[jdonn]

jtfanclub, on Sep 6 2007, 03:23 PM, said:

Hannie, on Sep 6 2007, 02:50 PM, said:

FYI, this is nonsense, both the method and the outcomes.

Maybe a C-. Sorry.

But hey, on the bright side at least you get credit for realizing it when it is pointed out to you. And it only took one person, not 10 In fact, I now see people are proving Bebop wrong with his own quoted sources! Snicker.

[gwnn]

There are 26 cards missing, so there are 26!/(13!*13!) possible ways of them splitting.

this is 10400600

In how many ways can a suit divide 4-0?

2(which opp is void?)*22!/(9!*13!) (which 13 cards does the opp with the void have out of the remaining 22?)

2*22!/(9!*13!)=994840

Exact percentage=9.5652173913043478260869565217391 (windows scientific calculator)

3-1?

2(which opp is singleton?)*4(which card is the stiff one?)*22!/(10!*12!) (which 12 cards does the opp with the singleton have?)

2*4*22!/(10!*12!)=5173168

Exact percentage=49.739130434782608695652173913043

2-2?

6(which 2 cards does LHO have?)*22!/(11!*11!) (how can 22 cards be dealt 11-11?)

6*22!/(11!*11!)=4232592

Exact percentage=40.695652173913043478260869565217

What does that say about the bridge hand? I have no idea. But the maths are correct.

[ralph23]

Using good ole' durango bills site:

A = No. of 6322 hands: 35,830,574,208

B = No. of 6331 hands: 21,896,462,016
C = B times 2 = 43,792,924,032 (because I can have 3 on left and 1 on right, or vice versa)

Ratio of C to A: 1.2222222

That is, for every time they divide 2-2 against me, they will divide 3-1 (or 1-3) against me 1.22222 times.

Compare against Pavlicek's calculator:Missing 4 cards:

E = Percentage Odds of EW dividing 2-2: 40.695652173913
F = Percentage Odds of EW dividing 3-1 or 1-3: 49.739130434783

Ratio of F to E: 1.2222222

[jtfanclub]

Darn it, Ralph, that's what I was trying to do. What did I do wrong?

[ralph23]

jtfanclub, on Sep 6 2007, 06:56 PM, said:

Darn it, Ralph, that's what I was trying to do. What did I do wrong?

Well, I don't know.... I thought you very cogently pointed out to bebop that he had simply failed to count for both 3-1 and 1-3. But the point is, of course, the durango numbers on the web are correct; as is Pavlicek.

As is the other bridge calculator on the web that I cited and, I'm sure, he failed to even experiment with and wonder "Gee, I wonder why my numbers are different".

And as is the Encyclopedia of Bridge (and yes, I have one too). In fact all the published sources agree.

It's not the instrument that had a problem; it's the musician.

[Stephen Tu]

Quote

The layout of cards in two hands do affect the probability of the cards in the other two hands, because if you swap 63 to 54 you have to affect 2 other cards in each of the two hands, which affects the layout of other suits in the two hands

If you change 6-3 to 5-4, you are just trading cards in other suits from north to south & vice versa, you don't have to touch East/west's cards.

Say after each hand is shuffled & dealt, North & South examine their cards, and South always gives North all his spades, and North hands South the appropriate number of random non-spade cards in exchange. Why should the distribution probability of East/West change?

gwnn's calculations are the normal, direct way to do this in my mind. Jdonn calculated in a more time consuming way but also valid & the same answer. I don't quite comprehend how you are trying to do this.

[ralph23]

Stephen Tu, on Sep 6 2007, 07:53 PM, said:

Quote

The layout of cards in two hands do affect the probability of the cards in the other two hands, because if you swap 63 to 54 you have to affect 2 other cards in each of the two hands, which affects the layout of other suits in the two hands

If you change 6-3 to 5-4, you are just trading cards in other suits from north to south & vice versa, you don't have to touch East/west's cards.

