[Trumpace]

bid_em_up, on Sep 7 2007, 01:10 PM, said:

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.)

What you say is totally irrelevant...

The problem in question has a clear mathematical proof, unlike the scientific theories of those days which did not have any proof (they were just theories, waiting to be proved/disproved). All we need to do is look at the proof.

During the times you mention most people weren't scientific minded, but were just stubborn believers.

The times have changed and these days the quite a number of educated people at least have a scientific bend of mind (especially in online forums) and look for the truth instead of proof of what they believe. So if a lot of people disagree with you, there is a good chance you are wrong. btw, good chance does not mean 100%.

Also, if we start trying to read the gibberish of every crackpot that comes along, no time would be spent on anything else (judging by the number of such people on the various forums I have visited).


These kinds of statements remind of the Calvin and Hobbes comic:

Calvin: "You know Einstein's grades were bad when he was a kid, well mine were are worse!"

I have seen this happen numerous times, the crackpot says something, many people disagree, the crackpot now instead of rethinking what he said, brings up arguments like these to convince himself that he is a genius...

[Fluffy]

Trumpace, on Sep 7 2007, 06:35 PM, said:

During the times you mention most people weren't scientific minded, but were just stubborn believers.

The times have changed and these days the quite a number of educated people at least have a scientific bend of mind (especially in online forums) and look for the truth instead of proof of what they believe.

Looking at Ralph's posts I have my doubts, he seems so convinced that pavlicek or whatever his source is right that he doesn't even contemplate the fact that he might be wrong, he just laughs at Bebop for contradicting the obvious without even thinking.

I also see the analogy with Galileo or Columbus the way bid_them_up does.

[jdonn]

bid_em_up, on Sep 7 2007, 01:10 PM, said:

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.

Lol. BLINDLY?!?! He has been PROVEN wrong like 15 times in this thread! By at least three different valid mathematical methods, and a number of sources including HIS OWN!

Bebop, read JT's post about five before this one. It shows you the mistake you were making quite clearly. There is nothing else I can say.

[Trumpace]

Fluffy, on Sep 7 2007, 01:41 PM, said:

Trumpace, on Sep 7 2007, 06:35 PM, said:

During the times you mention most people weren't scientific minded, but were just stubborn believers.

The times have changed and these days the quite a number of educated people at least have a scientific bend of mind (especially in online forums) and look for the truth instead of proof of what they believe.

Looking at Ralph's posts I have my doubts, he seems so convinced that pavlicek or whatever his source is right that he doesn't even contemplate the fact that he might be wrong, he just laughs at Bebop for contradicting the obvious without even thinking.

I also see the analogy with Galileo or Columbus the way bid_them_up does.

Even if ralph is behaving as you say (which I think he is not, he is quoting sources which BebopKid cited and Pavlicek is a well known authority in these matters) it still does not falsify the statement: "Quite a number of educated people have a scientific bend of mind in online forums".

It just proves that you aren't one of the ones with a scientific bend of mind, as any statistician will tell you just one example is not enough to falsify that statement.

People may strongly believe whatever they want: God exists, a natural 2NT is forcing, or probabilities change depending on distribution of the 9 cards. The strength of the belief does not make them right.

Sorry, this thread is getting out of hand, I think I will stop participating.

[jtfanclub]

bid_em_up, on Sep 7 2007, 01:10 PM, said:

Where would we be if:

Columbus has listened to "everybody"?

Funny story, that. Everybody had known for centuries that the Earth was round. Some of the maps that Columbus was looking at were in Arabic miles, almost twice the size of Italian miles. As a result, Columbus thought that the distance from Europe to Asia Westward was much less than reality, about 3000 (modern) miles instead of the actual 12,000. The reason people laughed at him is because there was no way in hell that he had the supplies to travel 12,000 miles. And they were right.

Anyhow, this is a simple mathematical error, that even a middle schooler can figure out. 2/3 of 6331 hands with 6 cards in the South have 3 cards in the North, while only 1/3 of 6322 hands with 6 cards in the South have 3 cards in the North. That isn't to say that BeBop is bad at math, it's just one of those simple mistakes that all of us make. I used 2/3 instead of 2/6 for 6340 myself, after all, so I'm not one to judge.

