Silly question about randomizing

[Fluffy]

I always read some hands where top players are at defence and they are told to randomice their cards enough so no info is revealed.

 

I sadly play against too bad opposition and my randomizing is very weak to say the least.

 

 

But lets talk about a simple example:

 

[hv=n=sk1087&w=sqj&e=s32&s=sa9654]399|300|[/hv]

 

north plays the king, and if EW randmice enough he will have 2/3 finesing and 1/3 playing for the drop. EW will take 1/3 tricks every time a honnor drops behind.

 

 

now lets say we never randomice anything. And we play alwasy the lowest spot.

 

Now declarer knows that when the queen falls, he is 100% for a finese, but when the jack falls he is 50-50. We will again score exactly 1 trick for each 3.

 

 

Seems like randomicing doesn't give you any trick here.

[Jlall]

If you always play your lowest card, declarer picks up stiff Q, and QJ doubleton. This is better than picking up stiff Q and stiff J, so declarer has gained an edge.

[lmilne]

In the example you give, after West plays the Queen and East plays a small card followed by another small card, the a priori odds are 12 to 11 on West having the Jack. But there are two causes for West playing the Queen: either he has the Queen only and was forced to play it, or he chose to play it from Queen-Jack.

 

If West plays randomly, the 12 times he has QJ have to be reduced by half, making the odds 11-6 on finessing. So, if declarer always finesses in the situation (with the position of the final card unknown), he will win 22 times out of 34.

 

If you always knew what card West would play from QJ tight, you would be able to do a tiny bit better. The ratio of QJ to Q to J is 12-11-11 (those are the a priori probabilities from division of a 9-card suit). So QJ is a tiny bit more likely than stiff Q or stiff J, but (stiff Q or J) is almost twice as likely as QJ.

 

If you know what card West plays from QJ, you can discard that holding 11 out of 34 times (when he plays the other honor). If you finesse whenever e.g. the Jack appears, you will win 11 out of 34 times as just stated. Then, if you play for the drop whenever West plays the Queen, you win another 12 out of 34 times. Your success rate goes up to 23/34.

 

So, it only goes up 1/34. In practice, your opponents only have to play the other card 1 out of 6 to make your guessing worse than always finessing. So you should always finesse (and you can presumably get away without falsecard or always falsecarding).

[lmilne]

If you always play your lowest card, declarer picks up stiff Q, and QJ doubleton. This is better than picking up stiff Q and stiff J, so declarer has gained an edge.

Damn, I was gonna type just this, but I got carried away :P .

 

And the reason why picking up QJ doubleton is better than picking up stiff Jack is just vacant spaces or whatever its called.

[Jlall]

And the reason why picking up QJ doubleton is better than picking up stiff Jack is just vacant spaces or whatever its called.

Yeah I mean an easy rule for everyone for all of these situations is that a more even combination is always more likely than an uneven one.

 

Eg one 3-3 combo is more likely than one 4-2 combo, and in this case one 2-2 combo (QJ) is more likely than 1 3-1 combo (stiff J).

 

But of course you're right about the reason that this is true.

[Finch]

Here's another example that I think makes the point well. I played a match recently where both tables got to 6D after East had opened a vulnerable 3H and West raised to 4H (I may have the non-club honours slightly wrong between the hands. I only mention this becase I think we were on vugraph so someone keen might recognise the hand):

 

KJx

x

AQxx

KJ973

 

 

Q10x

Ax

KJxxx

A52

 

Assuming hearts are 3=7 you discover in due course that East's original shape is 2=7=2=2. You now need to play the clubs for 3 tricks. It's obvious to your opponents from trick 2 that this is what the hand is about (the defence started ace of spades, spade which RHO didn't ruff).

 

You cash the ace of clubs at some point.

Finally you lead a low one towards dummy and LHO plays another low one.

If Oppo always play their clubs strictly upwards, then whenever RHO plays the 10 on the first round you can drop Q10 doubleton offside with 100% certainty. You are obviously better off than when they play their cards at random.

 

At the table the 10 appeared on the first round, from Nick Sandqvist against me, and from either gnasher or catch22 at the other table, and both declarers finessed for a flat board in one off.

 

You can analyse this is more detail if you like:

 

Consider two scenarios:

1. Opponents play their non-queen clubs at random.

It is the same 3:2 in favour of the finesse that it always was. Nothing has changed.

