[helene_t]

http://tinyurl.com/nudgyno

How on Earth did Gib know that I had four diamonds?

[inquiry]

helene_t, on 2014-May-07, 13:27, said:

http://tinyurl.com/nudgyno

How on Earth did Gib know that I had four diamonds?

Hold your cards closer to your chest...

[johnu]

9 never, 8 ever

[uday]

GIB uses two play engines.

The simpler one runs at trick one and trick two.

It simply deals sample hands consistent w/the auction & play and takes the play - at each trick - that worked best in its sample of hands.
when something is close to 50-50 or the sample is skewed it can do things like this. I believe that that is what happened here.

The other engine kicks in at trick 3, assuming there is time left on its clock ( it is given a fixed amt. of time for everything ) and is smarter about life in general tho it too has its idiosyncrasies...

I'll check it out further to confirm but I'm fairly confident that this is the case

[hotShot]

uday ist right of cause.

If you take a closer look, you see that all relevant distribution of ♠ and ♥ will lead to 3 tricks each suit for declarer.
Declarer loosing a {CL] to the A is also unavoidable.
So the only difference in tricks that are likely to occur is from the 32% of 4-1 or 5-0 distributions in ♦.
If the long ♦ are with N, declarer will lose a ♦ trick as J98x(x) would be behind QT5 and there is only one save entry to the table.

So if you generate random distributions for NS there is a 16% chance that S hat 4 or 5 ♦ and these deals are the only ones that make a difference in the number of tricks (unless N has single J).

No x-ray vision just plain probabilities.

[1eyedjack]

hotShot, on 2014-May-07, 22:52, said:

If you take a closer look, you see that all relevant distribution of ♠ and ♥ will lead to 3 tricks each suit for declarer.
Declarer loosing a {CL] to the A is also unavoidable.
So the only difference in tricks that are likely to occur is from the 32% of 4-1 or 5-0 distributions in ♦.
If the long ♦ are with N, declarer will lose a ♦ trick as J98x(x) would be behind QT5 and there is only one save entry to the table.

So if you generate random distributions for NS there is a 16% chance that S hat 4 or 5 ♦ and these deals are the only ones that make a difference in the number of tricks (unless N has single J).

No x-ray vision just plain probabilities.

I don't really understand the above.

You cash D:A

If all follow including Jack you can claim 12 (first round finesse losing to Jack and they immediately cash C:A for one down).

If all follow low, cash another D, and if all follow to that, claim 12.

If either show out on the 1st or 2nd round of D, Jack still missing, then you can still establish a 12th trick by leaving off Diamonds provided that you successfully guess the location of C:J, BEFORE you have lost a D trick and BEFORE you cash your last top Diamond. Furthermore, prospects for bringing in the Club suit for 3 tricks and 1 loser are somewhat better than even odds. You can play either opponent for the Jack, and by the time that you need to rely on this, you will know who has short Diamonds and therefore more than likely the longer Club holding.

I don't need to learn up on percentages for that. The first round finesse of D:T is quite significantly inferior.

I was unaware of the two engines thing. I do get that the possibilities increase exponentially the more outstanding cards there are, so I see why it might be necessary. But given that the play to the first couple of tricks is often the most critical part of the hand it is disappointing that GIB thinks that way (as humans we are taught from the cradle to plan the entire hand before playing to trick 1). So easy to criticise, but I would not know where to start with the programming. Maybe Jack knows better.

[hotShot]

1eyedjack, on 2014-May-07, 23:45, said:

I don't really understand the above.

You cash D:A

If all follow including Jack you can claim 12 (first round finesse losing to Jack and they immediately cash C:A for one down).

If all follow low, cash another D, and if all follow to that, claim 12.

If either show out on the 1st or 2nd round of D, Jack still missing, then you can still establish a 12th trick by leaving off Diamonds provided that you successfully guess the location of C:J, BEFORE you have lost a D trick and BEFORE you cash your last top Diamond. Furthermore, prospects for bringing in the Club suit for 3 tricks and 1 loser are somewhat better than even odds. You can play either opponent for the Jack, and by the time that you need to rely on this, you will know who has short Diamonds and therefore more than likely the longer Club holding.

