Odds Question

[kenrexford]

I keep getting the same answer in my head, no matter how I think about it. I'm curious if what seems like nothing in the end is in fact nothing in the end, even though I want it to not be so.

 

Here's the question: Suits fall in one of two parities (I am dealt either three odd-numbered suits and one even-numbered suit OR three even-numbered suits and one odd. So, if I discover the nature of one of the suits, do the odds favor a different suit being of the ame nature? In other words, if LHO has three spades, do the odds favor him also having an odd number of hearts?

 

The math seems to suggest that the answer is no.

 

If spades are odd, then the "odds" are roughly 75% that this person has three odds and an even, right? When that is accurate, then 2/3 of the remaining suits will be odd. However, I only have a 75% reliability to the assumption that 2/3 of the suits will be odd. 3/4 of 2/3 is 6/12, or 50-50.

 

How about the opposite? 25% of the time, spades, if odd, will be the only odd suit. When that happens, all of the other suits will be even. That's 1/4. However, I have a large unreliability factor on the "it is the opposite" hypo, with 75% of the time this thesis failing, except that the false thesis will work 1/3 of that failed time. 3/4 of 1/3 is 3/12, or 1/4. 1/4+1/4=1/2. Same 50-50 scenario.

 

Knowing two suits does me no better.

 

What if I know one suit and need to then know if two suits will both behave in the same manner? 25% of the time, they will assuredly, because the known is the odd-man-out. When the known is one of three, 75% of the time, then the odds of the other two both being the same type are one in three. 3/4 of 1/3 is that stupid 1/4. 1/4+1/4=1/2.

 

Am I missing something, or does knowledge in this area ever give any odds advantage? Obviously, three knowns yield a known, but can any lesser knowledge help here? Also obviously two knowns yield a "known" of sorts (two matches yield two non-matches, but two non-matches yield a match), but these are always 100% knowns.

[hotShot]

Ken what you say applies to the suit distribution between the hands and to the pattern of a single hand.

You know your hands shape and dummies shape, if you additionally know something about LHO or RHO's length in one suit you can combine those informations, did you take that into account?

[MFA]

I think it's a blind lead, Ken.

 

If we know the spade distrubution and want to calculate odds about the heart distribution, then all the minor cards are 'equals'.

 

In a sense, it's just random that we call the 13 diamonds a suit and the 13 clubs a suit. Imagine a different game with 5 suits. Spades, hearts, diamonds, club 2-9, club honours. In this game with 5 suits, we would have a different hand pattern with odd/even parity hands. But surely your problem with the heart distribution is the same. The solution of this problem cannot depend on how we arbitrarily have defined the concept "suit".

 

In other words, the complexity of this problem only allow us to focus on three types of cards:

1 - cards that we can place for sure (here: spades)

2 - cards that we cannot place (here: the minors)

3 - cards that we want to make calculations about (here: hearts)

Splitting up category 2 is not giving us any extra information.

[ArtK78]

Unless I am missing something, there is nothing here.

 

You have 13 cards in each hand. If you know how many cards are in one suit, then you know how many cards are in the remaining 3 suits. The number of cards must add up to 13. Everything else follows from that.

 

It really is no more complicated than that.

[kenrexford]

I think it's a blind lead, Ken.

 

If we know the spade distrubution and want to calculate odds about the heart distribution, then all the minor cards are 'equals'.

 

In a sense, it's just random that we call the 13 diamonds a suit and the 13 clubs a suit. Imagine a different game with 5 suits. Spades, hearts, diamonds, club 2-9, club honours. In this game with 5 suits, we would have a different hand pattern with odd/even parity hands. But surely your problem with the heart distribution is the same. The solution of this problem cannot depend on how we arbitrarily have defined the concept "suit".

 

In other words, the complexity of this problem only allow us to focus on three types of cards:

1 - cards that we can place for sure (here: spades)

2 - cards that we cannot place (here: the minors)

3 - cards that we want to make calculations about (here: hearts)

Splitting up category 2 is not giving us any extra information.

That makes a lot of sense.

[skjaeran]

Try this site: http://prismsignals.com/

You don't need to use the signals to benefit from the theory.

[kenrexford]

Try this site: http://prismsignals.com/

You don't need to use the signals to benefit from the theory.

I have known about prism signals from Vinje back when I heard about it when the first George Bush was president. I never have understood why this is deemed "encrypted." But, that was the source of my question.

[Cascade]

I am not sure if this is what you want but you can easily calculate the a priori probabilities of having any number of hearts given you have a certain number of spades. These numbers would vary depending on how many hearts, diamonds and clubs you have in your own hand.

 

It turns out that if you see:

 

0, 1, 4, 5, 6, 10, 11, 12, 13 (trivially) spades then you are more likely to have an even number of hearts

 

and

 

2, 3, 7, 8, 9 spades then you are more likely to have an odd number of hearts.

 

This seems to suggest that if you see:

 

0, 4, 6, 10, 12 spades then the hand is more likely to have three even suits

 

3, 7, 9 spades then the hand is more likely to have three odd suits.

 

If you know two suits and the total is even then it is exactly 50-50 whether a third suit is even or odd.

 

If the total is 1, 5, 9, 13 then you are more likely to be even for the other suits.

 

3, 7, 11 then you are more likely to be odd for the other suits.