Say after each hand is shuffled & dealt, North & South examine their cards, and South always gives North all his spades, and North hands South the appropriate number of random non-spade cards in exchange. Why should the distribution probability of East/West change?

gwnn's calculations are the normal, direct way to do this in my mind. Jdonn calculated in a more time consuming way but also valid & the same answer. I don't quite comprehend how you are trying to do this.

Suppose after they are dealt (4 hands), NS just bunch their two hands in the middle. THey don't even look at their cards. This is the easiest way to see it, imo, but believe me, you're not going to convince him!

[joshs]

here are obviously 2 possible lines:
a. Cash trump A first and continue trumps (unless 4-0 onside), planning on hooking the club
b. use the entry to take the trump hook, and then take the other hook if trumps are 2-2

B Gains when:
Kx of trumps is onside
And when Kxx of trumps is onside and CK is offsides

A Gains when:
CK is on and [spade K is off or stiff SK is on]

Probabilities:
B: Kx in Spades on is 20%
Kxx on is 3/4 of 1/4=3/16
That AND CK off is thus 3/32
B gains 29.375% of the time

A:Spade K is off or stiff K is on=50%+1/4*1/4=9/16
So that and CK on is 9/32=28.125%

So it looks like B is slightly better. I probably need to think about the 4-0 breaks a little bit since you will not ALWAYS be able to repeat the club finesse as I have been assuming here, but that will only reduce the effectiveness of A a very little bit.

Anyway, I probably did my math wrong, so I will leave it to the peanut gallery to do 13,000 simulations

[Fluffy]

skaeran, on Sep 6 2007, 08:10 PM, said:

The notion that the distribution of the 9 known cards between the two known hands should alter the odds is.....I haven't got words.

This is true for hand-dealt hands that didn't get shuffled properly.

Oh damn, you will alll kill myself for stating this

[FrancesHinden]

Jlall, on Sep 7 2007, 01:02 AM, said:

I went through some crude analysis with han but it seemed like crossing and finessing was definitely a better MP line than cashing spade ace, crossing, and leading a spade up

Maybe we should split this thread into two...

You are right that crossing and taking a spade finesse, compared with SA, cross, spade up is going to win, because you gain every time spades are 2-2 with the king onside, and you only lose to singleton king offside which is obviously much less likely.

What's insteresting is to think of the Ace of spades, cross, jack of clubs line.

Suppose we cash the SA, cross, run the CJ, play a second club. Compared to crossing in diamonds and taking a spade finesse.

- loses one trick to Kx of spades onside (20%)
- loses one trick to Kx of spades offside with Kxx in clubs (4%) [assuming they find the ruff]
- loses one trick to K9xx clubs offside and Kxx spades onside (1%)

- gains one trick to Kx or Kxx of clubs onside with all 3-card spade holdings offside (25% * 43%) = 11%
- gains one trick to singleton SK offside and CK wrong (about 3%)
- gains two tricks to singleton SK offside and CKx or Kxx onside (about 2%)
- gains one trick to Kx of spades offside and K9xx clubs onside (a bit under 1%)
- gains one trick to KJ10x of spades offside and CK onside, not to 4 (about 2%)
- gains one trick to Kx of clubs onside with Kxx of spades (4%)

4-0 spades onside is a bit complicated, as you have to decide what to play for

That makes the spade finesse line very slightly superior, but some of my sums are a bit approximate, so I'm not yet certain.

At imps, by the way, it's definitely right to cash the SA first, as that guards against going off with KJ10x spade foul and the club finesse right. And it clearly doesn't lose a great deal in terms of trick expectation.

Now how about SA, cross, CJ, spade? I don't like this, because RHO can cover the club whenever he has KJx of spades, and not cover the club whenever he has Kxx and you never win.

[FrancesHinden]

joshs has also looked at the other line of Ace-and-another-trump, and seems to come to similar conclusions (the odds are very close but the spade finesse is fractionally better).

Maybe I conclude that the only line that's clearly wrong is SA, DK, Spade up and anything else is not worth more brainpower.