I don't need to learn up on percentages for that. The first round finesse of D:T is quite significantly inferior.

I was unaware of the two engines thing. I do get that the possibilities increase exponentially the more outstanding cards there are, so I see why it might be necessary. But given that the play to the first couple of tricks is often the most critical part of the hand it is disappointing that GIB thinks that way (as humans we are taught from the cradle to plan the entire hand before playing to trick 1). So easy to criticise, but I would not know where to start with the programming. Maybe Jack knows better.

GIB does not play like a human and it does not have a "plan". It does not use something like suitplay to solve a play problem.

GIB generates random deals that have the same cards in its own and and in dummy. It also places the played card into the unknown hands. The rest of the cards are dealt randomly (using information from the auction). GIB generates a number of such deals and solves each of them DD. After that GIB plays the card that is best in most of the deals. This is why GIBs play gets better the more cards are played. With less unknown cards and more information about the distribution, the pool of generated deals is closer to the real deal and with less cards involved the DD-Analysis is faster so that GIB can test more deals in the same amount of time.

To understand GIBs play you have to look at the pool of similar deals it generates.
In this case the pool must have had a hand with the 4th♦J in the South hand. Perhaps there was no hand generated where finessing the J failed because it was in the N hand.

From a strategy point of view GIBs weakness is the first 2 tricks.Especially if your side did not bid at all. The DD-Analysis for the first trick takes the longest time. Therefor the samplesize of the pool of generated deals is small. With little information available, this small sample could include deals that differ a lot from the actual deal.
GIBs play in the context of the actual deal could than seem strange.

[helene_t]

A human would think "6 ever 7 never" and go for the drop.

GIB starts by a small from his hand because DD that is winning regardless of whether it is going to finesse or drop. Then it sees that the 2 appears and now it simulates again. South's holding can be:

Finesse wins:
J982
J962
J862

Drop wins:
9862
982
962
92
862
82
62

Both win:
J92
J82
J62
J2

Both lose:
J9862
2

This is not quite accurate since with J9862 in South there is still a chance of a strip if South has ♣A sec. This requires GIB to play low from dummy rather than the 10, though. Probably there are some other minor inaccuracies.

GIB doesn't know restricted choice so it thinks all those holdings are appr equally likely (give or take an empty slots argument) which means that there are 3 cases in which the finese wins and 7 in which the drop wins.

For each sample size from 2 to 50 I simulated 1000 GIB deliberations based on the (crude) assumption that all 16 holdings are equally likely and that GIB will flip a coin in case of a tie. I found that the probability that GIB will finesse, as a function of sample size, is:

2: 32%
5: 22%
10: 13%
20: 6%
50: 0.5%
100: 0.0%

[1eyedjack]

My reading of Uday's post is that GIB behaves in a fundamentally different way in the first two tricks than it does in the tricks 3 and subsequent.

I am familiar with the principle of the way that GIB operates at tricks 1 and 2, and to frank until Uday posted here I assumed that this is how it behaved throughout. I expected it to be less accurate in the early game simply because the ratio of simulated permutations to the total population of possible permutations is much higher in the early game.
How GIB behaves different in the later stages is a mystery to me, but I just have to assume that it would consume excessive resources to apply those techniques at tricks 1 and 2. Perhaps this explains GIB's reluctance to lead an Ace against a grand slam at trick 1.

But this does not really invalidate my point or validate those of Hotshot. It does not HAVE to think like a human to develop "a plan". Running enough sims should provide the same conclusion. My "plan" came to mind after roughly 30 seconds to a minute of my sluggish human thought. In that time I have no idea how many simulations GIB could run but I would expect many thousand.And having simulated a possible distribution of the unseen cards, I would not expect it to identify the preferred line by reference to just one suit in isolation.

[Stephen Tu]

1eyedjack, on 2014-May-08, 04:42, said:

My reading of Uday's post is that GIB behaves in a fundamentally different way in the first two tricks than it does in the tricks 3 and subsequent.

