[TylerE]

Inspired by this thread: http://www.bridgebas...825#entry726825

Given:

North holds a 15-17 mainstream 1NT opening (So, no 5431, 6333, 7222 or other semi-bal)
South holds Kxxxxx of a major, Kxx of another suit, and two small doublestons

How often, on all hands, can north take 10 tricks playing in south's major.
How often, when north would accept an invite (Say, 16-17 with 3, or 15 with 4 trumps)
How often, when we don't take 10 tricks, do we make exactly 9?

For bonus points, maybe restrict east to not having an obvious call over 1NT (Say, <18 highs, and no 7 card suits)


Can anyone run a sim on this?

I stated my (apparently less mainstream than I thought) opinion in the linked thread, and I'm curious if simulations back this up.

[bgm]

Using Bridge Analyser

Enter South's hand exactly as ♠T8 ♥K86543 ♦85 ♣KT8

North hand constrained as (4333), (4432) 5m(332) with 15-17 HCP

East hand constrained as no 7 card suit, < 18 HCP

Simulating 100000 deals for Q2.

No. of deals satisfying
15 w/ 4♥: 7850
16-17 w/ 3+♥: 38895

So a total of 46745 out of 100000 deals, or around 46.745%

Simulating 10000 deals for Q1 and Q3, running DD analysis calculate the number of tricks won when North declare a ♥ contract.

Here is the frequency table

(No. of tricks: Frequency)
5-: 0
6: 39
7: 330
8: 1639
9: 3830
10: 3358
11: 769
12: 32
13: 3

So a total of 4162 out of 10000 deals winning 10+ tricks in ♥, i.e. around 41.62%

A total of 7992 out of 10000 deals winning 9+ tricks in ♥, i.e. around 79.92%

in which 3830 deals winning exactly 9 tricks.

[TylerE]

Thanks!

[bgm]

Perhaps a simple use of the frequency table is to compare Texas signoff at 4♥ and JTB signoff at 2♥, assume vulnerable.

(No. of tricks: Total Points Difference, IMP Difference)

7-: -200, -5
8: -310, -7
9: -240, -6
10+: 450, +10


Then can calculate the expected IMP gain for 4♥ which is +5.322.

I believe JTB with invitational raise will gain over direct 4♥, using the invitational rule you set. However due to the program limitation the result cannot be obtained here so let other helps to verify this.

[JLOGIC]

Partner will accept the invite with 2 hearts and 17 always, with 2 hearts and 16 sometimes, and with 15 and 3 hearts sometimes.

[TylerE]

So based on frequency, I've come up with the following total point EVs when RED:

Always pass 2: +140.8
Always invite and pass 3: +102.7
Always bid 4: +178.0
Perfect Invite: +290.0 (Basically, scored as stopping in 3 whenever making 3 or less, or bidding game when it's making)
Random invites: +140.4 (Responder accepts the invite exactly half the time, at random)
Good invites: +185.8 (See below, a bit of a hack)

Good Invites EV;

Responder accepts the invite when game is...

Never when down -3 or more
5% of the time when -2
25% of the time when -1
50% of the time when =
75% of the time when +1
100% of the time when +2 or +3

So this suggests that invites might be a bit better, it's not as huge of an edge as you might think, and if your invites are not pretty good they may well be worst than just blasting.

[Wwchang]

I'd tweak this a little bit. I put this together (I don't know how to make the table look nice):


..........................Invite.........Diff....IMPS...Weighted
................Blast.....Go.....Stop....on stop.stop....IMPS
6....39..0.0039.-400.....0.......0.0039..100......3.....0.0117
7...330..0.0330.-300.....0.......0.0330..100......3.....0.099
8..1639..0.1639.-200.....0.......0.1639..100......3.....0.4917
9..3830..0.3830.-100.....0.1915..0.1915..240......6.....1.149
10.3358..0.3358..620.....0.1679..0.1679.-450....-10....-1.679
11..769..0.0769..650.....0.0769..0.0000
12...32..0.0032..680.....0.0032..0.0000
13....3..0.0003..710.....0.0003..0.0000
10000

What I've done is to assume the quality of the invite as x% making the right decision on borderline hands. I'll assume that on any hand where game is -2 or more, the invite is always rejected, and where game is +1 or more, it is always accepted. So on the borderline hands (making 9 or 10 tricks), the the invite will be accepted on x% of the hands that it makes game, and rejected on x% of the hands that it goes down 1.

The table above is for x = 50 (i.e., no better than chance, unless 8 tricks or more, or 11 tricks or less). It shows inviting would be worth 0.072 imps/hand. The one-trick difference when game goes down 2 or more turns out to be pretty costly for blasting to game, eating up all the advantage of the 10:6 bonus for going to game.

If your invite acceptances are better than random, we get better results for invite:

55: +0.355 imps
60: +0.638
65: +0.921
70: +1.204
75: +1.486
80: +1.769
85: +2.052
90: +2.335
95: +2.618
100:+2.900

Of course, this doesn't take into account E/W bidding over 2H or 3H. I don't know what a reasonable accuracy percentage is, but maybe 70%+.

[johnu]

I ran some simulations using Dealmaster Pro for opener with 15-17 balanced.


Opener has 2 Hearts 3 Hearts 4 Hearts

15 points ____10% ____33% ____36%
16 points ____22% ____51% ____59%
17 points ____40% ____69% ____80%

The percentages seem to match what I expect opener to do based on his hand. With only 2 hearts, only accept with prime cards and close to a maximum, with 3 hearts, accept with more than a minimum, and with 4 hearts, accept with almost any decent minimum or better.

[mycroft]

Nobody ever bids over 1NT-p-2♦? Have I been playing weak NTs so long I've forgotten that that is "our auction" in Real Bridge?

[Edit: actually make the transfer, Mycroft]