 

2. Both opponents play their clubs strictly upwards, lowest first.

i) If RHO played the 10 on the first round, you drop Q10 offside.

ii) If LHO plays the 10 on the second round, you finesse with 100% certainty

iii)If the 10 has not appeared after two cards from LHO and 1 card from RHO, you are exactly 50:50

 

Now you are making 100% of the time LHO has

 

Q108

Q106

Q104

864

 

and 50% of the time LHO has

Q86

Q84

Q64

1086

1084

1064

 

or 7/10 of the time. THis is a full 10% better than your 60% chance when they play pips at random.

 

For any deterministic play of the cards you can show you must be better off.

[Fluffy]

Thx for the replies.

 

So if I understand this correctly the first example randomizing gives you an extra 1/34 of a trick, and on the second (more kind of cooked) it gives around +10%.

 

IMO I have more important areas to improve, but I will try to pay more attention in the future.

 

 

 

Also from frances example: I think you don't need to randomice as long as you fool declarer into thinking you can randomice :P.

[Finch]

My example wasn't "cooked" it came up at the table.

 

I have seen more than one vul game swing against poor players by assuming they always play their pips upwards. It is honestly quite a big deal: you effectively give declarer free "restricted choice" information every time they have a guess if you don't play at random.

[EricK]

You don't actually have to randomize as long as declarer believes you randomize. If they believe you randomize they will always take the finesse in restricted choice situations.

 

Note also that if declarer doesn't believe you randomize and you have a good idea how they think you differ from truly random then you can gain an edge by differing from random in a different way.

[Fluffy]

sorry, I didn't mean cooked, but with "kind of cooked" I meant the example wich you just remembered wich made the biggest difference. Wich makes me beleive more critical examples won't make it up to 15% difference.

 

 

I might regret from stating this publically :P, but my point is.... if you suspect I might randomice because I am not so poor (wich I indeed are), then those percentages drop dramatically to a point where trying to wieight all to take advantage of it its just not worth the effort (IMO).

[gnasher]

Also from frances example: I think you don't need to randomice as long as you fool declarer into thinking you can randomice :D.

I think that most of us are sometimes saved from embarrassment by this factor, and also by declarer's fear of looking foolish.

[Jlall]

I will say if you actually know the suit is 3-2 and you don't play for the drop when they drop the ten on the right, you're making a huge mistake against most people imo. Of course against Gnasher or Sandqvist you should hook though.

 

Edit: There was a hand in the vanderbilt where I had AJxx opp KTxx, so I led low to the king, and RHO dropped the 9. Then I led the ten, and LHO played the 8. So I LOLed and played the ace dropping the queen. Because people, even "experts," play nowhere close to randomly, I was able to drop Qx in this specific scenario. If you don't believe that playing somewhat randomly matters, you are really wrong.

[Mbodell]

One of my partners doesn't sort his cards and then in situations where he needs to randomize just plays the left most card in his hand. If you do something like this (especially if you shuffle your cards before looking at them), you will play randomly well enough to stop most declarers.

[bluecalm]

Edit: There was a hand in the vanderbilt where I had AJxx opp KTxx, so I led low to the king, and RHO dropped the 9. Then I led the ten, and LHO played the 8. So I LOLed and played the ace dropping the queen. Because people, even "experts," play nowhere close to randomly, I was able to drop Qx in this specific scenario. If you don't believe that playing somewhat randomly matters, you are really wrong.

 

Interesting variation of this is playing against "tricky experts" who always try to fool you (especially if they don't know you or think you are weak or just can't restrain themselves). For example if you have :

 

AJ32 to K954

 

if you play the king and and 4 and N played say a 7 and S 6 and 8 you now play for the drop. That's because "tricky expert" would always play the T if he had one sitting on N so if T didn't appear it is with S.

[dburn]

Worth another look, that combination:

 

AJ32

 

K954

 

If, needing four tricks, you play the king, you have already blundered. If, needing three tricks, you play the king, you have also already blundered. If, needing two tricks, you play the king, this is not necessarily a blunder, although given your previous record no one would be particularly surprised to see you overtake it with the ace.

[rogerclee]

If, needing two tricks, you play the king, this is not necessarily a blunder, although given your previous record no one would be particularly surprised to see you overtake it with the ace.

The two tricks are still there, actually.

[bluecalm]

Worth another look, that combination:

 

AJ32

 

K954

 

If, needing four tricks, you play the king, you have already blundered. If, needing three tricks, you play the king, you have also already blundered. If, needing two tricks, you play the king, this is not necessarily a blunder, although given your previous record no one would be particularly surprised to see you overtake it with the ace.

 

Interesting. When needing 3 tricks I can see that playing A and low to the 9 is 100% line, but I don't see why playing a king when 4 tricks are needed is a blunder.

