

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Posted 2020-September-30, 17:36

View PostAL78, on 2020-September-28, 10:38, said:

My bridge partner has just told me a situation which cropped up on BBO where she got a bottom because they were diverted from the killing lead by one of the opponents doing what sounded to me like a psyche, but she is adament they were cheating.

Her opponents bid up to a slam, and on the way her LHO bid 3, which was alerted as 0-1 spades. I'm not sure whether or not her RHO had bid spades naturally in the auction, it is possible. Her partner on lead holding the spade ace decided on the basis of this description not to lead it. It turned out that the person who bid 3 and alerted it held two losing spades, and a spade lead was necessary for the defence to take two spade tricks before the losers were thrown on diamonds. She seems to believe this was deliberate mis-information and therefore cheating, whereas I am inclined to believe it was a psyche aimed to divert the killing lead. What are your thoughts?

The director was called at the time and questioned the opponents. The one who made the 3 bid claimed he got his spades and clubs mixed up, e.g. he/she was looking at the club void and clicked on the wrong black suit. The result was allowed to stand.

She asked one or two senior players at the club (who are very experienced directors) who sided with her saying it was out of order, and there seems to be a view that psyches should be illegal.


Does anyone mind me asking what the best lead was with/without the alleged psych
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#46 User is offline   Zelandakh 

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Posted 2020-September-30, 17:55

Pil, you are engaging once again on a dangerous course in a thread where you are simply wrong. Everyone here knows you are wrong. As I mentioned in a previous thread, take a deep breath and step back. Look back objectively over what has been written here and see where you are going off the rails.

This is a public forum - when you post things that are straight up wrong you can expect other posters to point it out to you. There is nothing personal in that, it is just how forums work. On the other hand, when you react to criticism by getting personal with people, you should not be surprised to find that you start copping some serious flak back, and at times even personal comments such as that from Richard. If you want to avoid that then try engaging with people in a less aggressive and antagonistic way.

You have the potential to become a useful and productive member of the BBF community but you are getting yourself off to a very rocky start and are fast approaching the point where many of the posters here will write you off, perhaps forever. So I urge you to think about it and try to post calmly and constructively for a while. I promise you, you will get much more from these forums if you do.
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#47 User is online   hrothgar 

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Posted 2020-September-30, 18:23

View Postthepossum, on 2020-September-30, 17:36, said:

Does anyone mind me asking what the best lead was with/without the alleged psych


Defense is not my strong suit, however, on the actual auction I think that banging the spade Ace is really bad. On anything but a spade lead, the slam is going to make via the ruffing finesse. Note that even if you get a Spade lead, partner is going to signal for a club shift, and odds are that the slam will STILL make.

Let's assume a more normal auction (without the misbid). You'll probably see an auction like

1H - 2N
3C - 3D
3H - 4C
4H

Here, seeing the defense cash two Spades off the top is a lot more likely.
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#48 User is offline   pilowsky 

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Posted 2020-September-30, 18:24

View PostZelandakh, on 2020-September-30, 17:55, said:

Pil, you are engaging once again on a dangerous course in a thread where you are simply wrong. Everyone here knows you are wrong. As I mentioned in a previous thread, take a deep breath and step back. Look back objectively over what has been written here and see where you are going off the rails.

This is a public forum - when you post things that are straight up wrong you can expect other posters to point it out to you. There is nothing personal in that, it is just how forums work. On the other hand, when you react to criticism by getting personal with people, you should not be surprised to find that you start copping some serious flak back, and at times even personal comments such as that from Richard. If you want to avoid that then try engaging with people in a less aggressive and antagonistic way.

You have the potential to become a useful and productive member of the BBF community but you are getting yourself off to a very rocky start and are fast approaching the point where many of the posters here will write you off, perhaps forever. So I urge you to think about it and try to post calmly and constructively for a while. I promise you, you will get much more from these forums if you do.


Zel, I take nothing personally, it's not my style. Look back over what I actually said instead of what people think that they would like me to have said. It's just a little silly.
Richard has a habit of making puerile ad hominem attacks on just about anything that moves - it seems to be his style. It's a bit odd but it's his problem, not mine.


