[benlessard]

Here is a small abstract game that relate to the optimization of ranges for "passing,competing or bidding game" depending on the opening range.

I apologize in advance if you find this pointless and a waste of time. I know it wont be interesting for everybody.

1♠-(3♥)-???

You are lucky enough to have spades support for partner with no desire to play elsewhere than 3S/4S or defending against 3H. I am going to look at different type of ranges and try to optimize them. Im using the good old HCP as a baseline but IMO its irrelevant I could use any evaluation method and the overall idea will be the same.

I am using 24 pts as the break even case where being in game or not doesnt matter, with 25 you want to be in game, with 23 pts you dont want to be in game. To break ties ive considered that missing a 25 game is a slightly worse failure than going overboard with 23 pts. In didnt take into account the frequency of the hands like 13-12 is more frequent than 21-4. I didnt count the fact that being in game with 22 pts is a worse failure than being in game with 23 pts. I also didnt count the under competing (passing 3H but 3S would make) nor do the balancing auctions.

Ive done the optimization for you.

A) 11-21 standard, The best we can do is 9 failures.

The optimal strategy is is for responder to

pass = 0-5, 3S = 6-10, 4S =11+,
opener will raise 3S to 4S with 16-21.

One 26pts missed games; 21-5.
Two 25 missed game; 20-5,15-10

Six overboard. 11-11,11-12,12-11,16-6,16-7,17-6

A quick proof to show this is the optimal strategy,

if responder bid 3S with 5pts instead of passing you win 20-5,21-5 but you get overboard 18-5,17-5,16-5

if responder pass with 6pts instead of raising to 3S you dont get overboard with 17-6,16-6 but you miss 21-6,20-6,19-6)

if responder blast to game with 10+ he win find the 15-10 games but will go overboard 11-10,12-10,13-10

if responder doesnt blast with 11 he will avoid to go overboard 11-11,12-11 but he will miss 14-11,15-11.

if opener pass with 16 he avoid going overboard with 16-7,16-6 but hes missing 16-10,16-9

if opener raise with 15 he will find the 15-10 game but will go overboard too often.

The range somehow match my real life experience but I dont draw any conclusions here.


B) 11-17 (like Polish club) but its the same for 9-15 (agressive precision) where you are correcting (+2 pts) just to have the same baseline.

The best we can do is 3 failures. The optimal strategy is

pass = 0-7, 3S = 8-11, 4S = 12+, over responder 3S opener will raise to 4S with 15-17

Here you only miss 1 game (14-11) & go overboard twice 11-12 & 15-8.

Quick proof.

If responder pass with 8 you miss 17-8 but avoid 15-8

If responder blast with 11 you have 2 overboard 11-11 & 12-11 but you gain 14-11.

If responder doesnt blast with 12 you miss 13-12,14-12 but you avoid 11-12.

If opener doesnt raise with 15 you miss 15-10, 15-11 but you avoid 15-8

If opener raise with 14 you get 14-11 but go overboard with 14-9,14-8

3 failures is pretty good compared to 9 IMO.


IRL there is a cost of selling out to 3 hearts when responder got 6-7 and pass but 3S would have made.

Ive rarely played PC or agressive precision so I don't know if these range somewhat match real life bridge.



C) 11-14 or 18-21 a splitted range openings like in my system.

The best you can do is 4 failures with the following strategy

pass 0-4, 3S = 5-11, 4S = 12+. Over responder raise opener will pass with 11-14 and keep bidding with 18-21.

You miss 2 games 21-4 & 14-11.

You go overboard with 18-5 and 11-12.

Im sure you get the idea even without the "proof"

This somewhat match my real life bridge experience that you can bid a wide ranging 3S with 6-11.
Note that you are more agressive and are somewhat less likely to selling out to 3H however you may endup in many hopeless 3S (11-5)

What I find curious is that there is 4 failure for a range of 8 compared to 3 failure for a range of 7 and 9 failures for a range of 11.



11-21 = a 11 continous range = 9 failures

11-17 a 7 continous range = 3 failures

11-14 or 18-21 = 2 four range = 4 failures.

[benlessard]

D) 11-18 and 8 pts ranges like in my split range system.


The best we can do is 4 failures. The optimal strategy is

pass = 0-7, 3S = 8-11, 4S = 12+, over responder 3S opener will raise to 4S with 15-18

miss 2 games 18-7 & 14-11 & go overboard twice 11-12, 15-8.

