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Game theory -- game invitation and acceptance small abstract game.

#1 User is offline   benlessard 

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Posted 2013-November-05, 08:41

1S---3C (some sort of bergen raise)

Here im making a small game where

0- no interest in game
1- small interest
2- medium interest
3- big interest.

each player have a 0-3 number and if the total of both players is 4 or more you want to be in 4S while with 0-3 you want to be in 3S.



3---------4----4----4

2--------------4----4

1-------------------4

0--------------------

-----0----1----2----3

What should be the meaning of each bid ??

I suggest you to think about it a little before reading on.








All the solutions have one thing in common is that 3D should be used twice as often than 3H.

solution one is a fast arrival. Declarer sign off with 0, bid 3H with a small 1 and bid 3D with 2or3. Over 3D responder bid 3H with a 1.

3S = 0
3H = 1
3D = 2 or 3

3D-3H = responder is showing 1.

all number are permutable and you can do any solutions as long as 3D has a double meaning.

3S=3
3H=2
3D=1 or 0.
or
3S=2
3H=1
3D=0or3

3D-3H-3S equal the lowest of the 2 options in 3D.
3D-3H-4S mean that you are willing to play game even facing the lowest option.

Note that both opener and responder are able to split their hand in 4 ranges wich should lead to a good amount of precision. This is because there is four roads that lead to the 3S signoff.

3S
3H-3S
3D-3S
3D-3H-3S

So this equal 4 ranges.

What if you have H instead ??

1H--- (3C bergen)


Now there is only 2 road to sign off to 3H, this mean that responder will only be able to split his hand in 2 ranges (0,1) and Idem for opener.

1-------2

0--------

----0---1

The best you can do is ask for extras and responder will accept with the 50% top of his range.

One important caveat is that we are talking about game tries that doesnt raise you a level so these game tries have low cost. Game tries after 1S--2S are a different story because 3S might go down while 2S was making.

IMO the practical application of this is that some hands around 25 centile (slight invite,good minimum) deserve to make a gametry if there is a counter-game try available while without the counter game try available these are sign off. Same for big invite, some hand are clear acceptance after 1H--3C can afford to become invites after 1S--3C.

I didnt want to discuss about the merit of a 3H game try ask for help in H and pts location lead directing X etc ...

but im pretty sure that if you have 2 game try you should use the cheapeast game try twice as often as the most expensive game try.
From Psych "I mean, Gus and I never see eye-to-eye on work stuff.
For instance, he doesn't like being used as a human shield when we're being shot at.
I happen to think it's a very noble way to meet one's maker, especially for a guy like him.
Bottom line is we never let that difference of opinion interfere with anything."
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#2 User is offline   kenrexford 

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Posted 2013-November-05, 14:20

The same principle applies with Splinters, BTW, and gets even more interesting.

One under is a go-or-no-go.

Two under allows two options.

Three under allows four options. (decline, invite one under, invite two under and accept, invite two under and decline)

Four under (e.g., 1-P-3) allows seven options (decline, invite one under, invite two under and accept, invite two under and decline, invite three under and accept one under, invite three under and accept two under, or invite three under and offer after two under)
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#3 User is online   nige1 

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Posted 2013-November-05, 14:38

After 1, you can adopt a similar structure if your initial replies are:
  • 1 - 2 = Jacoby GF
  • 1 - 2N = Invitational 0-3 as above,

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#4 User is offline   dake50 

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Posted 2013-November-05, 16:36

Both 'game theory' and 'information theory' should be applied by system designers.
Both in the raw suggestion phase and in the critical stages.
I doubt the few mathematical minds capable of these applications would persuade the pedagogues.
"Listing is not analysis" -- my philosophy professor.
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#5 User is offline   mikeh 

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Posted 2013-November-05, 17:10

Frankly, I think you are wasting effort.

If opener has a '3', then in my opinion he bids game. Defence is the toughest part of play and opening lead the most random. When opener bids game with a hand that is possibly just a strong interest in game up to a hand just not quite interested in slam, and the opps are unable to tell which, then declarer gets an edge.

In addition, how hands mesh is far more important than whether they, in ignorance of partner's shape and location of hcp, have mild or medium or strong game interest.

Say my interest is because I hold a 5=3=4=1 with my minors as KJxx x. Give partner only one honour in the minors....say the Q. The diamond Q is huge...the club Q is waste paper.

My advice, if you are interested in game tries to this extent, is to consider something simple such as 1 33 natural gametry, 3 a game try that can't use 3.

This will allow responder to accept with diamond help, or to bid 3 with no help but good hearts (so opener can choose 3 if either red suit will be enough) and 3 with no help in either red suit (thus implying club help).

While far from perfect, because one has consumed valuable bidding space in obeisance to the LOTT, it seems to me to be far more practical than each partner doing this 0,1,2,3 arithmetic.