You seem to take joy in commentating on the qualities of others. Again not my style but if it brings you pleasure go for it.

I have absolutely no interest in either you or Richard or other people that seem to want to commentate on me. If you don't find anything of use in my comments or opinions then ignore them - I'm ignoring yours.
Perhaps you should think about why you have these rather grandiose ideas about which people may or may not be 'useful and productive'.
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#49 User is offline   PeterAlan 

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Posted 2020-September-30, 18:28

Pilowsky, on, I hope, a more constructive note, I thought I saw a remark of yours somewhere about developing a spreadsheet for the numbers of hands of certain shape(s), points, etc. If I'm not mistaken in this, I may well already have what you want and I'm happy to share it. If this of interest, please let me know.

Peter
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#50 User is online   hrothgar 

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Posted 2020-September-30, 18:39

View Postpilowsky, on 2020-September-30, 18:24, said:


Richard has a habit of making puerile ad hominem attacks on just about anything that moves - it seems to be his style. It's a bit odd but it's his problem, not mine.


Actually Pilowsky, I am able to engage quite constructively with the majority of the people on the forums.
However, I have zero use for trolls, dimwits, and the like.

In your your own case, it was pretty damn clear that you were damaged goods early on, and certainly dating back to some of your posts on "Statistics".

The reason that I decided to write you off completely were the personal side messages that you sent me gloating about dragging thepossum.

You're a bored little troll, clutching at pearls
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#51 User is offline   pilowsky 

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Posted 2020-September-30, 19:27

View PostPeterAlan, on 2020-September-30, 18:28, said:

Pilowsky, on, I hope, a more constructive note, I thought I saw a remark of yours somewhere about developing a spreadsheet for the numbers of hands of certain shape(s), points, etc. If I'm not mistaken in this, I may well already have what you want and I'm happy to share it. If this of interest, please let me know.

Peter


Thank you - in fact, I had made this spreadsheet, but later discovered - that as with most of the great and useful things - it's available from multiple other sources. Playbridge, Wikipedia etc
Reconstructing it was helpful though and useful in embedding some of the probabilities.
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#52 User is offline   PeterAlan 

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Posted 2020-September-30, 19:38

View Postpilowsky, on 2020-September-30, 19:27, said:

Thank you - in fact, I had made this spreadsheet, but later discovered - that as with most of the great and useful things - it's available from multiple other sources. Playbridge, Wikipedia etc
Reconstructing it was helpful though and useful in embedding some of the probabilities.

Beware: Wikipedia is not reliable. In particular, the statistics on the numbers of hands with X losers were hopelessly wrong when I last looked a while ago.
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#53 User is offline   pilowsky 

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Posted 2020-September-30, 19:43

View PostPeterAlan, on 2020-September-30, 19:38, said:

Beware: Wikipedia is not reliable. In particular, the statistics on the numbers of hands with X losers were hopelessly wrong when I last looked a while ago.


Thanks - The playbridge site also has the ACBL data. All the hands that I produce - apart from BBO and Step come from here http://www.playbridge.com/
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#54 User is offline   blackshoe 

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Posted 2020-October-01, 13:07

View Postshaky44, on 2020-September-30, 04:34, said:

<snip>
<snip>

I've always assumed that when I am explaining my own bid online, that I am explaining what the bid means, not what my partner thinks it means. Is that incorrect?

I've seen many players -- and I've done it myself -- explain their bid as a mis-click. In this situation (where I've mixed up two suits) I would explain the bid as a mis-click / mistake. Maybe I should just give an explanation based on our agreements, even if it's wrong.

Whoever is doing the explaining shouldn't be explaining what either player thinks the bid means or what the player who made the bid intended to convey by the bid. What should be explained is the partnership understanding as to the meaning of the bid (call, actually). Explaining that one has mis-clicked is extraneous and not required by the rules of the game or by its ethics.

Doing what one has seen many others do is quite common, and quite human. And quite often wrong.
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#55 User is offline   thepossum 

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Posted 2020-October-01, 16:11

View Posthrothgar, on 2020-September-30, 18:23, said:

Defense is not my strong suit, however, on the actual auction I think that banging the spade Ace is really bad. On anything but a spade lead, the slam is going to make via the ruffing finesse. Note that even if you get a Spade lead, partner is going to signal for a club shift, and odds are that the slam will STILL make.

