Best-hand dealing?

[allfail]

I believe the dealing rules are not completely random (by which I mean dealing randomly, and give the highest HCP hand to S) right now. I feel a change during perhaps, the end of January.

 

Statistically speaking, in my recent 100 boards both my point count and the point count combined for NS are low compared to average (if dealt randomly), roughly at 1 standard deviation; the chance for partner to have the worst hand among all players is too high compared to average, it's 40% and again at around 1 std deviation. I believe the more previous tournaments are similar I just yet to look at the records.

 

The worst stats I have (for now) is the chance for combined HCP>=24. In this 100 boards I only had 37% of my hands with 24 or more HCPs, whereas if dealt randomly it should be 46.5% and the standard deviation for 100 boards is ~5%. Of course it can just be that I am extremely unlucky (1 out of 40?) but it would be easy to check.

 

I am not saying adjusting how to deal is not a good thing. For one thing, this may help to reduce people winning just by playing very fast. Nevertheless, in my opinion for this to be a fair game, if the hands are not dealt randomly then the precise rule must be given so that people can plan their strategy accordingly.

[arigreen]

I believe the dealing rules are not completely random (by which I mean dealing randomly, and give the highest HCP hand to S) right now. I feel a change during perhaps, the end of January.

 

Statistically speaking, in my recent 100 boards both my point count and the point count combined for NS are low compared to average (if dealt randomly), roughly at 1 standard deviation; the chance for partner to have the worst hand among all players is too high compared to average, it's 40% and again at around 1 std deviation. I believe the more previous tournaments are similar I just yet to look at the records.

 

The worst stats I have (for now) is the chance for combined HCP>=24. In this 100 boards I only had 37% of my hands with 24 or more HCPs, whereas if dealt randomly it should be 46.5% and the standard deviation for 100 boards is ~5%. Of course it can just be that I am extremely unlucky (1 out of 40?) but it would be easy to check.

 

I am not saying adjusting how to deal is not a good thing. For one thing, this may help to reduce people winning just by playing very fast. Nevertheless, in my opinion for this to be a fair game, if the hands are not dealt randomly then the precise rule must be given so that people can plan their strategy accordingly.

The dealing is random. We deal the cards normally, then make South the hand with the most HCP. If two or more hands tie for the most HCP, South is chosen randomly from among those hands.

 

Your recent streak is unlucky, but it doesn't appear to be improbably unlikely to me. Consider that if there are 100 players who play 100 boards, 2 or 3 of them are likely to be as unlucky as you are. If you can find more than a few people who have experienced this unlucky streak during the same period of time (last 100 boards played) then I would be more surprised.

[allfail]

Well, I wanted to believe you but my stats just tell otherwise.

 

I just looked at my most recent 5 hand records (which I am the 1st place for one of them, and won money back in 2 or 3.), independent of the stats stated above. In those 123 boards, only in 38% of them, 47 boards, did NS have a combined HCP of 24 or more. Again I stressed that if the hands are dealt as you said, this probability should be around 46.5%. In addition, in those five tournaments not even a single one is above this number!

 

So combined with the above stats, one has to be 1/1000 to be this unlucky if the hands are dealt randomly. Even if we assume that is the case it still doesn't make sense. Why not? The reason is that I still have a net income (albeit small)! It's unimaginable if I am 1/1000 unlucky I can still get my money back since this is a -20% total sum game.

[cherdanno]

Where do you get the 46.5 % from?

[allfail]

That's the number I got by dealing 1,000,000 deals my self according to the rule stated above.

[arigreen]

I dealt a million hands using dealer, throwing out hands where any player had more HCP than South. NS had 23.2 HCP on average. NS combines for 24 or more HCP on about 44.3% of the hands.

 

I also produced 123 hands using dealer, constrained to give South the best hand. I repeated this experiment 100 times. In 11 of the 100 cases, NS had 24+ HCP on less than 39% of the hands.

 

 

So it seems that you have been a little bit unlucky, but not prohibitively so.

[bb79]

let's call the event that your side gets 24 or more hcp A. According to your values, A happens with p=46.5% (success) , doesn't happen with 1-p=53.5%. you repeated this experiment 123 times. you got 47 successes. mean was 57.2. standard deviation= sqrt(n*p*(1-p)) = 5.5317.

 

With Gaussian approximation, your z value is -1.75. Probability that you will get 47 or less successes is about 4% . not one in thousand.

[jdonn]

Instead of dealing a bajillion hands and comparing with someone else's bajillion hands and getting different results, can't someone just calculate this? Although there are a huge amount of possible bridge hands it's still a finite number, and we have a lot of talented people around....

[kenrexford]

I sat down and shuffled a new deck, and I dealt out five full deals in a row. Each time, I had at least one seven in my hand, but not one of them was the seven of diamonds. That's bullshit.

[allfail]

to bb79,

 

That is the same way as I calculated. 1/1000 is from the fact that if you take my open post into account...

