[whereagles]

bid_em_up, on Dec 4 2008, 04:51 PM, said:

Here, I will save you the trouble of having to search for it.

Thanks. A quick calculation shows that weak 2s are more frequent than muiderbergs at a rate of around 3 to 2. (Under assumptions of weak 2 in D/H/S, muiderberg Mm and 2♦ as multi.)

[kenrexford]

whereagles, on Dec 4 2008, 02:06 PM, said:

bid_em_up, on Dec 4 2008, 04:51 PM, said:

Here, I will save you the trouble of having to search for it.

Thanks. A quick calculation shows that weak 2s are more frequent than muiderbergs at a rate of around 3 to 2. (Under assumptions of weak 2 in D/H/S, muiderberg Mm and 2♦ as multi.)

Isn't the question simply whether, for instance, 2♥ as a weak two comes up more than 2♥ as Muiderberg?

If a weak two can be a five-card suit, with or without a minor, then the weak two comes up more than Muiderberg, because X+Y>X if X and Y are not negative.

If the two bids are mutually exclusive (Muiderberg never 6-card; weak two never 5-card), then the simple question is whether a hand with 5 hearts and 4-5 of either minor (and the appropriate HCP range) occurs more frequently or less frequently than hand with six hearts (and maybe not four spades), again with the required HCP range. You would also, it seems, need to tweak the HCP situation for each to eliminate hands where "too much" is on the outside.

The link does little to answer that complete question.

[han]

kenrexford, on Dec 4 2008, 02:16 PM, said:

X+Y>X if X and Y are not negative.

Hmm.

Quote

The link does little to answer that complete question.

Agree.

[fromageGB]

maggieb, on Dec 3 2008, 11:10 PM, said:

I must say I am really surprised that you didn't know multi is not allowed in pair games, which US have you been living in?

Well, thanks for the info. Another good reason to live in the UK

Agree with Ken. I don't play Muiderberg but I do play 5card 2M bids, and there would then be serious gaps in my hand coverage if I couldn't play a multi. Having said that, they are separate conventions so there is no reason to have similar permissions.

[whereagles]

kenrexford, on Dec 4 2008, 07:16 PM, said:

The link does little to answer that complete question.

Well, you just sum up probabilities of the respective shapes and then count cases.

[kenrexford]

whereagles, on Dec 5 2008, 05:50 AM, said:

kenrexford, on Dec 4 2008, 07:16 PM, said:

The link does little to answer that complete question.

Well, you just sum up probabilities of the respective shapes and then count cases.

But, shape is not the only concern.

[whereagles]

You can add as many requirements as you want. I'm only interested in the higher-order effect: shape. All other effects are second to this one, thus my simplifications.

[mtvesuvius]

I love to play a Multi 2♦ and a Muiderberg 2M, however since Multi has been banned and my partners don't like my 5332 openings, I implemented Muiderberg... We now also open any 9+ HCP with a six card suit. Also, with less and a good suit, the 3 level is still always available. Muiderberg seems to go well with Multi, however it can stand alone. I am extremely dissapointed that Muiderberg is defined as a Mid-Chart convention, it is extremely simple, and all weak 2 treatments still apply. It should make no difference that it has an agreement of showing only 5 and an outside suit! I would love to be able to play Muiderberg in a side game or at the club, but unfortunately I will not be able to do so for a long time.

[kenrexford]

whereagles, on Dec 5 2008, 08:31 AM, said:

You can add as many requirements as you want. I'm only interested in the higher-order effect: shape. All other effects are second to this one, thus my simplifications.

Well, that seems kind of strange.

Make a pronounced thesis.
Prove it by proving unrelated facts.

Not sure that works.

What I meant by other concerns:

1. The number of hands with a required range seems to be governed to some degree by the pattern. If I have a six-card suit, and no other suits of 4+ length, then I have two cards that cannot be honors. If I have a five-card suit and a suit of 4-5 cards in length, then I have 1.5 cards that cannot be honors. That seems to slightly shift the possibility of certain patterns having the required range.

2. The location of high cards is also critical. As a simple point, I doubt people would view a 2♠ opening as appropriate with a range of 6-11 with ♠xxxxxx ♥Axx ♦Kx ♣Ax. A weak two generally requires some limited COV in one suit, whereas a Muiderberg allows for limited COV in two suits.

Adding into this is the problem that, although the definition of a Muiderberg opening seems fairly standardized, the definition of an appropriate weak two is not remotely standarized. Knowing which weak two definition is being considered seems rather important, as there is a vast difference between "six-card suit with two of the top three honors and three of the top five honors" and "a five-card or longer suit with any quality and any shape, even five-card side suits being possible."

[cherdano]

whereagles, on Dec 5 2008, 04:50 AM, said:

kenrexford, on Dec 4 2008, 07:16 PM, said:

The link does little to answer that complete question.

Well, you just sum up probabilities of the respective shapes and then count cases.

Or, as in your case, miss some (or was it missum?) cases...

[whereagles]

cherdano, on Dec 5 2008, 05:51 PM, said:

Or, as in your case, miss some (or was it missum?) cases...

Dont be silly.

[hrothgar]

whereagles, on Dec 5 2008, 08:55 PM, said:

cherdano, on Dec 5 2008, 05:51 PM, said:

Or, as in your case, miss some (or was it missum?) cases...

Dont be silly.

Your results really don't match any of the ones that I've seen.

It would be helpful if you could provide a thorough description what you're doing so we can show precisely where you're making your mistake.

For example what set of shapes are you judging to be appropriate for a weak two opening in Hearts?

Precisely what set of shapes are you using for a Muiderberg 2♥ opening?