Let's assume a more normal auction (without the misbid). You'll probably see an auction like

1H - 2N
3C - 3D
3H - 4C
4H

Here, seeing the defense cash two Spades off the top is a lot more likely.


Thx Richard

It's just to me, with my fairly simple approach to things, and possibly not even noticing the implications of said alleged misleading bid I would have led my Ace anyway with that hand. But my play is certainly not up to the level of the protaganists at the table that day

Note, just ran a quick sim and that suggests the bid should not have changed the preferred lead (although obviously the superiority of the Ace lead is massively reduced). But my sims are not at that level either and am nervous even commenting in this company :)
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#56 User is online   hrothgar 

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Posted 2020-October-01, 16:28

View Postthepossum, on 2020-October-01, 16:11, said:


It's just to me, with my fairly simple approach to things, and possibly not even noticing the implications of said alleged misleading bid I would have led my Ace anyway with that hand. But my play is certainly not up to the level of the protaganists at the table that day



In my experience, banging an Ace against a slam often works well. You may very well blow a temple (or worse yet lose the opportunity to cover a King), but balanced against this you get to see dummy and see whether partner is signally for an obvious shift.

However, banging an Ace in a suit where the opponents have shown shortness add an additional element of risk. If they have a void, you might very well see your Ace ruffed out. This happens way too often for my liking.

YMMV
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#57 User is offline   thepossum 

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Posted 2020-October-01, 16:36

View Posthrothgar, on 2020-October-01, 16:28, said:

However, banging an Ace in a suit where the opponents have shown shortness add an additional element of risk. If they have a void, you might very well see your Ace ruffed out. This happens way too often for my liking.




Of course I appreciate that, and that risk is borne out by the Sim result. But even reducing your chance of making the Ace was not enough to totally wipe out the advantages of the Ace lead (in my veiw anyway), although depends on how you use means and confidence intervals. I should have mentioned the changes such that the CIs would now overlap with all other leads - but to me I'm still going with the estimated mean chance of defeating the contract - which is fairly slim :)

But as I said, my style of play is fairly basic and I was brought up with attacking rather than passive leads

Dislaimer - the above does not constitute professional opinion or advice in any discipline including statistics
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#58 User is online   hrothgar 

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Posted 2020-October-01, 16:41

View Postthepossum, on 2020-October-01, 16:36, said:

Of course I appreciate that, and that risk is borne out by the Sim result. But even reducing your chance of making the Ace was not enough to totally wipe out the advantages of the Ace lead (in my veiw anyway), although depends on how you use means and confidence intervals. I should have mentioned the changes such that the CIs would now overlap with all other leads - but to me I'm still going with the estimated mean chance of defeating the contract - which is fairly slim :)

Dislaimer - the above does not constitute professional opinion or advice in any discipline including statistics


FWIW,in my experience if you are posting results based on simulations, it's often a good idea to post your code.

This gives folks a chance to understand what assumptions you are making and helps provide more confidence with respect to results.
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#59 User is offline   thepossum 

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Posted 2020-October-01, 17:17

View Posthrothgar, on 2020-October-01, 16:41, said:

FWIW,in my experience if you are posting results based on simulations, it's often a good idea to post your code.

This gives folks a chance to understand what assumptions you are making and helps provide more confidence with respect to results.


OK will post my sim details. I need to regenerate them first. Or at least run another few thousand hands

Actually, as an interesting aside (maybe relating to another thread a few years back about Jacoby) I had to deal 2 million hands to get 1000 that fitted my constraints with the "misbid"
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#60 User is offline   thepossum 

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Posted 2020-October-01, 17:40

On request for Richard. Note that this is still (and always will be) a draft. It is not a complete reviewed document, or anything and should never be used for any purpose other than Richard seeing my code etc

It was done purely as an interest exercise when I maybe should have been doing other things, with constant distractions, and also some anxiety about posting anything like this without it being properly checked and written up etc

