Bots, bot standard, pick-up games, etc

[kenberg]

Lately I have been playing some with the bots. For 25 cents you play 8 hands with the stronger bots.  As best I recall, I have not yet had a bidding misunderstanding with them. They don't declare, if our side wins the auction I then play the hand, switching seats if need be. I gather that I am always seated so as to have the best hand so we declare more often than we defend, but we sometimes defend.

Much to my surprise, I have no complaints about the bots. I would not say the same for the bots that are free on the first of the month, and cheap for monthly renatl. But the upscale bots seem pretty good. Somewhere between most and all of the bad results have been due to me, not my tin head partner. I will illustrate this below.

All this leads to a thought: When playing pick-up on IAC why not use the bot convention card? We don't usually have time to discuss a lot, so why not bot standard? The cc does not cover everything, of course not. I give  an example below of a bid maybe not on the cc, but it would take care of a lot. And when things go off the rails, there would be a common starting point for discussion.

OK, now some hands.

Matchpoints:
http://tinyurl.com/ybnpafah

At the conclusion of the auction I was switched to North to declare the hand.

Was it crazy to take the first diamond trick? Maybe, it certainly did not work out well. But if the Q is on my right [which it probably is not, given the play of the King] it is safe to do so, and if the Q is on my left it will be best to take the A whenever the A is also on my left. So the issue is not where the Q is, the issue is where the A is.  Anyway, I took the A and led a club. Down  1 for 38.2%.  Oops.


Another hand, this time with a better result:

http://tinyurl.com/ybpu9xdn

Both the auction and the play matter here. I opened 1 in 4th position. Partner bid a drury 2C. We are of course going to play in at least 4 but I saw no point in going there directly. I bid 2 showing a full opener and partner bid 2 showing spades. That didn't sound so great to me so I settled for 4 .  Some pairs were in 6 . There is no play for this, but that is not the bot's fault.

The opening lead is the J ducked, and a is continued. Ten tricks seem likely but this is matchpoints. Is there a play for 11 tricks? I think so. If clubs are 4-3 and hearts 3-2 this should come in. Making 5 was worth 82.8%.  Again, those who are in 6 off 1, and those in 4 making only ten tricks, should not complain about the bots. [Added: It's true that if pard had the K instead of the !d Q I have a decent but not certain play for 6. There is no certainty in bridge.]

Now an example of a bidding gadget from a bot. imps this time.

http://tinyurl.com/yb455pl8

1 on my right, I overcall 1 , X on my left and partner now bids 3 . The bots explain their bids and this was a mixed raise. I am not sure that you find this on their cc, but it was explained and it was just what I needed to bid 4 . Is it a sure thing on the auction so far? Hardly. That doubleton heart was a life-saver. But I thought it a good bet so I went with it.

Back to my general view of the bots. I see a lot of criticism of the bots. Being bots, I assume they do not take offense. But I have been pretty happy with the advanced ones.  Other people also play with the bots, so using the bot cc as a default when playing pick-up might be an easy way to cope, ok to partially cope,  with the "How do you play that, pard?" problem. Just a thought.

[OliverC]

Hand 1: This seems like a difficult question, but in reality I don't think it is:


Pre-supposing that you're ultimately going to make 3 Club tricks...

• Winning trick 1 works any times when East has the Ace of Clubs (50%) or when the Diamonds are no worse than 5-3 (80%) whoever has the Ace of Clubs.
• Ducking trick 1 only wins over winning trick 1 when the Diamonds are 6-2 exactly (17%) and West has the Ace of Clubs, which comes out at an 8.5% chance (50% of 17%). Ducking loses only the 8.5% of the time when the Diamonds are 6-2 and East has the Ace of Clubs

If the Diamonds are 5-3 or 4-4 it really doesn't matter (Because Opps are only ever going to get 4 Diamonds and the Ace of Clubs). If Diamonds are 7-1 it doesn't matter what you do, because West can never continue Diamonds. So it only matters what you do the 17% of the time when East has exactly Q109xxx in Diamonds, and West has the Ace of Clubs, so you're down to whether you play for that 8.5% chance or the 80% chance of the Diamonds being 4-4 or 5-3.

At Matchpoints I think I have to play for the 88.5% because I have more of a chance for an overtrick, but at IMPs I feel I have to play safe by catering for that 8.5% chance, because you're also only going to lose out 8.5% of the time when the Diamonds are exactly 6-2 and East has the Ace of Clubs. At IMPs the overtrick(s) are largely irrelevant, but at MPs, the 50% chance of an extra trick by winning trick 1 is worth the risk.

[kenberg]

There are a couple of features of probability worth commenting on here. That 17% probability of a 6-2 split is for a 6-2 split one way or the other, The probability that E has 6 and W has 2 is half that. Perhaps mote important, these are a priori probabilities.  For a simple exammple, suppose an a different hand  auction goes 1NT-3NT. The opening lead is a J. The a priori probability that that hand hold the ten is 50%. After the elad of the J you and everyone else would regard the probability as approximately 100%.
On this hand the opening lead is the Ten and  produces the K. It is highly unlikely W falsecarded so E has the Q, People, and bots, don't usually lead the T from QT unless theya lso have the 9 And probably not simply the 3 card holding QT9. So we can reasonably assume Ehas at least four diamonds headed by the QT9. This considerably ups the probability that he holds six card in the suit.