[Free]

bid_em_up, on Sep 6 2007, 06:55 PM, said:

Well, to be honest, thats what I thought originally, but,

The percentages you list (which are the ones normally given) are for all combined holdings of 9 cards (missing 4 cards).  A little further crazy thought says, the percentages for a 5-4, 6-3, 7-2, 8-1 and 9-0 breaks are likely different from each other though, no?

What a load of crap! What's the difference if you switch 2 ♠s from one hand with 2♣s from the other hand? Distributions are different, splits remain exactly the same since opps still have the same cards...

[BebopKid]

Trumpace, on Sep 6 2007, 02:10 PM, said:

BebopKid, on Sep 6 2007, 01:48 PM, said:

jdonn, on Sep 6 2007, 01:32 PM, said:

There are numerous ways to calculate this, but the most easily understood by people with little math background would be the following:

Since I have over 20 hours of college math, I didn't use the non-math method.

What university, who was the professor and what grade did you get? Did the math include probability theory?

Sorry, this statement of yours is quite annoying. You don't have to answer the questions above, but making statements like these to try and support your argument only shows that you don't have a convincing logical argument which is pertinent to the discussion at hand.

When I have already stated the Math as my argument, and no one seems to understand that, I have not much more to argue.

I'm looking at the evidence, and see clearly that my method for the distribution of the cards fits in with the probability theory. I have explained my method.

I've even tested it in practice. I've then looked at the evidence from the test which matches the probabilities that I generated using probability theory.

It's staring me right in the face, so yes the Earth does revolve around the Sun.

"E pur si muove."

[FrancesHinden]

Maybe, just maybe, when absolutely everybody tells you that you are wrong - including a number of people with maths degrees - it might be a good idea to get your head of the sand and have a bit of a re-think.

There are plenty of books and websites around giving the probability of 2-2, 3-1, 1-3, 4-0 and 0-4 breaks.

Now, I agree it's possible that they are ALL incorrect.
But do you really think that's likely?

[jtfanclub]

BebopKid, on Sep 7 2007, 11:45 AM, said:

When I have already stated the Math as my argument, and no one seems to understand that, I have not much more to argue.

It's not even hard to understand where your error is.

"6322 occurs 5.642490% of all hands (~54.2%)
6331 occurs 3.448188% of all hands (~33.1%)
6430 occurs 1.326226% of all hands (~12.7%)"

But not all 6332s, 6331s, and 6430s count. We don't need to include the case where EAST has 6 and WEST has 3, right? I think that one's right out.

South has to always have 6, right? That's 3/4 of the hands that we can pitch.

So in each case, if South has 6...

6322: Can be-
S6, W3, N2, E2
S6, W2, N3, E2 <----
S6, W2, N2, E3
Only that one 6322 is possible (out of 3), as the others we know can't be true, as North has 3 cards. Therefore, only 1/12 of 6322s fit.

6331: Can be-
S6, W1, N3, E3 <----
S6, W3, N1, E3
S6, W3, N3, E1 <---
There are two 6331s possible (out of 3), so 1/6 of the 6331s fit.

6430: Can be-
S6, W4, N3, E0 <----
S6, W4, N0, E3
S6, W3, N4, E0
S6, W3, N0, E4
S6, W0, N4, E3
S6, W0, N3, E4 <---

There are two 6430s (out of six, not out of 3), so 1/12 of the 6331s fit.

1/12 of the 6322s is .470275% (40.70%)
In other words, in .47% of all deals we have a 6322 with South having 6 and North having 3.
1/6 of the 6331s is .574698% (49.74%)
1/2 of the 6430s is .1105188% (9.565%)


Which is EXACTY the same numbers as Pavlicek got. Your source and their source agree that you are wrong.

My mistake earlier was forgetting that while there's only 12 possible combinations of 6331 and 6322, there are in fact 24 possible combinations of 6430, because there are no duplicate numbers. Sorry about that! The method was right, I just couldn't count.