But when you won't look at your own math when people point out an arithmatic error to you, it stops being math, and starts being religion. These flights of fancy into Columbus and the like are amusing, and all, but it's just math.

If you seriously think BeBop's right, then you should be able to find the error in my reckoning. By all means, find it.

[ralph23]

jtfanclub, on Sep 7 2007, 03:36 PM, said:

bid_em_up, on Sep 7 2007, 01:10 PM, said:

Where would we be if:

Columbus has listened to "everybody"?

Funny story, that. Everybody had known for centuries that the Earth was round.

http://www.talkorigi.../flatearth.html

Well..... apparently not EVERYBODY lol.

The best line I've seen or heard for a long time is on this website: "Please do not send us feedback to tell us that the Earth is a sphere; we are already aware of this fact."

[Halo]

Jlall, on Sep 6 2007, 05:58 PM, said:

A very interesting hand is posted and it turns into this.....

So what is the right line? My intuitive line is to cross to the DK and hook the spade. I recognize that this is effectively a math problem though so would like those who are good at these things to figure out what is the best line. Sorry if someoen did this and I missed it amongst the noise.

As previously posted I agree with the above.

I am not sure math is the issue on this hand.

In a practical situation I would ignore 40/04.

31/13 balance out. 22 King offside doesn't matter.

So Bridge wise (I believe) it comes down to 22 King onside versus stiff king onside and offside. So I still say the the finesse is the correct matchpoint play by a significant margin.

[BebopKid]

I need some help explaining these numbers.

I ran through 400 hands generated by Bridge Baron 16.

200 with NS having 6 spades in North and 3 Spades in South, the opponents hands were
17 4-0 split
90 3-1 split
93 2-2 split

200 with NS having 5 spades in North and 4 Spades in South, the opponents hands were
21 4-0 split
105 3-1 split
74 2-2 split

This is closer to my predictions than to Pavlicek's predictions. After so many people telling me I was wrong, I'm confused that the samples conformed somewhat close to my predictions made from my inadequate knowledge of probability theory.

Can someone please tell me where I went wrong with the samples? I can give the 400 deal #'s to anyone who would like to verify.

[han]

I suggest you try a larger number, the error should get smaller then.

[Stephen Tu]

Or perhaps simply Baron's deal generator when you put in constraints doesn't work correctly and provide true randomness. Try Thomas Andrew's Deal, or van Staveren et al's dealer

[BebopKid]

Thanks for the suggestion Hannie. And Stephen.

I made 65,000 deals, of those 27411 deals had 6/3 suit splits between two hands

14681 split 2-2 (53.56%)
9155 split 3-1 (33.40%)
3575 split 4-0 (13.04%)

64348 deals had 5/4 suit splits between two hands

33606 split 3-1 (52.23%)
27478 split 2-2 (42.70%)
3264 split 4-0 (5.07%)

Could someone please explain why these deals do not match Pavlicek's calculations but instead match my probability calculations?

[Trumpace]

I thought I will stay away, but BebopKid's simulation results forced me to respond.

I did a simulation of my own, using Deal 3.08.

Here are the results:

for 5 spades with North and 4 with south with 30,000 deals these are the results:

2-2 split = 12165 (~40.55%)
3-1 split = 14971 (~49.9%)
4-0 split = 2864 (~9.54%)

for 6 spades with North and 3 with south, with 30,000 deals these are the results:

2-2 split = 12231 (~40.77%)
3-1 split = 14900 (~49.66%)
4-0 split = 2869 (~9.56%)


Here is the condition script used:

Quote

source format/none
set ns 6
set ss 3
set count 0
set ttcount 0
set tocount 0
set fzcount 0

main {
    if {[spades north] == $ns && [spades south] == $ss} {
        set sw [spades west]
        if {$sw == 2} {set ttcount [expr $ttcount + 1]}
        if {$sw == 1 || $sw == 3} {set tocount [expr $tocount + 1]}
        if {$sw == 4 || $sw == 0} {set fzcount [expr $fzcount + 1]}
        set count [expr $count + 1]
        accept
    }
    reject
}

deal_finished {
    puts "Deals = $count"
    puts "2-2 split = $ttcount"
    puts "3-1 split = $tocount"
    puts "4-0 split = $fzcount"
}

BebopKid, please post the simulation code/method you used.