My guess is that the conditional probability of a six card suit given that he holds at leas four cards headed by the QT9 is somewhere around one-third. That's just a guess, I have to run but I may calculate it out later. 

The important ting is that we should not just go be the 17%, or by half the 17%.


Added: I like to try to think these things through afterward to see if I had a reasonable plan that failed or if I should have acted otherwise. IN this case I have come to think I should have ducked. Going up with the A could have been right, I don't think it was crazy, but on balance I think ducking is more likely to be the winning play.

[kenberg]

I did a quick calculation that I have not checked carefully, and got 32% for the conditional probability of a six card holding given that E holds at least four diamonds headed by the QT9. I am a little surprised because as I was driving I was thinking that my 1/3 estimate was high, that it should be more like 28% or so. Anyway, even if  32% is not quite right it should be something like that.

My mistake, playing the hand, was thinking "Oh, he led a diamond, well, the probability of him having 6 of them is small I am not going to worry about that". But he didn't just "lead a diamond" he let specifically the T of diamonds and W produced the K, making it highly likely that E held the QT9 and others.  This matters, and you do not really need any mathematical training to think about why. We have placed four of the cards, the K,Q,T,9. There are four spots left and they can be anywhere, except that we assume at least one is with E since a lead from QT9 tight seems unlikely. So E has 1,2,3 or 4 spots with 2 presumably the most likely. So I think 5 cards is the most likely, but 6 fairly likely. Certainly a big enough chance that it should be given serious consideration.

When E holds 6 diamonds and W 2, the chances are better than 50% that W holds the A. So ducking the first is looking good.



But back to my original post for a moment: Right or wrong, putting up the A was my choice. I have so far been seeing an advanced bot as a pretty decent partner. So maybe using bot standard in pick-ups would be good.

[kenberg]

Probability arises from time to time and I have said a few words. Perhaps the most important thing is that applying it is not easy. The a priori probabilities, meaning the probability of an EW distribution based just on looking at the NS cards before anyone does anything, can generally be found in tables. This can help, but caution is required. In the case at hand, I am assuming that the lead of the T by E and the subsequent play of the K by W locates not only the K and the T but also the Q and the 9.  This seems reasonable, at least to me, but it depends on assumptions. If we really want to get into it, we also have to think about what an opponent would do if he held QT9x in diamonds and JT9x in hearts. I would probably lead the J. This affects the inferences that can be made when I lead the T.

What we are after is an estimate of the chances that E has six diamonds given that he led the T and W played the K.  This cannot be separated from the question of under what circumstance would E lead the T, and when would he lead something else.  As mentioned, the Bridge Encyclopedia lists probabilities of success of various lines  for developing a suit. They frequently comment on adjustments that must be made depending on your assessment of your opponent's abilities ot tendencies. And that's just for the suit layout. When we consider the hand as a whole, far more of this comes into play.

The Wikipedia article on bridge probabilities includes Théorie Mathématique du Bridge  by Emile Borel as  a reference. I have never read it.
 Borel was a major mathematician, see https://en.wikipedia.org/wiki/%C3%89mile_Borel  .  And he may well have been a fine bridge player, I don't know.  But the math only takes us so far.

[OliverC]

You don't need to be fixated on the 6-2 split, Ken, but it's the only split that gives you a potential problem, so it's the only one you need to cater for at IMP scoring (when it's not worth taking the risk). If the Diamonds are 5-3 or 4-4, Opps are only going to win 4 or 3 Diamonds respectively and that plus the Ace of Clubs is only 5 or 4 tricks for the defence, if you can garner 3 Club tricks.

If Opps are playing strong 10's then the lead of the 10 from Q109xx(x) and the play of the King by Partner is completely to be expected, whatever the distribution of the suit.

[kenberg]

Agreed. The T  could be from QT9x or QT9xx or QT9xxx or even QT9xxxx.

The problem is what to do about it. At least at imps, we need only worry about the QT9xxx,  assuming we can bring in the clubs for three tricks.


So what to do?


If E holds QT9xxx and the A we make the contract if we go up with the A at T1 and we go down if we duck since W witll lead back his last establishing the suit.
If E holds QT9xxx and W holds the A we make the contract if we duck at T1 and we go down, as I did, if we take the A.

At imps, I think it is clear to duck. As you say, we are only worried about the case where  E led from QT9xxx. And in that case, with splitting 6-2, the odds favor any specific non-diamond lying with W.  W has 11 empty spaces, E has 5.

Now at mps:  I was careless, that's what it comes down to. I figured that usually E will not have 6 and maybe I can negotiate an overtrick if I just take the at T1. 

That might have been a good idea, at mps,  on some diamond leads, a low spot for example. We cannot really say "Oh, E led a spot so that ups the probability he has the A. He had to lead something.   But the lead of the T, with W producing the K, very substantially increases the likelihood  of a 6-2 split. Matchpoints or not, my first obligation is to make my contract. There can be exceptions to that when I am in some weird contract, but this is a normal contract, making it should be a normal score and often odd things happen at the other tables so it becomes a normal+ score.

So I assign the blame to me on this one. I'm not into doing penance or anything like that, I just like to look at a hand thinking whether I would do the same thing again next time hoping for better luck, or whether I would go the other way. Here I would duck next time, right or wrong, imps or mps.


In a hand that I played yesterday I think my bot could have done better. In  one today where I am still thinking about it, and there was another today where the result was just odd. They are from the day long robot tourneys so I cannot see the hand records yet for today, but I will probably post them, or one ore two of them, later.