[ralph23]

BebopKid, on Sep 7 2007, 12:45 PM, said:

Trumpace, on Sep 6 2007, 02:10 PM, said:

BebopKid, on Sep 6 2007, 01:48 PM, said:

jdonn, on Sep 6 2007, 01:32 PM, said:

There are numerous ways to calculate this, but the most easily understood by people with little math background would be the following:

Since I have over 20 hours of college math, I didn't use the non-math method.

What university, who was the professor and what grade did you get? Did the math include probability theory?

Sorry, this statement of yours is quite annoying. You don't have to answer the questions above, but making statements like these to try and support your argument only shows that you don't have a convincing logical argument which is pertinent to the discussion at hand.

When I have already stated the Math as my argument, and no one seems to understand that, I have not much more to argue.

I'm looking at the evidence, and see clearly that my method for the distribution of the cards fits in with the probability theory. I have explained my method.

I've even tested it in practice. I've then looked at the evidence from the test which matches the probabilities that I generated using probability theory.

It's staring me right in the face, so yes the Earth does revolve around the Sun.

"E pur si muove."

Isn't this simply hilarious?

I opined earlier that no one (or no amount of evidence) could convince him he's wrong. Not even the simple comparison of durango and pavlicek, which would have raised at least a clue to .... er, most people would suffice, so you just must admit he's hopelessly confused.

[ralph23]

FrancesHinden, on Sep 7 2007, 12:52 PM, said:

Maybe, just maybe, when absolutely everybody tells you that you are wrong - including a number of people with maths degrees - it might be a good idea to get your head of the sand and have a bit of a re-think.

There are plenty of books and websites around giving the probability of 2-2, 3-1, 1-3, 4-0 and 0-4 breaks.

Now, I agree it's possible that they are ALL incorrect.
But do you really think that's likely?

Doesn't matter. You might as well argue with someone from the Flat Earth Society.

Maybe he'll email one of the world class teachers he had, but I doubt it. Evidence is irrelevant.

[bid_em_up]

FrancesHinden, on Sep 7 2007, 11:52 AM, said:

Maybe, just maybe, when absolutely everybody tells you that you are wrong - including a number of people with maths degrees - it might be a good idea to get your head of the sand and have a bit of a re-think.

There are plenty of books and websites around giving the probability of 2-2, 3-1, 1-3, 4-0 and 0-4 breaks.

Now, I agree it's possible that they are ALL incorrect.
But do you really think that's likely?

Where would we be if:

Columbus has listened to "everybody"?
Newton had gone on about his business like everybody else when the apple fell?
The Wright Brothers had listened when told they could not fly?
Kennedy had paid attention to those smarter than him who said it was impossible to put mankind on the moon?

and countless other similar events in history, where somebody has stopped to question the norm.

Much knowledge and advancement of mankind has come directly from asking "What if?" or not taking what is said as gospel, just because everyone says its so.

Now, I said it was a "crazy" thought that possibly it might make a difference if the suit split 5-4 or 8-1. I did not claim that the current (and what I also believe to be accurate) probabilities were not accurate, I simply had an admittedly crazy "What if" thought.

But while you say:

Quote

Maybe, just maybe, when absolutely everybody tells you that you are wrong - including a number of people with maths degrees - it might be a good idea to get your head of the sand and have a bit of a re-think.

I, say, maybe, just maybe when everybody else is telling you something can't be done or isn't possible, or it simply has to be that way, it might be a good time to think harder about how to go about proving them to be incorrect.

Mind you, I am not saying they are incorrect. But if you always simply blindly accept statement of the sorts being made here, then advancements cease to be made.

"Always listen to experts. They'll tell you what can't be done, and why. Then do it." -- Lazarus Long, Time Enough for Love

(Amusing that Ralph mentions the Flat Earth society, in defense of the other sides opinion. I see it as exactly the opposite. Everybody else would be the Flat Earth Society in Columbus's time, while Bebop would be Columbus.)