[Cascade]

Worth another look, that combination:

 

AJ32

 

K954

 

If, needing four tricks, you play the king, you have already blundered. If, needing three tricks, you play the king, you have also already blundered. If, needing two tricks, you play the king, this is not necessarily a blunder, although given your previous record no one would be particularly surprised to see you overtake it with the ace.

lol

[rogerclee]

Worth another look, that combination:

 

AJ32

 

K954

 

If, needing four tricks, you play the king, you have already blundered. If, needing three tricks, you play the king, you have also already blundered. If, needing two tricks, you play the king, this is not necessarily a blunder, although given your previous record no one would be particularly surprised to see you overtake it with the ace.

 

Interesting. When needing 3 tricks I can see that playing A and low to the 9 is 100% line, but I don't see why playing a king when 4 tricks are needed is a blunder.

You can pick up singleton queen in one of the directions, but it's not the direction you're thinking.

[bluecalm]

nvm, right; playing small to the jack is right; I have a lot to learn :)

I wonder how bad they need to be at randomizing to make playing the K more profitable than picking Q - xxxx

[dburn]

Worth another look, that combination:

 

AJ32

 

K954

 

If, needing four tricks, you play the king, you have already blundered. If, needing three tricks, you play the king, you have also already blundered. If, needing two tricks, you play the king, this is not necessarily a blunder, although given your previous record no one would be particularly surprised to see you overtake it with the ace.

 

Interesting. When needing 3 tricks I can see that playing A and low to the 9 is 100% line, but I don't see why playing a king when 4 tricks are needed is a blunder.

The king is a common - probably the most common - of what is called a "danger play"; it guards against making the contract when West has the singleton queen. Since this is the only 4-1 break against which you can take four tricks, correct is low to the jack.

[gnasher]

I will say if you actually know the suit is 3-2 and you don't play for the drop when they drop the ten on the right, you're making a huge mistake against most people imo. Of course against Gnasher or Sandqvist you should hook though.

That's a flattering comparison, but I'm not sure that you're right. It's a lot easier to be a good player on the BBO forums than in real life.

 

I was, in fact, West, and I'm fairly sure I played my clubs in ascending order. It's almost as important for West to randomise with xxx as it is for East to randomise with 10x. OK, this might have been the 1/3 of the time that I should play the lowest two, but I'm sure that in practice I do it more often than that.

 

I think David Burn had my cards at the other table. It would be interesting to know whether he remembered to plays his clubs in a random order.

[lmilne]

I notice that I randomize whenever it's costless, but when there's some risk that partner might play me to be making some obtuse signal, I normally just play up the line. Most people I play most of the time aren't watching anyway :)

[dburn]

I will say if you actually know the suit is 3-2 and you don't play for the drop when they drop the ten on the right, you're making a huge mistake against most people imo. Of course against Gnasher or Sandqvist you should hook though.

That's a flattering comparison, but I'm not sure that you're right. It's a lot easier to be a good player on the BBO forums than in real life.

 

I was, in fact, West, and I'm fairly sure I played my clubs in ascending order. It's almost as important for West to randomise with xxx as it is for East to randomise with 10x. OK, this might have been the 1/3 of the time that I should play the lowest two, but I'm sure that in practice I do it more often than that.

 

I think David Burn had my cards at the other table. It would be interesting to know whether he remembered to plays his clubs in a random order.

I have some vague recollection of the deal, but to be honest I do not remember whether I was the player with three low clubs or the player with ♣Q10. I do remember thinking at some early stage in the play that declarer would take the club finesse and go down, but I do not remember any specific attempts to avoid dissuading him from this course.

 

I am not sure, though, to what extent it is possible to "remember" to do something in random fashion. Human beings are particularly bad random number generators - if you ask someone to pick a number "at random" between one and ten, you will get the answer "seven" far more often than 10% of the time. If you find yourself in a position where you need to do (or appear to do) something "at random" and try to think consciously about how to do it, the chances are that you will fail.

 

I do have a habit of trying to work out early in the course of a defence whether I will actually need to play equals in some random order; if so, I will use some external aid such as the vulnerability on a board - NV I will play low from QJ, VUL I will play high. I recall once having to play from J109 when declarer held Axx and dummy KQ8x. Since there are six orders in which one can play those cards, I took the board number modulo 6 and selected what turned out to be the order 10-9-J. That jack fell under dummy's queen, of course, and declarer said "I knew you were trying to fool me by petering with 10-9 to show a doubleton".

[Little Kid]

"I knew you were trying to fool me by petering with 10-9 to show a doubleton".

LOL