Please bear with me - editing a few times to add results. It would take too long for me to format into friendly form so am just pasting Lua code (constraints) which I used with Bdeal (Beling) and the raw results with or without the 3S psych/misbid/mistake/whatever etc

Important note. It is a crude sim looking simply at defeating the contract or not and not making any assessment on number of tricks won/lost for matchpoint considerations etc I have a very simple approach to bridge, especially defence against a slam. I have in the past tried to work out a more sophisitcated distribution of the outcomes and how that distribution changes with different leads and the different bids. Its not much more code but could be provided if necessary. As I said it was a very simple sim :)

Results show mean number of tricks for declarer with each card led, with a 95% CI (I think it may be 1.96 SEs its not clear - I think the funny An symbol is +/-) but the Standard deviation and number of hands is also listed etc

As you can see without the 3S bid the 95% CIs do not overlap and the Ace (for me) is clearly the best lead in terms of average tricks and chance of defetaing the slam

With the 3S bid the difference in mean estimates is smaller and the 95% CIs do overlap. For me that doesn't affect thinking that the Ace is still a slightly superior lead etc

I'm not sure of the bdeal version but it was built on 27/11/18 (Australian date style)

Run on an HP Spectre 360X using Windows 10 etc on a sunny Friday morning somewhere in Australia

They are very basic scripts and assumptions. For example minium point ranges for E and W and assumption of 6+ hearts for W and 4+ hearts for E and (when used) the splinter being 0 or 1 tricks. I didn't put any other constraints on hand shapes - eg assumptions on Jacoby or number of losers in each hand etc
I didn't put any assumptions on controls etc. To make it more sophisticated I could have put in some loser and control assumptions that would lead to a 6H bid etc The configuration section has the North hand and requests bdeal to generate enough hands to get 1000 that fit the constraints.
The stats section calculates means and CIs for number of tricks and chance of declarer making slam for each possible card led

Note the funny copyright symbol is in the rendered HTML. It should be the letter c in parenthesies, ( c ) © "©"

--------------------------------------------------------------------------------------------------
--LUA Script for Bdeal v17.10.0 (Piotr Beling. http://bcalc.w8.pl/) without the 3S bid (my interpretation of point ranges etc)
--Written and run by the possum on 2nd Oct 2020

conf = {
N="at743.3.j962.j87",
num = 1000
}

function filter()

return W:hcp()>13 and W:hearts()>5 and E:hcp()>12 and E:hearts()>3
--and W:spades()<2
end

function stats()
for c in N:cards() do -- for each card c in the hand N:
local t = tricks(W, "H", c) -- tricks to take by E-W
count("E-W tricks after " .. tostring( c ), t)
count("chance to defeat after " .. tostring( c ), t < 12)
end
end


