"probabilistic" opening bids

[semeai]

So who's responsibility is it to perform these calculations? Is it reasonable to describe the hand as in the OP, and expect opponents to calculate the probabilities themselves at the table? Or should the pair playing this system figure this out, so that they can provide more useful disclosure?

 

I have no laws expertise, but I think OP (plus randomization method) is enough disclosure, and it's up to the opponents to work out that this makes it less likely it's the spade hand.

[hrothgar]

 

Concerning practical realization of the RNG, there is a very simple method - shuffle your hand before you look at it and then interpret red cards as zeros and black cards as ones - you get 13 bits of randomness, which should be enough for any practical purpose!

 

 

Unfortunately, these bits are strongly correlated with the shape of your hand...

 

A better scheme might be to measure "transitions"

 

Shuffle your cards.

Look at card 1

 

If card 1 is higher in rank than card 2, code a 1

If card 2 is lower in rank than card 2, code a 0

If you have a tie, ignore this bit

 

Move to card 3

 

If card 3 is higher in rank than card 4, code a 1

If card 3 is lower in rank than card 3, code a 0

If you have a tie, ignore this bit

 

Move to card 5...

 

You'll end up with less than six bits of randomness, but I think this will eliminate a lot of issues with covariance...

[gombo121]

The 2♥ bid is affected as well. It changes the probability that he has a heart hand or a spade hand. Without the 20% it would be much more likely it was the spade hand, but with that it's probably close to even.

 

That's exactly the point of the method - to introduce a weak option, but don't let it to be too frequent.

 

2hrothgar: Thank you for very enlightening piece.

[gombo121]

Unfortunately, these bits are strongly correlated with the shape of your hand...

 

Valid point. Then we can use "even" cards as zeros, "odd" as ones and ignore aces - that should not to correlate to any game-related factor.

[hrothgar]

Valid point. Then we can use "even" cards as zeros, "odd" as ones and ignore aces - that should not to correlate to any game-related factor.

 

>> Rank = 1:13;
>> Rank = Rank'

Rank =

    1
    2
    3
    4
    5
    6
    7
    8
    9
   10
   11
   12
   13

>> sum(Rank(1:2:end))

ans =

   49

>> sum(Rank(2:2:end))

ans =

   42

 

Trust me, transitions is the way to go

If you need additional bits you can build in whether the suit is higher or lower in rank...

(more chances of a tie here, but you'll still get a few more bits)

[gombo121]

Or he might open a 3532 15-count sometimes 1NT and sometimes 1♥. Does it really matter if it is random, semirandom or completely deterministic which of these hands he chooses which opening bid with?

 

Well, it may.

Like, you counted opponent's hand to be 3532 and know him to hold AK in hearts in K in both spades in diamonds;you need to place him with either ♥Q or ♣Q. If the opponent never opens 1NT with weak doubleton, you have a clear-cut case for ♣Q; if he choose randomly, it is probably for ♥Q; if it is semirandom, you'd really like to have an idea about factors affecting his choice.

 

True, it is not often when it would matter, but it may.

[gombo121]

ans = 42

I like the answer, but I didn't get the point. :) I suggested interpreting sequence like 6 5 Q A K 10 2 J as 0101001 (ace is ignored so that number of zeros and ones are equal).

 

And, yes, transitions certainly work.

[hrothgar]

I like the answer, but I didn't get the point. :) I suggested interpreting sequence like 6 5 Q A K 10 2 J as 0101001 (ace is ignored so that number of zeros and ones are equal).

 

And, yes, transitions certainly work.

 

I am (obtusely) noting that there is a correlation between hand strength and bits...

[barmar]

I am (obtusely) noting that there is a correlation between hand strength and bits...

Is there? Take a hand and convert it to bits using the odd/even rule . Replace one of the cards with the next higher card, and one of the bits will flip. But the same thing happens if you replace that card with the next lower card. The bits for QJT QJT QJT QJT9 are the same as for 432 432 432 5432.