[dake50]

Opponents SILENT with 11 ! ! hearts? Hearts must break 6-5/5-6 with KJ/AJ 5th in last to speak. Factor in the 6331/6322/6340 that only 7/6 slots remain. This reduces the unbalanced cases. I expect 2-2 spades is well over 54%

[BebopKid]

Excel macro with sheets in the workbook: "Hands", "Distributions", and "Summary"

Dim Deck(52) As Integer, DeckS(52) As Integer
' DeckS has the hands sorted by suit and rank, so that the Deck remains the unsorted master to retain random distribution
' Face value is card mod 13
' Suit value is int(card / 13)
' Examples: 51 is Ace of Spades, 3 is 4 of Clubs
Dim Faces(13) As String
' Faces contains a map to card ranks

Sub start_deck()
Dim i As Integer
For i = 0 To 51
Deck(i) = i
Next

i = 0
Faces(i) = "2"
i = i + 1
Faces(i) = "3"
i = i + 1
Faces(i) = "4"
i = i + 1
Faces(i) = "5"
i = i + 1
Faces(i) = "6"
i = i + 1
Faces(i) = "7"
i = i + 1
Faces(i) = "8"
i = i + 1
Faces(i) = "9"
i = i + 1
Faces(i) = "T"
i = i + 1
Faces(i) = "J"
i = i + 1
Faces(i) = "Q"
i = i + 1
Faces(i) = "K"
i = i + 1
Faces(i) = "A"

End Sub


Sub shuffle()
' Perform a realistic shuffle
Dim Deck1(26) As Integer, Deck2(26) As Integer
' Two half decks of equal size to be shuffled
Dim i As Integer, j As Integer, k As Integer
Dim total As Integer, flex As Integer
Dim i1 As Integer, i2 As Integer, i3 As Integer
Dim pick As Integer
total = 4 ' number of shuffles
flex = 4 ' maximum cards from each half deck to be shuffled per iteration

For j = 1 To total
' Make two half decks
For i = 0 To 25
Deck1(i) = Deck(i)
Deck2(i) = Deck(i + 26)
Next
i1 = 0 ' number of cards shuffled so far on this iteration
i2 = 26 ' number of cards left in half deck 1
i3 = 26 ' number of cards left in half deck 2
Do While i1 < 52 ' keep shuffling until the deck is full
If i2 > 0 Then ' make sure cards are left in half deck 1
pick = Int(Rnd * flex + 1) ' randomly choose number of cards to be shuffled
For k = 1 To pick ' add each shuffled card to the deck
If i2 > 0 Then
i2 = i2 - 1
Deck(i1) = Deck1(i2)
i1 = i1 + 1
End If
Next
End If
If i3 > 0 Then ' make sure cards are left in half deck 2
pick = Int(Rnd * 6 + 1) ' randomly choose number of cards to be shuffled
For k = 1 To pick ' add each shuffled card to the deck
If i3 > 0 Then
i3 = i3 - 1
Deck(i1) = Deck2(i3)
i1 = i1 + 1
End If
Next
End If
Loop
Next

End Sub

Sub sort_hands()
Dim i As Integer, j As Integer, temp As Integer, hand As Integer
For i = 0 To 52
DeckS(i) = Deck(i) ' copy deck order to a second eck to be sorted
Next
For hand = 0 To 3 ' sort by hand
For i = 0 + 13 * hand To 12 + 13 * hand - 1 ' use a selection sort to sort by suit and rank
For j = i + 1 To 12 + 13 * hand
If DeckS(i) < DeckS(j) Then
temp = DeckS(i)
DeckS(i) = DeckS(j)
DeckS(j) = temp
End If
Next
Next
Next
End Sub