Quick proof.

If responder pass with 8 you miss 18-8 17-8 but avoid 15-8

If responder bid with 7 you have 2 overboard 16-7 and 15-7 but you gain 18-7.

If responder doesnt blast with 12 you miss 13-12,14-12 but you avoid 11-12.

If opener doesnt raise with 15 you miss 15-10, 15-11 but you avoid 15-8

If opener raise with 14 you get 14-11 but go overboard with 14-9,14-8

so 4 failures.

[rbforster]

Interesting comparison of the different ranges. Obviously it's a toy model, but one thing to consider if you wanted to refine it would be the relative likelihoods of the different HCP splits as they are not all equally likely (so counting a 11-12 loss vs a 21-5 win shoudd be a net loss since even splits of HCPs are more likely all else being equal). I imagine this changes the boundaries in some edge cases, but not the qualitative picture you've outlined.

[yunling]

Sometimes opener can still act over 1♠-(3♥)-P-(P)-?, so responder don't need to stretch a lot to bid 3♠ here.
The disadvantage of standard is overestimated.

[awm]

I agree with yunling's post; normally opener will balance with 19-21 so you don't really need to account for this range in "standard" bidding.

It's also worth keeping in mind that it's possible to go for a number in 3♠ if holding (for example) 11 opposite 6 (I assume all your ranges are adjusted appropriately for shape). There may be losses even for stopping at the three-level with less than 19 or so, bad breaks and a penalty double both being possibilities on this sequence.

Yet another point is that not all the hcp values are equally likely, so "losing" on extreme cases like 18 opposite 7 is not nearly so bad as "losing" on cases like 14 opposite 11.

[benlessard]

Its something I started writing at 3h am so I didnt draw any serious conclusions (and it wasnt meant to draw serious conclusions).

Oviously the need to compete and the frequency should be counted.

The drawback of agressive ranges like agressive precision range like 9-15

the numbers are taken from 11-17 but adjusted

pass = 0-9, 3S = 10-13, 4S = 14+

but obviously passing with 8-9 will miss too many partscore swings so of course you will shorten the pass range and all others ranges will have to adapt.

However all the 9-10 pts hand that youve opened and hit responder with fit and 10-13 pts you will compete to 3S while it may go
pass--(3H)--AP at the other table for a partscore swing, yes the passed hand could balanced with 3S on a 5 card suit but hes somewhat taking a stab.


As for the balancing in the original problem I have seen many sucessful

1M-(3m)-P-(P)
X -(P)-4OM


where responder bid 4 in the OTHER majors with a crappy hand not good enough to make a negative X. However I have seen more failures than sucess when responder jump in 4M in opener suit. Most of the success were 3M bids anyway. So IMO balancing will help you compete to 3M, it will help you bid game if you had 2 card support and some pts but it wont help you bid you game if you already have a fit but werent able to bid 3S. The range of the balancing X is still quite large that passing and bidding game is mostly taking a stab.

If the balancing range is 15-21 jumping to 4M with exaclty 6 pts is marginal succes (in the model problem).

[awm]

I'd look at this a bit differently...

Suppose:

1. Pass 0-7, 3♠ 8-11, 4♠ 12
2. With 19-21, opener forces game after the 3♥ bid.
3. With 15-18 opener bids game after 3♠

Losing cases:

14-11 (missed game)
11-12 (overbid)
15-8 (overbid)
19-[0 to 4] (overbid)
20-[0 to 3] (overbid)
21-[0 to 2] (overbid)

This seems on the surface like more losing cases. However, the range of 0-4 is actually quite uncommon (5-7 is more frequent).

[benlessard]

Ok... Yes I agree that IRL you can open 1M non forcing and later force yourself to game whne partner show a preference but didnt show any values. Just for those hand everybody is going to be in game anyway so the correct way to see this is that the range in standard isnt 11-21 but rather 11-18 since with the 19-21 you are going to force to game the instant partner show a 2 card preference.

IRL i wouldnt "raise myself" to 4S with a 5143 with 19 but with a 20-21 sure ill do it the 4-6 hands are way more frequent than 0-3 and frequency is everything.

[dake50]

Yes I see an abstract on game decisions.
Now flesh it out using these many inputs, esp those frequencies:
19-6 rarer than 14-11, so ding 14-11 missed proportionately more than 19-6.
I would be interested in those fleshed-out results.