 

Ignoring aces seems to mess this up, since replacing a King with an Ace causes you to lose bits. I suggest that Aces be assigned bits based on the color or shape of the suit (not rank, as that would then correlate with whether your hand is major or minor-oriented).

[hrothgar]

Is there? Take a hand and convert it to bits using the odd/even rule . Replace one of the cards with the next higher card, and one of the bits will flip. But the same thing happens if you replace that card with the next lower card. The bits for QJT QJT QJT QJT9 are the same as for 432 432 432 5432.

 

 

Which hand is stronger?

 

♠ QT86

♥ QT86

♦ QT86

♣ QT

 

or

 

♠ KJ97

♥ KJ97

♦ KJ9

♣ KJ

 

On average, the "even" cards are weaker than the odd cards.

[Free]

While discussing building a system with a friend I arrived to a curious question: suppose I'd like to introduce an two-way opening 2♥, which promise

1) 11-15, 6+♥

2) 5-8, 5+♠, 20%(!)

but with a twist - second variant is used not each time when a suitable hand presents itself, but in only, say, 20% cases chosen completely at random.

 

Is there any general regulations against such agreements (besides it is being obviously brown sticker)? I feel that probably there are some, but cannot come up with any concrete example.

I haven't read everything in the thread, but I want to point out that this opening is NOT brown sticker. There's only 1 weak version in there, and the suit is known in that case.

[JanM]

I haven't read everything in the thread, but I want to point out that this opening is NOT brown sticker. There's only 1 weak version in there, and the suit is known in that case.

 

I think you are misreading the definition of Brown Sticker bids. The rule that a bid is not BS if its only weak meaning promises a specific suit is:

The bid always shows at least four cards in a

known suit if it is weak. If the bid does not show a known four

card suit it must show a hand a king or more over average

strength.

 

10-15 does not promise a king or more over average strength.

[ggwhiz]

Kudos to whomever arranged to have such calls known as "BS" bids.

 

This one is more like "Probable Ballistic".

[Vampyr]

It does seem like any attempt at randomisation will be highly influenced by the shape and/or strength of the hand. But that is OK, because since the method of randomisation must be disclosed to the opponents anyway, this will promote fuller disclosure.

[hrothgar]

It does seem like any attempt at randomisation will be highly influenced by the shape and/or strength of the hand. But that is OK, because since the method of randomisation must be disclosed to the opponents anyway, this will promote fuller disclosure.

 

Wrong

 

The high-low / low-high transition scheme that I described in this thread is uncorrelated with shape or strength

[JanM]

Kudos to whomever arranged to have such calls known as "BS" bids.

 

I believe that would be Edgar Kaplan :)

[lamford]

Concerning practical realization of the RNG, there is a very simple method - shuffle your hand before you look at it and then interpret red cards as zeros and black cards as ones - you get 13 bits of randomness, which should be enough for any practical purpose!

(OK, it won't work in online bridge, but then you probably can use RNG of your PC directly).

A much better method of randomising an opening bid, which you can disclose easily to opponents, and will have considerable advantages in the play, is the following, which we employ against strong clubbers, where ANY defence is permitted:

Bid Description Frequency

1NT Any deuce 0.696

1S Any trey 0.212

1H Any four 0.064

1D Any five 0.020

The lower card takes priority for deciding which bid to make. So 1D means you have a five, but no card of lower rank.

 

There are many advantages when defending because you know, if your partner overcalls 1S, he has no deuce and at least one three, so information may be available to you but not to declarer. You need to be careful playing the card you are known to have sometimes! This method is, bizarrely, allowed over a two-card club suit at level 2 in the Newbridge Novice Pairs under Orange Book 11M2. Disclosure under OB10A6 can certainly be full and frank. I think it is Brown Sticker for an opening bid, however.

[lamford]

An idea that is often floated around the poker community is to use the position of the seconds hand of your watch as an RNG.