I am familiar with the principle of the way that GIB operates at tricks 1 and 2, and to frank until Uday posted here I assumed that this is how it behaved throughout. I expected it to be less accurate in the early game simply because the ratio of simulated permutations to the total population of possible permutations is much higher in the early game.

This is only for the "advanced" GIBs as declarer (not defense); the basic GIBs are lobotomized. The advanced GIBs have the "GibSon" algorithm kicking in after a few tricks. This is a true single-dummy algorithm, much smarter. It kind of does "plan", it figures out it can make vs. such&such various suit splits and defenders holding certain cards. Avoids intrinsic double-dummy engine flaws like assuming that it will always be able to guess a two-way finesse (e.g. double dummy engine can't figure out that endplay works better than simply playing the suit & assuming it's going to guess right). It would be better of course if it just used this algorithm from the beginning, but at the time it was developed, it was just way too slow with 13 cards left. Don't know if this is still the case.

[1eyedjack]

In that case I remain somewhat in the dark concerning how it currently behaves at tricks 1 and 2. We are informed that it runs simulations. What use, then does it make of those simulations if not to form a plan?

uday, on 2014-May-07, 17:05, said:

The simpler one runs at trick one and trick two.

It simply deals sample hands consistent w/the auction & play and takes the play - at each trick - that worked best in its sample of hands.

How is this not making a plan?

[helene_t]

1eyedjack, on 2014-May-08, 11:47, said:

How is this not making a plan?

For example, in the OP hand, it starts with a small diamond from the hand because that is always right DD. Regardless of whether it needs to play the ten in dummy or not, playing low from the hand keeps the door open for the winning line.

This is not making a plan because it hasn't yet decided whether to play the ten or not. If it had already decided to play high in dummy, it might as well play the first trick from the dummy instead.

[FM75]

helene_t, on 2014-May-08, 02:55, said:

A human would think "6 ever 7 never" and go for the drop.

GIB starts by a small from his hand because DD that is winning regardless of whether it is going to finesse or drop. Then it sees that the 2 appears and now it simulates again. South's holding can among other holdings be:

Finesse wins:
J982
J962
J862

Drop wins:
9862
982
962
92
862
82
62

Both win:
J92
J82
J62
J2

Both lose:
J9862
2

This is not quite accurate since with J9862 in South there is still a chance of a strip if South has ♣A sec. This requires GIB to play low from dummy rather than the 10, though. Probably there are some other minor inaccuracies.

GIB doesn't know restricted choice so it thinks all those holdings are appr equally likely (give or take an empty slots argument) which means that there are 3 cases in which the finese wins and 7 in which the drop wins.

For each sample size from 2 to 50 I simulated 1000 GIB deliberations based on the (crude) assumption that all 16 holdings are equally likely and that GIB will flip a coin in case of a tie. I found that the probability that GIB will finesse, as a function of sample size, is:

2: 32%
5: 22%
10: 13%
20: 6%
50: 0.5%
100: 0.0%

First of all, I like your thinking. Just noticing this and posting it is pretty cool. If I could find a good bridge teacher, I would want one that forced me to think like this.

I am not sure, from what you have mentioned, what "sample size" has to do with this problem. But it seems to me that the only thing that matters is the diamond suit.

I am wondering if your analysis has ignored GIB's option of leading the ♦ 3 or 4. Does GIB, at trick two. have an intrafinesse (I just happened to be reading that section of Rodwell in the last 2 days) option up its sleeve in the trick 1/2 version. Does GIB's analysis in this version consider whether South covers a 7 with a missing intermediate card in some of those holdings? Opponents have 3 cards that beat the 7, and 4 that beat a small diamond. Is there a bug, in its trick 1/2 version?

Finally, I think that your analysis is based on the 16 distributions to be of equal probability, when they are not. I regret that I do not have an answer, only further questions.

[hotShot]

FM75, on 2014-May-08, 16:48, said:

I am not sure, from what you have mentioned, what "sample size" has to do with this problem. But it seems to me that the only thing that matters is the diamond suit.

