Possible subject for BrBr

[Mbodell]

My partner and I recently switched to 10-13 nt range in 3rd seat. We play with a 12-15 nt range in 1st, 2nd, and 4th. We play a strong club system where our 1d,1h,1s,2c, and 2d are all constructive bids with ~10-15 points although we do upgrade some 8 and 9s and down grade some 10 and 11s in early seats so points are only a guide. But our basic theory was we like the preemptive value and our nt ladder became 10-13, 14-17 and 18+ in 3rd seat. Our 1c opener in 3rd seat is 16+ unbal or 18+ bal whereas in other seats it is 16+ any. One of the other reasons we made this change is we wanted more safety in passed hand positive responses which we have when the 3rd seat 1c is a little stronger.

 

So far we've mainly had system wins when the 10-13 nt comes up with the only bad board being when my partner psyched the call and the opponents ended up playing 3ntx+5 when my 7 hcp hand doubled them for penalty. If I were allowed I would have preferred a 8-13 nt in 3rd seat, at least nv, for pure preemption value when I'm certain we aren't missing game. We play all natural after 1nt EXCEPT for the run outs so we can't open sub 10 HCP hands 1nt in the ACBL since the run outs are pretty important.

[awm]

How does passing in 1st or 2nd seat deny a 10 count?

I didn't suggest anything like this.

 

Suppose I don't look at my hand. If I am in first chair, how many points do I think my hand will contain?

 

Well of course I have no idea, but it's a reasonable bet that I'll have close to ten points. This is the "average" number of points to hold. I'm much more likely to hold a balanced 10-count than a balanced 15-count.

 

But now, suppose I am in fourth chair. Remember, I still have not looked at my hand. I see three players pass in front of me. What does this tell me? None of these people had enough to open. Assuming that they are reasonable players using fairly standard bidding systems and did look at their hands, this means they have at most something like a balanced 11. Could I have a balanced 10-count? Sure, maybe everyone at the table has a balanced 10-count. But having seen three players pass in front of me the odds of my having a pretty good hand go dramatically up! In fact, so much so that it's a pretty reasonable bet that after Pass-Pass-Pass I hold close to fifteen points, and given the information that none of the other three players could muster an opening bid, I am in fact more likely to hold a balanced 15-count than a balanced 10-count.

[hotShot]

Edit: Ignore, see awm calculation below instead.

 

This is drawing totally the wrong conclusions.

 

If I am in first chair, no one has yet done anything, their average strength is 10 HCP each.

You better reconsider that.

The average of 10 HCP results from hands from 0 HCP up to 37 HCP with using their frequency as weight. If a player is using methods that would open any 12 HCP hand, than his pass means that his hand is from the subset of hands with 0-11 HCP. The average strength of these hands is ~8HCP.

As a consequence the remaining 3 player have 2 more HCP to distribute. So the average of the 2nd pass moves up 2/3 HCP.

This is just basic math.

After two passes, the average strength of two people at the table is substantially less than 10 HCP.

 

This means the odds of a 15-17 notrump go up in 3rd and 4th chair. The odds of a 12-14 notrump in fact go down.

Now you compare odds, but which odds are you comparing?

What I do is:

There are 23 1/3 HCP to distribute to 2 Player obviously the maximum of the distribution curve will be at 11 4/6 = 11 2/3. This means that the odds to hold 12-14 HCP are much bigger than those of holding 15-17.

 

Assuming everyone plays fairly standard methods, in fourth chair after three passes you are more likely to hold 15-17 balanced than you are to hold 12-14 balanced!

If the 3rd seat passes too and by that denies to have 12+ HCP, than indeed in 4th seat you hold an average of 12 1/3. This is better than the average 10 in 1st seat so you are more likely to have 15-17 hCP than in 1st seat, but still it is more likely that you hold 12-14 HCP than holding 15-17.

In general opening 1NT is not so good when opponents hold the majority of the strength. Occasionally you can "steal" when their strength is equally divided between the hands (it becomes hard for them to figure out that they have game) but usually the 1NT opening works better when either the points are roughly equally divided or when it's the opening side's hand. Knowing that partner is a passed hand (esp. if you open a lot of ten counts) decreases the odds of this working out and increases the odds of the bad case where it's opponents hand and your LHO has enough points to double.

You will find that weak NT opener don't play 1NT if they are weak, they use some escape sequence to get into a "better" contract.

Edited April 18, 2008 by hotShot

[awm]

What you are missing is that the second seat pass effects the strength of the first seat pass. Given that the auction has started with two passes, the distribution of high card points in the first two hands will be the same.

 

In any case here are some statistics:

 

In first seat weak notrump (12-14) hands occur about 9.2% of deals whereas strong notrumps (15-17) occur 5.4% of deals. This means a weak notrump is about 1.7 times more common than a strong notrump.

 

Now assume we are in third seat after two passes.

 

The average strength for the passed hand in first seat is 7.877 hcp.

The average strength for the passed hand in second seat is 7.877 hcp.

The average strength for the hand we hold will be 12.12 hcp.

 

In this situation, a weak notrump occurs about 12.84% of the time (yes it goes up since the "average" hand is now closer to a weak notrump). However, a strong notrump is also more frequent, occuring 10% of the time. This means a weak notrump is only 1.28 times more common than a strong notrump.

 

In fourth chair after three passes:

 

The average strength for the passed hand in first seat is 8.478 hcp.

The average strength for the passed hand in second seat is 8.478 hcp.

The average strength for the passed hand in third seat is 8.478 hcp.

The average strength for our fourth seat hand will be 14.556 hcp.

 

In this situation, a weak notrump occurs about 15.6% of the time whereas a strong notrump occurs about 16.7% of the time. This means a weak notrump is less frequent than a strong notrump.

 

In fact when I modeled this I assumed fairly conservative "standard" opening style in all the first three seats (i.e. pass with less than 12 hcp and no six card suit). Almost all modern players open more aggressively, at least in third chair. This will change the expectations with the net effect of increasing the expected strength of the fourth hand after three passes thus making a strong notrump even more the favorite.

[Al_U_Card]

I wonder what those numbers might be for the 10-12 NT?

[hotShot]

What you are missing is that the second seat pass effects the strength of the first seat pass. Given that the auction has started with two passes, the distribution of high card points in the first two hands will be the same.

You are right!

 

@Al_U_Card

Ignoring shape my sample says:

After pass - pass 3rd seat is

(All HCP ranges should sum up to 36,7% of all deals)

10-12 10.6% combined average 19.2

12-14 10.4% combined average 20.8

15-17 6.7% combined average 23.2

 

 

After pass- pass - pass 4th seat is

(All HCP ranges should sum up to 17.2% of all deals)

10-12 4.2% combined average 20.8

12-14 5.8% combined average 22.0

15-17 5% combined average 23.9