Function sort_hand(ByVal Cards, idx) As String
' break each hand into suits
Dim retval As String, hand As Integer, suit As Integer, i As Integer
Dim temp As Integer
retval = ""

For suit = 0 To 2 ' use a modifed selection sort
For i = suit + 1 To 3
If Cards(idx, suit) < Cards(idx, i) Then
temp = Cards(idx, suit)
Cards(idx, suit) = Cards(idx, i)
Cards(idx, i) = temp
End If
Next
Next

For suit = 0 To 3
retval = retval + Str(Cards(idx, suit))
Next

sort_hand = retval

End Function

Function sort_suit(ByVal Cards, idx) As String
' break each suit into hands
Dim retval As String, hand As Integer, suit As Integer, i As Integer
Dim temp As Integer
retval = ""

For hand = 0 To 2 ' use a modified selection sort
For i = hand + 1 To 3
If Cards(hand, idx) < Cards(i, idx) Then
temp = Cards(hand, idx)
Cards(hand, idx) = Cards(i, idx)
Cards(i, idx) = temp
End If
Next
Next

For hand = 0 To 3
retval = retval + Str(Cards(hand, idx))
Next

sort_suit = retval

End Function

Sub print_dist(row As Long)
' output the distributions to the worksheet
Dim i As Integer, suit As Integer
Dim Hands(4, 4) As Integer, hand As Integer
Dim Suits(4, 4) As Integer
Dim temp As Integer
i = 0
For hand = 0 To 3 'count the distribution of hands
For suit = 3 To 0 Step -1
temp = 0
Do While (DeckS(i) >= suit * 13 And i < (hand + 1) * 13)
temp = temp + 1
i = i + 1
Loop
Hands(hand, suit) = temp
Next
Next

Worksheets("Distributions").Range("A" & row).Value = sort_hand(Hands, 0)
Worksheets("Distributions").Range("B" & row).Value = sort_hand(Hands, 1)
Worksheets("Distributions").Range("C" & row).Value = sort_hand(Hands, 2)
Worksheets("Distributions").Range("D" & row).Value = sort_hand(Hands, 3)
Worksheets("Distributions").Range("E" & row).Value = sort_suit(Hands, 3)
Worksheets("Distributions").Range("F" & row).Value = sort_suit(Hands, 2)
Worksheets("Distributions").Range("G" & row).Value = sort_suit(Hands, 1)
Worksheets("Distributions").Range("H" & row).Value = sort_suit(Hands, 0)

End Sub

Sub print_deal(row As Long)
' output the hands to the worksheet
Dim i As Integer, suit As Integer
Dim Hands(4) As String, hand As Integer
Dim Suits(4) As String
i = 0
For hand = 0 To 3 'insert a decimal character between the suits
Hands(hand) = ""
For suit = 3 To 0 Step -1
Do While (DeckS(i) >= suit * 13 And i < (hand + 1) * 13)
Hands(hand) = Hands(hand) + Faces(DeckS(i) Mod 13)
Suits(suit) = Suits(suit) + Faces(DeckS(i) Mod 13)
i = i + 1
Loop
If suit > 0 Then Hands(hand) = Hands(hand) + "."
If hand < 3 Then Suits(suit) = Suits(suit) + "."
Next
Next

Worksheets("Hands").Range("A" & row).Value = Hands(0)
Worksheets("Hands").Range("B" & row).Value = Hands(1)
Worksheets("Hands").Range("C" & row).Value = Hands(2)
Worksheets("Hands").Range("D" & row).Value = Hands(3)
Worksheets("Hands").Range("E" & row).Value = Suits(3)
Worksheets("Hands").Range("F" & row).Value = Suits(2)
Worksheets("Hands").Range("G" & row).Value = Suits(1)
Worksheets("Hands").Range("H" & row).Value = Suits(0)

End Sub

Sub deal()
Dim total As Long, i As Long
total = 65000 'number of deals
Call start_deck 'initialize all 52 cards

For i = 1 To total
If i Mod 500 = 0 Then Worksheets("Distributions").Range("I1").Value = i ' show progess on the worksheet
Call shuffle 'shuffle the cards
Call sort_hands 'sort the hands by suit and rank
Call print_deal(i + 1)
Call print_dist(i + 1) 'print the distribution to the worksheet
Next

Worksheets("Distributions").Range("A:H").Copy 'copy the distributions
Worksheets("Distributions").Range("J1").PasteSpecial 'paste the distributions to the columns where summary formulas are pointed

End Sub

[Trumpace]

BebopKid, looks like your shuffle algorithm isn't correct.