If GIB would know all 4 hands, it could do a Double-Dummy-Analysis and play perfectly. This is not the desired behavior, so GIB only knows his own hand, the played cards, the bidding and the cards in dummy.
All GIB can do is Double-Dummy-Analysis, so it needs a deal to analyze. So GIB generates a random deal that has the same properties than the actual deal. The random deal can be close to the real board but it could also be to far away from the real thing.
This is where the sample size comes into play. Instead of looking at one random deal, it generates and analyses "sample size" many deals playing the card that is best in most of them.

In this deals if the sample size is 2, GIB analyses 2 random deals.
For the first card played in trick 2:
If N has the ♦ J in both of these 2 deals, GIB will start trick 2 assuming the finesse fails.
If N has the ♦ J in one of these 2 deals, the finesse will be less attractive to GIB
If the ♦J is with S in both samples (and S has 4♦) GIB will go for the option finesse.

Note that even if GIB has lead a card to trick 2, it does not yet know what it will do when it's dummy's turn. But of cause the played card influences the options GIB has when it's dummy's turn.

When GIB is about to play the 3rd card to trick 2, it generates and analyses 2 new random deals, because now GIB knows that the S hand had the ♦2.
If N has the ♦ J in both of these 2 deals, GIB will have to play for the drop..
If N has the ♦ J in one of these 2 deals, GIB will see a draw between drop and finesse and will randomly pick one of the options.
If the ♦J is with S in both samples (and S has 4[DI), GIB will play the 10.


So if you look at helene_t's statistic on the sample size, you realize that with more deals in the sample, the finesse gets less attractive.
The reason for that is that with the bigger sample the finesse often fails and since the 3-2 split has 68% and the 4-1 split only 28%. playing for the drop has the better chances.

Given a sample size big enough, GIB might even discover that playing the [DI]A first is a good idea.

[lycier]

lycier, on 2014-May-10, 18:25, said:

---

Ruffing ♦5 is unnecessary since Gib N know exactly Gib W have ♣K

Can you tell me this play is lucky or wise?

Who can tell me this is not X-ray vision?

[uday]

Back to the original hand ( sorry, Lycier )


Helene sort of had it right.

Summary: Sample size effectively too small, increasing the odds than an inferior play ( the DT in this case ) is chosen

Details:

( this is the first engine, the one that runs at trick1 and trick2 and occasionally later. This is the only engine used in the basic bot ).

Gib generates 25 deals that it believes match the auction & play to date. This is the "sample"

For each of these hands, gib looks at all the legal plays. In our case, the DQ, the DT, the D5. It matchpoints the double dummy result achieved by playing each card against the results achieved by the other cards.

Then it plays the card with the best average matchpoint score, resolving ties in favour of the lower ranking card ( and some other minor things like "is this the correct signal" in some cases )

This is all fine and dandy, but the smaller the sample set, the more likely it is to go wrong.

What I observed is that over tens of thousands of iterations of the same hand with different random number seeds, different random number generators (gib's built in one, the system one, and "deal" ) , the results were very similar.

Over 1000 hands , for instance:

Using 10 deals in the sample, it plays the Ten 27% of the time.
Using 16 deals in the sample, it plays the Ten 20% of the time.
Using 25 deals in the sample, it plays the Ten 10% of the time.
Using 50 deals in the sample, it plays the Ten 4% of the time.
Using 100 deals in the sample it plays the Ten .02% of the time.
Using 200 deals in the sample it did not play the Ten



We believe strongly that what's happening is this - too many of the 25 deals "don't matter" ( Ten and Q achieve the same outcome ) so that the remaining deals , where the T or the Q are required , are the only ones that count.

So the sample size of 25 becomes an effective sample size that is far smaller, about half the size (?) and thus the volatility increases, and the Ten is played more often than we like.


For the next version of GIB I'm probably going to increase the sample size, either by brute force to tell it to use more deals, or find a way to discard the "neutral deals" and generate more.