A breach of 40C3(a) in bridge, however; a watch could not be used, for example, to decide which to play from QJ doubleton.

[barmar]

On average, the "even" cards are weaker than the odd cards.

You're right, because the lowest card is even, and the highest card is odd. So there's an assymetry in my "increase by 1 = decrease by 1", because you can't increase beyond an ace or decrease below 2.

 

The person who suggested the odd/even method said to ignore aces because they cause an imbalance between even and odd. But including them would solve this problem, since the highest and lowest cards would be even.

[aguahombre]

The person who suggested the odd/even method said to ignore aces because they cause an imbalance between even and odd. But including them would solve this problem, since the highest and lowest cards would be even.

Are you sure that one or 13 is even?

[hrothgar]

You're right, because the lowest card is even, and the highest card is odd. So there's an assymetry in my "increase by 1 = decrease by 1", because you can't increase beyond an ace or decrease below 2.

 

The person who suggested the odd/even method said to ignore aces because they cause an imbalance between even and odd. But including them would solve this problem, since the highest and lowest cards would be even.

 

What's more significant in terms of the difference in trick taking?

 

The difference between a King and a Queen or the difference between a deuce and a trey?

[barmar]

What's more significant in terms of the difference in trick taking?

 

The difference between a King and a Queen or the difference between a deuce and a trey?

Even better point. Maybe ignore all honor cards, and compute the parity of the spot cards.

[hrothgar]

Even better point. Maybe ignore all honor cards, and compute the parity of the spot cards.

 

Or, alternatively, use a system that works like the one I showed earlier...

[phil_20686]

You could get a very simply, and fairly accurate way of getting simple fractions by doing modulo arithmetic. Give every card a number between 1 and 13, total them, and now if you divide by, say 3, and take the remainder, it is very close to a 1/3 chance.

 

Interestingly, this is a simple appplication of the central limit theorem, it works because there are so many cycles of modulo three, up to a typical hand total, that the probability distribution is essentially Gaussian (and hence uncorrelated). You could use this to give you accurate fractions of anything up to about 6 I think. This ought to be enough randomisation.

[hrothgar]

You could get a very simply, and fairly accurate way of getting simple fractions by doing modulo arithmetic. Give every card a number between 1 and 13, total them, and now if you divide by, say 3, and take the remainder, it is very close to a 1/3 chance.

 

Interestingly, this is a simple appplication of the central limit theorem, it works because there are so many cycles of modulo three, up to a typical hand total, that the probability distribution is essentially Gaussian (and hence uncorrelated). You could use this to give you accurate fractions of anything up to about 6 I think. This ought to be enough randomisation.

 

For anyone who needs a simple explanation:

 

Let's assume that there is some action that you want to take 1/4 of the time.

 

1. 
    
   
2. Add up the value of all your cards using a 1:13 scale
   
3. Divide by 4
   
4. If the remainder is 1, take the action
   
5. If the remainder is not one, do something else
   

 

If you wanted to take an action 20% of the time (1/5th of the time) simply divide by 5

 

There are a couple problems with this technique:

 

1. Here, once again, the strength of your hand is correlated with the RNG

 

2. When we sum the cards, we get something that looks close to a bell curve. When we take the mod of the sum, numbers close to the peak are going to occur more often. (Hence Phil's comments about choosing small values like 1/2 - 1/6)

 

Personally, I still like my transitions scheme which generates a uniform distribution.

If we can pull eight bits off the transitions - which seems reasonable if we include both rank and suits - and marry this to the Phil's modulus suggestion we get the best of both worlds...