E-W tricks after C7: 12064 / 1000 = 12.064 Ań 0.0485418 (95% conf.) min: 10 max: 13 sdev: 0.782243
E-W tricks after C8: 12064 / 1000 = 12.064 Ań 0.0485418 (95% conf.) min: 10 max: 13 sdev: 0.782243
E-W tricks after CJ: 12070 / 1000 = 12.07 Ań 0.0486684 (95% conf.) min: 10 max: 13 sdev: 0.784283
E-W tricks after D2: 12066 / 1000 = 12.066 Ań 0.0479729 (95% conf.) min: 9 max: 13 sdev: 0.773074
E-W tricks after D6: 12067 / 1000 = 12.067 Ań 0.0479274 (95% conf.) min: 9 max: 13 sdev: 0.772341
E-W tricks after D9: 12073 / 1000 = 12.073 Ań 0.0480542 (95% conf.) min: 9 max: 13 sdev: 0.774384
E-W tricks after DJ: 12079 / 1000 = 12.079 Ań 0.0481777 (95% conf.) min: 9 max: 13 sdev: 0.776376
E-W tricks after H3: 12085 / 1000 = 12.085 Ań 0.0460116 (95% conf.) min: 10 max: 13 sdev: 0.741468
E-W tricks after S3: 12275 / 1000 = 12.275 Ań 0.0462453 (95% conf.) min: 10 max: 13 sdev: 0.745235
E-W tricks after S4: 12275 / 1000 = 12.275 Ań 0.0462453 (95% conf.) min: 10 max: 13 sdev: 0.745235
E-W tricks after S7: 12275 / 1000 = 12.275 Ań 0.0462453 (95% conf.) min: 10 max: 13 sdev: 0.745235
E-W tricks after SA: 11714 / 1000 = 11.714 Ań 0.0383639 (95% conf.) min: 10 max: 13 sdev: 0.618226
E-W tricks after ST: 12276 / 1000 = 12.276 Ań 0.0461807 (95% conf.) min: 10 max: 13 sdev: 0.744194
chance to defeat after C7: 232 / 1000 = 0.232 Ań 0.0261938 (95% conf.) min: 0 max: 1 sdev: 0.422109
chance to defeat after C8: 232 / 1000 = 0.232 Ań 0.0261938 (95% conf.) min: 0 max: 1 sdev: 0.422109
chance to defeat after CJ: 231 / 1000 = 0.231 Ań 0.0261543 (95% conf.) min: 0 max: 1 sdev: 0.421472
chance to defeat after D2: 229 / 1000 = 0.229 Ań 0.0260747 (95% conf.) min: 0 max: 1 sdev: 0.420189
chance to defeat after D6: 228 / 1000 = 0.228 Ań 0.0260346 (95% conf.) min: 0 max: 1 sdev: 0.419543
chance to defeat after D9: 225 / 1000 = 0.225 Ań 0.0259129 (95% conf.) min: 0 max: 1 sdev: 0.417582
chance to defeat after DJ: 224 / 1000 = 0.224 Ań 0.025872 (95% conf.) min: 0 max: 1 sdev: 0.416922
chance to defeat after H3: 214 / 1000 = 0.214 Ań 0.0254503 (95% conf.) min: 0 max: 1 sdev: 0.410127
chance to defeat after S3: 156 / 1000 = 0.156 Ań 0.0225169 (95% conf.) min: 0 max: 1 sdev: 0.362855
chance to defeat after S4: 156 / 1000 = 0.156 Ań 0.0225169 (95% conf.) min: 0 max: 1 sdev: 0.362855
chance to defeat after S7: 156 / 1000 = 0.156 Ań 0.0225169 (95% conf.) min: 0 max: 1 sdev: 0.362855
chance to defeat after SA: 319 / 1000 = 0.319 Ań 0.028923 (95% conf.) min: 0 max: 1 sdev: 0.466089
chance to defeat after ST: 155 / 1000 = 0.155 Ań 0.0224579 (95% conf.) min: 0 max: 1 sdev: 0.361905
Number of hands dealt: 696262. CPU time usage [sec]: 6.21 (x8 threads).
----------------------------------------------------------------------------------------------------

Notes
Without the 3S bid the Ace is the only lead with a mean number of tricks less than 12 (approx 11.75) 95% CI approx +/- 0.04-0.05 tricks
Chance of defeating the slam is approximately 32% with the Ace but only of the order of 22-23% with any other suit. CI +/- approx 2-3%

Clearly you would never lead a small spade - I could have excluded them from the sim :)







---------------------------------------------------------------------------------

--LUA Script for Bdeal 17.10.0 (Piotr Beling. http://bcalc.w8.pl/) with the 3S bid (my interpretation of point ranges etc)
--Written and run by the possum on 2nd Oct 2020

conf = {
N="at743.3.j962.j87",
num = 1000
}

function filter()

return W:hcp()>13 and W:hearts()>5 and E:hcp()>12 and E:hearts()>3
and W:spades()<2
end

function stats()
for c in N:cards() do -- for each card c in the hand N:
local t = tricks(W, "H", c) -- tricks to take by E-W
count("E-W tricks after " .. tostring( c ), t)
count("chance to defeat after " .. tostring( c ), t < 12)
end
end