For example, you hypothetically might post something like the following:

Weak 2♥ Opening = 3.06%

All 6322 hands = 5.64% x .25
All 6331 hands = 3.45% x .25
All 6421 hands with a 4 card minor = 4.7% x .25 x .66666

Muiderberg 2♥ opening = 4.471%

All 5431 hands with a 4 card minor = 12.93% x .25 x .66666
All 5422 hands with a 4 card minor = 10.6% x .666666
All 6421 hands with a 4 card minor = 4.7% x .25 x .666666

[cherdano]

I think this thread is a good example for the difference between confidence and arrogance.

[Echognome]

Good exercise for a simulation...

[awm]

Weak 2♥ Opening:

6322 patterns 5.64% times 0.25 (because the six-card suit must be heart): 1.41%
6331 patterns 3.45% times 0.25 (because the six-card suit must be heart): 0.8625%
6421 patterns 4.7% times 0.25 times 0.66 (six-card suit ♥, 4-card suit not ♠): 0.783%

Total: 3.056%

Muiderberg 2♥:

5431 patterns 12.93% times 0.25 times 0.66 (5♥ and 4-card suit not ♠): 2.155%
5422 patterns 10.6% times 0.25 times 0.66 (5♥ and 4-card suit not ♠): 1.767%
5521 patterns 3.17% times 0.33 (six suit pairs, we're interested in two of them): 1.057%
5530 patterns 0.895% times 0.33 (six suit pairs, we're interested in two of them): 0.298%
6421 patterns 4.7% times 0.25 times 0.66 (six ♥ and 4-minor): 0.783%

Total: 6.06%

So having the "right shape" for muiderberg is roughly twice as common as having the "right shape" for a six-card weak two bid. We could add in 6-5 hands and the like, but they would add the same amount to both tallies. The only question is whether point count and/or suit quality somehow biases this, but the reality is that the correlation between the odds of having a point count in some range like 6-10 and having a particular shape is pretty low (at least for commonly appearing shapes). Suit quality restrictions on openings vary pretty widely based on the people bidding and the vulnerability, so they're hard to model, but assuming similar suit quality rules for the two bids they are unlikely to swing things much.

[hrothgar]

whereagles, on Dec 4 2008, 10:06 PM, said:

bid_em_up, on Dec 4 2008, 04:51 PM, said:

Here, I will save you the trouble of having to search for it.

Thanks. A quick calculation shows that weak 2s are more frequent than muiderbergs at a rate of around 3 to 2. (Under assumptions of weak 2 in D/H/S, muiderberg Mm and 2♦ as multi.)

Are you on crack ???

Let's play a simple little substitution game and assume that:

All hands that are suitable for a weak 2H / 2S opening are also suitable for a multi 2D opening. (Probably not realistic, lets use this a simplifying assumption)

In this case, when you compare the frequency of

(weak 2 in D/H/S)

versus

(muiderberg Mm and 2♦ as multi)

we get to cancel

weak 2 in Hearts and Spades on one side, and cancel the multi on the other

We are now comparing the frequency of a

Weak 2 in Diamonds versus (Muilderberg 2♥ + Muilderberg 2♠)

And you're claiming that your "calculations" show that a weak two in Diamonds is about 1.5 times more frequent....

[TimG]

hrothgar, on Dec 5 2008, 03:31 PM, said:

whereagles, on Dec 4 2008, 10:06 PM, said:

bid_em_up, on Dec 4 2008, 04:51 PM, said:

Here, I will save you the trouble of having to search for it.

Thanks. A quick calculation shows that weak 2s are more frequent than muiderbergs at a rate of around 3 to 2. (Under assumptions of weak 2 in D/H/S, muiderberg Mm and 2♦ as multi.)

weak 2 in Hearts and Spades on one side, and cancel the multi on the other

We are no comparing the frequency of a

Weak 2 in Diamonds versus (Muilderberg 2♥ + Muilderberg 2♠)

And you're claiming that your "calculations" show that a weak two in Diamonds is about 1.5 times more frequent....

To get the 3:2 ratio you'd have to open a weak two in diamonds more than 1.5 times as often as Muilderberg in either major (unless your weak two and multi frequencies are zero).

[hrothgar]

TimG, on Dec 5 2008, 11:35 PM, said:

hrothgar, on Dec 5 2008, 03:31 PM, said:

whereagles, on Dec 4 2008, 10:06 PM, said:

bid_em_up, on Dec 4 2008, 04:51 PM, said:

Here, I will save you the trouble of having to search for it.

Thanks. A quick calculation shows that weak 2s are more frequent than muiderbergs at a rate of around 3 to 2. (Under assumptions of weak 2 in D/H/S, muiderberg Mm and 2♦ as multi.)

weak 2 in Hearts and Spades on one side, and cancel the multi on the other

We are no comparing the frequency of a

Weak 2 in Diamonds versus (Muilderberg 2♥ + Muilderberg 2♠)

And you're claiming that your "calculations" show that a weak two in Diamonds is about 1.5 times more frequent....

To get the 3:2 ratio you'd have to open a weak two in diamonds more than 1.5 times as often as Muilderberg in either major (unless your weak two and multi frequencies are zero).

Thanks for clarifying my original post...

This would all be much easier if the forum software support [snark] and [/snark]

[TimG]

hrothgar, on Dec 5 2008, 03:44 PM, said:

This would all be much easier if the forum software support [snark] and [/snark]

Sorry if I mistook snark for a lapse in mathematical reasoning.

[whereagles]

Richard: I compared

6 card weak 2 in D/H/S
vs
muiderberg Mm 54 or 55

and found a 3/2 rate to 1st case. I forgot what I had in mind when I wrote "2♦ as multi". Now, if one is to compare

6 card weak 2 D/H/S
vs
muiderberg Mm 54 or 55 AND 2D as multi

then the 2nd is more frequent, of course.