Simple metrics are very attractive to a certain type of player. I don't think many experts find them useful.
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#6 User is offline   PhilKing 

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Posted 2013-November-05, 17:30

If in doubt, just bid game. There is a cost in all these invitations:

1. It wastes time.

2. It allow lead directing doubles of the responses.

3. It gives the defence the knowledge that we have a marginal try.

4. You give up bids for game tries that could be used to investigate slam.

In the sequence given, you need at most one try (3), to which you have a yes/no response. 3 should be a slam try with generic responses not just invented for this specific spot.
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#7 User is offline   jogs 

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Posted 2013-November-06, 09:35

View Postmikeh, on 2013-November-05, 17:10, said:

Frankly, I think you are wasting effort.

If opener has a '3', then in my opinion he bids game. Defence is the toughest part of play and opening lead the most random. When opener bids game with a hand that is possibly just a strong interest in game up to a hand just not quite interested in slam, and the opps are unable to tell which, then declarer gets an edge.

In addition, how hands mesh is far more important than whether they, in ignorance of partner's shape and location of hcp, have mild or medium or strong game interest.



Subdividing your hand into 4 groups only assist opponents for their defense. Either bid game or not.

If you're really thinking of the best game theory response, consider stop playing Bergen raises. 4432 patterns are not worth pushing to the 3 level.
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#8 User is online   nige1 

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Posted 2013-November-06, 14:12

IMO benlessard's suggestion is more interesting than implied by comments so far. For example suppose your response structure to 1 is, say ...
  • 2N = Jacaoby GF
  • 3 = Pudding raise 4+ 0-11 HCP (i.e. wide range) classified as 0-4 = type 0, 5-7 = type 1, 8-9 = type 2, 10-11 = type 3. Freeing up other bids. Say ...
  • 3 = Shortage
  • 3 = Shortage
  • 3 = Shortage ()
  • and so on

Now after 1 - 3-; opener rebids, say ...

  • 3 = Invitational over type 2-3
  • 3 = Invitational over type 1
  • 3 = Not interested

Then after 1 - 3 -; 3 responder clarifies, say ...

  • 3 = Type 1
  • 3 = Type 0
  • More = Type 2-3

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#9 User is offline   mikeh 

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Posted 2013-November-06, 15:03

View Postnige1, on 2013-November-06, 14:12, said:

IMO benlesard's suggestion is more interesting than implied by comments so far. For example suppose your response structure to 1 is, say ...
[list][*]2N = Jacaoby GF[*]3 = Pudding raise 4+ 0-11 HCP (i.e. wide range)


You lost any interest I might have had with this start.

Why not just go play roulette? You seem to prefer games of chance.....raising to the 3 level on 0-11 is insane and unplayable.
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#10 User is offline   FrancesHinden 

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Posted 2013-November-06, 15:41

View Postmikeh, on 2013-November-06, 15:03, said:

You lost any interest I might have had with this start.

Why not just go play roulette? You seem to prefer games of chance.....raising to the 3 level on 0-11 is insane and unplayable.


I'm not saying I like his structure, but you don't seem to have understood the suggestion.
There are plenty of people currently you play 3C, 3D and 3 major as (in some order) pre-emptive, mixed and limit raises. That's basically 0-11 or so. Nige's idea is to put all of those into the 3c bid and allow opener to ask which partner has, thus freeing up the other 3-level responses for something else.
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#11 User is offline   benlessard 

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Posted 2013-November-06, 23:36

A more practical approach is on a 8+ Drury.

responder is a passed hand

1S-2S = 5 to a bad 7

1S-2C = good 7 to 11
??

2S = no interest.
2H = only if your in the 75-100% of your range.
2D = normal or heavy invite

2D-2H= im accepting a heavy invite but refusing a medium invite.
----------------------------------------------
Or over a strong club or setup is something like.



1C-1D-1NT = 17-18
1C-1D-1H-1S-1nt = 15-16
1C-1D-1H-1S- jumping =19-20


being able to stop at the 1 level when 19-20 vs 0-5 is pretty powerful. Same for staying at 1NT when 17-18 vs 6.

------------------------------------------------
In montreal what is popular is 3C is 7-11 (4 trumps), 3D is 3 card limit with some shape and 1NT semi-forcing.
From Psych "I mean, Gus and I never see eye-to-eye on work stuff.
For instance, he doesn't like being used as a human shield when we're being shot at.
I happen to think it's a very noble way to meet one's maker, especially for a guy like him.
Bottom line is we never let that difference of opinion interfere with anything."
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#12 User is offline   Fluffy 

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Posted 2013-November-08, 11:06

I consider this thing information theory, not game theory.