What in the world are you trying to do writing your own shuffling code?

In order to do simulations, you really need a very very good random number generator. The RND function is a really bad random number generator.

Even if it was good, I don't think your shuffle function would generate deals with uniform probability.

Basically, your random hand generation code is wrong.

[BebopKid]

Trumpace, on Sep 7 2007, 11:05 PM, said:

BebopKid, looks like your shuffle algorithm isn't correct.

Try it out. It works. It comes up with the expected results.

Anything else?

[han]

I can't take it anymore, sombody stop me.

[ralph23]

BebopKid, on Sep 8 2007, 12:22 AM, said:

Trumpace, on Sep 7 2007, 11:05 PM, said:

BebopKid, looks like your shuffle algorithm isn't correct.

Try it out. It works. It comes up with the expected results.

Anything else?

I think you should email Richard Pavlicek and explain your reasoning and results to him, and then take up writing Bobby Wolff and the bridge editor of the NY Times.

Don't pay any attention to the experimental results obtained by Trumpace; you know his simulations can't be right; because they don't match your results. Yours after all come up with the "expected results" (expected from your analysis that is); his doesn't.

After Pavlicek understands where he went wrong, and why his calculator and the other bridge calculators and sources are in error on the probabilities, based on your experiments, he'll probably offer you an introduction to them, and that will offer a considerably wider and more public forum.

After all, look at the consequence: you've disproved what everyone else thought they knew for a long long time. It's basically the Copernican Revolution in bridge probability theory. You'll be at least as famous as Goren, probably more so. You shouldn't waste another second in getting right on this.

[jtfanclub]

BebopKid, on Sep 7 2007, 11:22 PM, said:

Trumpace, on Sep 7 2007, 11:05 PM, said:

BebopKid, looks like your shuffle algorithm isn't correct.

Try it out. It works. It comes up with the expected results.

Anything else?

Oh Crap. I didn't even notice how bad this was until now.

Quote

I made 65,000 deals, of those 27411 deals had 6/3 suit splits between two hands

No. No no no no no no NO.

You tested when one player has six cards in a suit AND AT LEAST ONE OTHER PLAYER HAS EXACTLY THREE CARDS IN THE SUIT.

We want to know when one player has six cards in a suit AND HIS PARTNER HAS EXACTLY THREE CARDS IN THE SUIT.

What's the difference?

Let's deal out spades six times (this should look familiar by now):
1. S: 6 W: 3 N: 2 E: 2
2. S: 6 W: 2 N: 3 E: 2 <----
3. S: 6 W: 2 N: 2 E: 3
4. S: 6 W: 3 N: 3 E: 1 <----
5. S: 6 W: 3 N: 1 E: 3
6. S: 6 W: 1 N: 3 E: 3 <---

Your algorithm counts ALL SIX: 3 6322, 3 6331.
But in Fact, only THREE qualify, #2, #4, and #6: 1 6322, and 2 6331.

For the other three, there's a 3 card suit out there, all right, but it's not with partner, so it doesn't qualify.

So in other words, you're STILL double counting 6322s.

And the reason why your algorithm and your sample came out the same is because YOU MADE THE SAME BASIC ERROR IN BOTH OF THEM.

Man, if you still can't see it, I can't help you.

[jdonn]

Just to try and make sure it happens....

Bebop PLEASE read the post immediately prior to this one, and respond to it directly. Please. I'm begging. It shows why you are wrong. Clearly. You will understand. I promise. Just read it.