 

Here are the numbers for the number of hearts given each number of spades:

 

No Spades

0	0.00128048
1	0.015457218
2	0.074194646
3	0.187032337
4	0.275047554
5	0.247542798
6	0.138971396
7	0.048639988
8	0.010422855
9	0.001316017
10	9.1549E-05
11	3.12099E-06
12	4.16132E-08
13	1.23116E-10

Even 0.50000852
Odd  0.49999148

One Spade

0	0.002469496
1	0.025682762
2	0.105941393
3	0.228501045
4	0.285626306
5	0.216474674
6	0.101021515
7	0.02886329
8	0.004919879
9	0.000475351
10	2.37675E-05
11	5.18564E-07
12	3.32413E-09

Even 0.50000236
Odd  0.49999764

Two Spades

0	0.004609727
1	0.041199431
2	0.145409756
3	0.266584552
4	0.280615318
5	0.17678765
6	0.067347676
7	0.01530629
8	0.001996473
9	0.000138644
10	4.43661E-06
11	4.65378E-08

Even 0.499983386
Odd  0.500016614

Three Spades

0	0.008355129
1	0.063892165
2	0.191676496
3	0.295921608
4	0.258931407
5	0.133164724
6	0.040352947
7	0.007017904
8	0.000657928
9	2.92413E-05
10	4.49866E-07

Even 0.499974358
Odd  0.500025642

Four Spades

0	0.014744346
1	0.095838248
2	0.242117679
3	0.310717689
4	0.221941206
5	0.09079413
6	0.021053711
7	0.002631714
8	0.000157903
9	3.37399E-06

Even 0.500014846
Odd  0.499985154

Five Spades

0	0.02539304
1	0.138993483
2	0.291886314
3	0.305785662
4	0.173741853
5	0.054388754
6	0.009064792
7	0.000725183
8	2.09188E-05

Even 0.500106918
Odd  0.499893082

Six Spades

0	0.042767225
1	0.194590876
2	0.333584358
3	0.277986965
4	0.120863898
5	0.027194377
6	0.002900734
7	0.000111567

Even 0.500116215
Odd  0.499883785

Seven Spades

0	0.070565922
1	0.262101996
2	0.357411813
3	0.227914779
4	0.071223368
5	0.010256165
6	0.000525957

Even 0.49972706
Odd  0.50027294

Eight Spades

0	0.114249588
1	0.337555601
2	0.352231931
3	0.161439635
4	0.032287927
5	0.002235318

Even 0.498769446
Odd  0.501230554

Nine Spades

0	0.181760708
1	0.410937253
2	0.30820294
3	0.090406196
4	0.008692903

Even 0.498656551
Odd  0.501343449

Ten Spades

0	0.284495021
1	0.46230441
2	0.221906117
3	0.031294452

Even 0.506401138
Odd  0.493598862

Eleven Spades

0	0.438596491
1	0.456140351
2	0.105263158

Even 0.543859649
Odd  0.456140351

Twelve Spades

0	0.666666667
1	0.333333333

Even 0.666666667
Odd  0.333333333

Thirteen Spades

0	1

Even 1
Odd  0

[pclayton]

Try this site: http://prismsignals.com/

You don't need to use the signals to benefit from the theory.

I have known about prism signals from Vinje back when I heard about it when the first George Bush was president. I never have understood why this is deemed "encrypted." But, that was the source of my question.

I got the Vinje book when Reagan was Prez. His 1st term :lol:

 

It is bizarre now as it was then. As a new player, I had no idea how complicated this game was. When I was reading it, all I could think was ".....wow, I'm just NOT getting this".

[xcurt]

I never have understood why this is deemed "encrypted."

I don't think these are encrypted. Encryption implies the presence of a key permitting the message to be unscrambled. Pattern-type signaling methods should be thought of as a different coding scheme. Instead of sending, for example, for a count-happy pair:

 

true -> even number of spades and then

false-> odd number of hearts

 

you send (count hearts) ^ (count spades). Later you send either count(hearts), or you send count(spades) -- it does not matter -- allowing the first message to be decoded.

 

It seems, at least if you believe the Vinje and Prism claims, that Prism is a more efficient coding scheme than sending count of the suits over one by one. My understanding of why this is is that you frequently have some information about declarer's hand pattern from the auction and when you factor this information in, you can count out more hands after only one signal.

 

The GCC says something about "mumble, mumble, only right-side-up or upside-down coding schemes, mumble mumble." I don't see why this prohibits pattern-type signaling methods as long as high-low ALWAYS means "odd pattern" or always means "even pattern."

 

This does not mean that your local cop^H TD won't enforce the rules to his liking, however.

[kenrexford]

Try this site: http://prismsignals.com/

You don't need to use the signals to benefit from the theory.

I have known about prism signals from Vinje back when I heard about it when the first George Bush was president. I never have understood why this is deemed "encrypted." But, that was the source of my question.

I got the Vinje book when Reagan was Prez. His 1st term :)

 

It is bizarre now as it was then. As a new player, I had no idea how complicated this game was. When I was reading it, all I could think was ".....wow, I'm just NOT getting this".

You're an old fart! :lol:

[skjaeran]

Try this site: http://prismsignals.com/

You don't need to use the signals to benefit from the theory.

I have known about prism signals from Vinje back when I heard about it when the first George Bush was president. I never have understood why this is deemed "encrypted." But, that was the source of my question.

I got the Vinje book when Reagan was Prez. His 1st term :)

 

It is bizarre now as it was then. As a new player, I had no idea how complicated this game was. When I was reading it, all I could think was ".....wow, I'm just NOT getting this".

You're an old fart! :)

Damn you Ken, you're insulting me. I got the Norwegian original book earlier (it was published in 1976). B)

[kenrexford]

I'm an old fart, too. I was just wet behind the years a little longer than I should have been back then. LOL

[jikl]

Trying to remember who wrote the book, but you want the Cheron book I think. Is is out of print but some people may still have it for sale second hand. This is the bible for odds.

 

Sean