 

Cards = 1:13

Cards = Cards'

Cards = repmat(Cards,4,1)

 

%% shuffle

 

simlength = 1000000

 

MC_Result = zeros(simlength, 1);

 

for i = 1:simlength

 

index = randperm(52);

Cards = Cards(index);

Card_Sum = sum(Cards(1:13));

Running_Card_Sum(i) = Card_Sum;

MC_Result(i) = mod(Card_Sum,4);

 

end

 

tabulate(Running_Card_Sum)

 

Value    Count   Percent
     1        0      0.00%
     2        0      0.00%
     3        0      0.00%
     4        0      0.00%
     5        0      0.00%
     6        0      0.00%
     7        0      0.00%
     8        0      0.00%
     9        0      0.00%
    10        0      0.00%
    11        0      0.00%
    12        0      0.00%
    13        0      0.00%
    14        0      0.00%
    15        0      0.00%
    16        0      0.00%
    17        0      0.00%
    18        0      0.00%
    19        0      0.00%
    20        0      0.00%
    21        0      0.00%
    22        0      0.00%
    23        0      0.00%
    24        0      0.00%
    25        0      0.00%
    26        0      0.00%
    27        0      0.00%
    28        0      0.00%
    29        0      0.00%
    30        0      0.00%
    31        0      0.00%
    32        0      0.00%
    33        0      0.00%
    34        0      0.00%
    35        0      0.00%
    36        0      0.00%
    37        0      0.00%
    38        0      0.00%
    39        1      0.00%
    40        0      0.00%
    41        1      0.00%
    42        2      0.00%
    43        3      0.00%
    44        5      0.00%
    45        9      0.00%
    46       12      0.00%
    47       13      0.00%
    48       32      0.00%
    49       41      0.00%
    50       54      0.01%
    51       80      0.01%
    52      105      0.01%
    53      149      0.01%
    54      178      0.02%
    55      274      0.03%
    56      367      0.04%
    57      453      0.05%
    58      635      0.06%
    59      773      0.08%
    60     1084      0.11%
    61     1318      0.13%
    62     1643      0.16%
    63     1957      0.20%
    64     2419      0.24%
    65     2962      0.30%
    66     3610      0.36%
    67     4431      0.44%
    68     5213      0.52%
    69     5923      0.59%
    70     6981      0.70%
    71     8252      0.83%
    72     9502      0.95%
    73    10853      1.09%
    74    12155      1.22%
    75    13781      1.38%
    76    15277      1.53%
    77    17014      1.70%
    78    18921      1.89%
    79    20259      2.03%
    80    21877      2.19%
    81    23693      2.37%
    82    25247      2.52%
    83    26853      2.69%
    84    28288      2.83%
    85    29350      2.94%
    86    30834      3.08%
    87    31693      3.17%
    88    32632      3.26%
    89    33040      3.30%
    90    33619      3.36%
    91    33486      3.35%
    92    33185      3.32%
    93    33083      3.31%
    94    32476      3.25%
    95    31501      3.15%
    96    30625      3.06%
    97    29393      2.94%
    98    28009      2.80%
    99    26812      2.68%
   100    25237      2.52%
   101    23647      2.36%
   102    22210      2.22%
   103    20280      2.03%
   104    18555      1.86%
   105    16760      1.68%
   106    15274      1.53%
   107    13500      1.35%
   108    12209      1.22%
   109    10933      1.09%
   110     9391      0.94%
   111     8353      0.84%
   112     7178      0.72%
   113     5965      0.60%
   114     5160      0.52%
   115     4391      0.44%
   116     3704      0.37%
   117     3176      0.32%
   118     2453      0.25%
   119     1965      0.20%
   120     1673      0.17%
   121     1303      0.13%
   122      999      0.10%
   123      828      0.08%
   124      624      0.06%
   125      463      0.05%
   126      340      0.03%
   127      279      0.03%
   128      222      0.02%
   129      153      0.02%
   130      108      0.01%
   131       73      0.01%
   132       48      0.00%
   133       38      0.00%
   134       25      0.00%
   135       15      0.00%
   136        9      0.00%
   137        5      0.00%
   138        4      0.00%
   139        5      0.00%
   140        2      0.00%
   141        1      0.00%
   142        2      0.00%
   143        1      0.00%
   144        0      0.00%
   145        1      0.00%