[shyams]

My upvote for uday's post. Your explanation helps a lot in understanding why gib does some strange things

uday, on 2014-May-13, 09:42, said:

For the next version of GIB I'm probably going to increase the sample size, either by brute force to tell it to use more deals, or find a way to discard the "neutral deals" and generate more.

Yes please! I'd really like to see this happen.

[uday]

People were asking about the second engine.


0. Advanced bot only. The basic one doesn't have the resources to be as good as the advanced one.

1. It is slow, and more so when there are more cards outstanding. I'm fiddling with allowing it to start a trick earlier but it might not work out ( might be too slow ). So far, it seems slow but not painfully slow.



Both engines use the same sample (of deals) : The author's explanation is below.



"

DD (engine 1) uses search to figure out an optimal line of play in a single hand.

SD (Gibson) is more complicated. It is actually trying to figure out "what to play for". Say that something you might play for (e.g., hearts 3-3) is an "assumption". Now SD is actually searching in *assumption space*. Assumption space is enormous, and you can't search all of it. So I'll leave out the tricks SD uses to figure out what assumptions to try. But the set of assumptions is based in the (usual) sample. So if N always has the CK, that will be an assumption but it's free (because it's true in every sample).

Now SD can distinguish between three types of assumptions: assumptions that are *optimal* in that playing for them scores more than playing for any other assumption, assumptions that are *perfect*, in that they meet the goal on every hand in the sample, and assumptions that are *guaranteed*, in that they involve no assumptions other than proven ones (e.g., N has shown out of clubs, so he has none). If you run GIBson in par mode, you'll see the "perfect" and "guaranteed" words floating by.

After the SD analysis finds what it believes to be the optimal assumption A, it checks to see if it's perfect. But then it does what might be called "hill climbing". It tries removing each assumption in A and seeing if it can still do as well (perhaps by modifying the line of play, perhaps not). That may give it a better line of play (i.e., weaker assumption) even if the difference never shows up in the sample. And if gives it a guaranteed line of play, it can claim.

"


Each card in DD is played with a fresh set of deals. So it is possible but rare for it to refuse to repeat a hook, say. So it is capable of playing for this on one trick and that on another trick. It does not filter for the fact that opps are not idiots.

GIBson decides what to play for and sticks with it, so it won't make this mistake.

also,

"
The way GIB works is that it decides "what to play for". Now as play proceeds, it can occasionally change the line if that allows it to play for *more* things, but not if that allows it to play for *different* things. That's because otherwise, it would fall for the old trick of allowing an entry to an entryless dummy so that declarer can take a losing finesse.

There is one exception. If the distribution or other stuff changes so that the original sample it used to decide what to play for is largely impossible, then (and only then) it recomputes. But it doesn't recompute from the point at which it currently finds itself (again, to avoid being fooled by being dumped in dummy). It recomputes from the *first* point at which it decided what to play for, figuring that it's ok to change its mind there, because the opponents won't have had a chance to confuse it.
"

I love discussing the internals of GIB. Simply muttering the word "GIB" is enough to make the wife back away slowly.

[1eyedjack]

This is (for me) fascinating stuff. I used to discuss with colleagues the benefits and flaws in an iterative approach to bidding system design: You make marginal variations to system and if they turn out to be an improvement you discard the inferior method, and then proceed with further marginal variations (to the revised method) until you come to a point when no marginal variation gives rise to an improvement. Like a man climbing Rum Doodle in a fog, you can cast your foot around to find out which way is "up" and follow that trail until there is no "up" option.

The problem with this approach is that the "peak" thereby achieved may be just a local peak in a mountain range where other peaks are higher (as indeed was the case in The Ascent of Rum Doodle), but you cannot see that unless your variation to be tested is so great that you effectively hop to a new mountain. The technique is not entirely futile because at least you can justifiably dismiss any method that is not a local peak in favour of one that is.

I expect that this is boring and trivial to those who actually studied game theory academically, unlike me who worked this out from scratch. What brought this to the fore in my mind is that it the same principles may apply not only to bidding system design but also to SD card play analysis.