E-W tricks after C7: 12265 / 1000 = 12.265 An 0.0499058 (95% conf.) min: 10 max: 13 sdev: 0.804223
E-W tricks after C8: 12265 / 1000 = 12.265 An 0.0499058 (95% conf.) min: 10 max: 13 sdev: 0.804223
E-W tricks after CJ: 12276 / 1000 = 12.276 An 0.0496369 (95% conf.) min: 10 max: 13 sdev: 0.79989
E-W tricks after D2: 12270 / 1000 = 12.27 An 0.0486684 (95% conf.) min: 10 max: 13 sdev: 0.784283
E-W tricks after D6: 12270 / 1000 = 12.27 An 0.0486684 (95% conf.) min: 10 max: 13 sdev: 0.784283
E-W tricks after D9: 12276 / 1000 = 12.276 An 0.0486179 (95% conf.) min: 9 max: 13 sdev: 0.783469
E-W tricks after DJ: 12282 / 1000 = 12.282 An 0.0485645 (95% conf.) min: 9 max: 13 sdev: 0.782608
E-W tricks after H3: 12289 / 1000 = 12.289 An 0.0466641 (95% conf.) min: 10 max: 13 sdev: 0.751983
E-W tricks after S3: 12494 / 1000 = 12.494 An 0.0385521 (95% conf.) min: 10 max: 13 sdev: 0.62126
E-W tricks after S4: 12494 / 1000 = 12.494 An 0.0385521 (95% conf.) min: 10 max: 13 sdev: 0.62126
E-W tricks after S7: 12494 / 1000 = 12.494 An 0.0385521 (95% conf.) min: 10 max: 13 sdev: 0.62126
E-W tricks after SA: 11951 / 1000 = 11.951 An 0.0407203 (95% conf.) min: 10 max: 13 sdev: 0.6562
E-W tricks after ST: 12495 / 1000 = 12.495 An 0.0384526 (95% conf.) min: 10 max: 13 sdev: 0.619657
chance to defeat after C7: 186 / 1000 = 0.186 An 0.0241459 (95% conf.) min: 0 max: 1 sdev: 0.389107
chance to defeat after C8: 186 / 1000 = 0.186 An 0.0241459 (95% conf.) min: 0 max: 1 sdev: 0.389107
chance to defeat after CJ: 182 / 1000 = 0.182 An 0.0239435 (95% conf.) min: 0 max: 1 sdev: 0.385845
chance to defeat after D2: 175 / 1000 = 0.175 An 0.0235787 (95% conf.) min: 0 max: 1 sdev: 0.379967
chance to defeat after D6: 175 / 1000 = 0.175 An 0.0235787 (95% conf.) min: 0 max: 1 sdev: 0.379967
chance to defeat after D9: 172 / 1000 = 0.172 An 0.0234182 (95% conf.) min: 0 max: 1 sdev: 0.37738
chance to defeat after DJ: 170 / 1000 = 0.17 An 0.0233098 (95% conf.) min: 0 max: 1 sdev: 0.375633
chance to defeat after H3: 156 / 1000 = 0.156 An 0.0225169 (95% conf.) min: 0 max: 1 sdev: 0.362855
chance to defeat after S3: 62 / 1000 = 0.062 An 0.0149648 (95% conf.) min: 0 max: 1 sdev: 0.241156
chance to defeat after S4: 62 / 1000 = 0.062 An 0.0149648 (95% conf.) min: 0 max: 1 sdev: 0.241156
chance to defeat after S7: 62 / 1000 = 0.062 An 0.0149648 (95% conf.) min: 0 max: 1 sdev: 0.241156
chance to defeat after SA: 213 / 1000 = 0.213 An 0.0254069 (95% conf.) min: 0 max: 1 sdev: 0.409428
chance to defeat after ST: 61 / 1000 = 0.061 An 0.0148516 (95% conf.) min: 0 max: 1 sdev: 0.23933
Number of hands dealt: 2044012. CPU time usage [sec]: 7.66 (x8 threads).

--------------------------------------------------------------------------------

Notes
With the 3S bid the Ace is the only lead with a mean number of tricks less than 12 (approx 11.95) but the 95% CIs overlap +/- approximately 0.05 tricks
Chance of defeating the slam is approximately 21% with the Ace but only of the order of 17-18% with any other suit. But the CIs overlap, they are +/- approx 2-3%

Note however the standard deviation for the Ace lead is now much larger etc. However the standard deviations for all other leads are very large too I could keep adding notes forever

Clearly you would never lead a small spade. I could have editted them out :)
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