To mikeh:If opener has a 3 among the 4 ranges that invite he should not bid game, he should bid game when his hand is better, if you decide that what for me is a 3 its a game drive (I doubt), then you exclude the 3s and rearrange the 0-2 into a 0-3 range. Splitting into 4 ranges is for sure an overkill, but this is a theoric/hypotethical question anyway (I hope)
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#13 User is offline   benlessard 

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Posted 2013-November-08, 23:20

How about

1S--???

3S-- preemptive raise
3H -- mini splinter
3D -- mini splinter (counter game try available)
3C -- mini splinter or mixed raise or limit

You have 3 raise and 3 splinters


1S--3C

3S = not interested
3D = disapointed by stiff C. (return to 3S = stiff C, 3H = mixed raise, higher = big raise
3H = disapointed by mixed raise or I need a D stiff or big raise
From Psych "I mean, Gus and I never see eye-to-eye on work stuff.
For instance, he doesn't like being used as a human shield when we're being shot at.
I happen to think it's a very noble way to meet one's maker, especially for a guy like him.
Bottom line is we never let that difference of opinion interfere with anything."
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#14 User is offline   benlessard 

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Posted 2013-November-08, 23:54

You even have 5 mini splinters

Another way to see it

after 1S–3C

where 3 clubs show either

1-limit
2- 9-10 club stiff
3 7-8 club stiff
4 - mixed raise


If you need a limit you bid 3D
If you need a club stiff 9-10 or a limit you bid 3H
If you need a club stiff or a big raise you bid 3D
If you need a mixed raise and really hate the club stiff you bid 3D

Note that you are going to play game vs all limits.
From Psych "I mean, Gus and I never see eye-to-eye on work stuff.
For instance, he doesn't like being used as a human shield when we're being shot at.
I happen to think it's a very noble way to meet one's maker, especially for a guy like him.
Bottom line is we never let that difference of opinion interfere with anything."
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#15 User is offline   fromageGB 

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Posted 2013-November-13, 05:31

View Postnige1, on 2013-November-06, 14:12, said:

suppose your response structure to 1 is, say ...
..3 = Pudding raise 4+ 0-11 HCP (i.e. wide range) classified as 0-4 = type 0, 5-7 = type 1, 8-9 = type 2, 10-11 = type 3. Freeing up other bids.

I think this suffers from the serious problem that you have now allowed much more room for opponents to speak. 3 is hardly a preemptive raise when it cuts out nothing.

Good discussion, and I think I'll stick to my preemptive
1 :
3 = 7-10 ( asks for good/bad)
3 = 11/12
3 < 7

(@jogs I think 4432 should not be excluded. @PK I sympathise with your just one try, but I have found many games with 3, rather more frequently I suspect than you have found slams. If you are trying for slam, you have plenty of room above 3)
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#16 User is offline   jogs 

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Posted 2013-November-13, 18:06

View PostfromageGB, on 2013-November-13, 05:31, said:

(@jogs I think 4432 should not be excluded. @PK I sympathise with your just one try, but I have found many games with 3, rather more frequently I suspect than you have found slams. If you are trying for slam, you have plenty of room above 3)

There is a misconception that one can safely bid up the level of their combined trumps. LoTT protects them. The math doesn't support this. With a 5-4 fit and 20 HCP you need singletons(or voids) to be a favorite to make nine tricks.
My statement is more for avoiding negative part scores than finding slams.
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#17 User is offline   fromageGB 

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Posted 2013-November-14, 09:50

You could well be right, and then it is not worth bidding 3 in the absence of competition if you have a 7/8 count with no shortage. In that case, for a useful game invitation and acceptance, the 3-level bids could be showing the shortage with a 9/10 count, which you may call a mini-splinter, and there is also room to have 9+ with no shortage. As there is no room for everything, a 7/8 non-specified shortage can jump to 3 with a reasonable expectation of making.

Is the following simple "Bergen-replacement" playable?
1 ...
2NT = 13+, may include shortage to be shown later
4 new suit = 11/12 shortage
3 = 9-10 shortage in diamonds or hearts (3/ invites game with that shortage, but 3 = no interest)
3 = 9-12 no shortage (3 invites for 11/12)
3 = 9/10 club shortage
3 = 7/8 unspecified shortage (3NT asks for slam purposes)

I don't like actually bidding the shortage, as that encourages a cheap X to invite competition in the short suit.
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#18 User is offline   fromageGB 

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Posted 2013-November-14, 09:51

Deleted, response problems
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#19 User is offline   fromageGB 

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Posted 2013-November-14, 09:51

Deleted, response problems
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#20 User is offline   jogs 

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Posted 2013-November-14, 12:57

I like fit jump shifts. With a double fit and shortage, slams are often available with two minimum opening hands.

Axxx x xxx AKxxx

KQxxx Axx x Qxxx
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