[allfail]

It is not as easy as it seems to calculate this probability exactly... Nevertheless, if we have an ideal random distribution it should be very accurate to just simulate it by dealing a lot of deals. In particular, by the calculation above one should expect the standard deviation (error bar) of the percentages above is ~0.05% for a million effective deals. (For arigreen's method it should be 250K effecitve deals and the error is ~0.1%).

 

Therefore it is actually an interesting thing that we get so different answers. I checked my program and didn't find any bugs, but the answers got from a million deals seems to vary too much. One of the possibility is that my random generator is cycling and I might have to reseed after some number of deals. Still, my expectation value is at least 45.9% (the least number I have seen for a simulation size larger than 10K) so we are still not consistent. I am using the open source randomlib for generating random numbers.

[Cascade]

I sat down and shuffled a new deck, and I dealt out five full deals in a row. Each time, I had at least one seven in my hand, but not one of them was the seven of diamonds. That's bullshit.

Fire the dealer.

[cherdanno]

I also get 44.3% as a probability, using Thomas Andrews' deal.

[Cascade]

Here are the probability distributions for the hcp in the best hand and the hcp in the best hand added to a random other hand:

 

10	0.003827362
11	0.05152155
12	0.117524213
13	0.161255334
14	0.168641459
15	0.147463208
16	0.116571669
17	0.084991426
18	0.058159037
19	0.03759938
20	0.023355396
21	0.013713674
22	0.007622938
23	0.004061244
24	0.002028862
25	0.000959125
26	0.000423469
27	0.000178074
28	6.73866E-05
29	2.4213E-05
30	7.97881E-06
31	2.21862E-06
32	6.23849E-07
33	1.27792E-07
34	2.5627E-08
35	3.56629E-09
36	3.42912E-10
37	2.28608E-11

 

The mean hcp in the best hand is 14.86342064

 

And by adding 1/3 of the remaining hcp the mean combined can be calculated from this as 23.24228043

 

14	0.000646546
15	0.002607918
16	0.008293366
17	0.018544076
18	0.036498711
19	0.059232247
20	0.087698383
21	0.106277789
22	0.122894349
23	0.113749227
24	0.112847868
25	0.087780504
26	0.077484416
27	0.053410929
28	0.042466469
29	0.026556234
30	0.019033764
31	0.010664609
32	0.006799004
33	0.003368797
34	0.00184661
35	0.000774677
36	0.000357965
37	0.000115896
38	3.98317E-05
39	8.79363E-06
40	1.02382E-06

 

The mean combined hcp is 23.24228043 which concurs with the above.

 

The probability of having 24 or more hcp is 0.44355739.

 

The numbers were calculated using a program that calculated the probabilities of each combination of high cards. It then checked to see if north had the most hcp (including ties) and then added the hcp for north and south if so.

 

The probability of having the highest number of hcp is 0.275540439

[hanp]

In browsing through my recent hands from the main bridge club, I felt that I had the diamond 4 quite often. And indeed, it turned out that in the last 100 hands, I had that card 39 times, 14 more than the expected 25! That's more than 2 standard deviations if I'm not mistaken, which proves that the dealer program must indeed be flawed.

 

Statistics can be dangerous.

[allfail]

While I agree generally with the comment, in light of the fact that we have 52 different cards in a deck, having any one of them being out of 2 standard deviations is actually quite normal.

 

However, if you always choose to watch, say how many Aces you got in average, then the number would "usually" turn out to be much normal.

[allfail]

Now I am getting really confused... anyone wanna help here?

 

I stabilized my random generator now it is working properly. The produced result always lies within the expected standart deviation. However, the number I got is

15.11+-0.002 for the best hand

and a 45.98%+-0.05% chance to have a combined HCP>=24.

 

My program is really simple. It just deals the 16 spotted cards to the four hands with probabilities proportional to the "vacancies" left in the hand. Then I chose the hand with the most HCP as the best hand and another random one as its partner.

[cherdanno]

Now I am getting really confused... anyone wanna help here?

Nope :)

 

Seriously, there are many ways to make mistakes with such a program.

[allfail]

For example?

[hrothgar]

I recommend searching on the user ID Bebopkid and looking at his travails...

[jdonn]

I recommend searching on the user ID Bebopkid and looking at his travails...

♥

[allfail]

Aha!

 

Now I know why there is such discrepancy. In fact, dealing randomly and give the best hand to South is quite different from dealing and discard those which South does not have the best hand.

 

The difference is subtle though, and that's why people (including myself) did not notice this previously. The problem comes in when there are ties: Imagine a layout of point counts. If the HCPs in all hands are different, then the accept rate (of the second method) is 1/4 whereas in the first method it is always 1. Now if there is a tie with two hands at the highest HCP then the accept rate for the second method would be 1/2, and vice versa. That is, the deal-and-throw-away-unwanted method has a higher accept rate for tied deals. But what point counts do the tied boards tend to have? They strongly tend to be weaker hands! For instance, a 10-count highest HCP board would always be accepted since every hand would have a 10-count and a 16-count board would be accepted only with a chance everslightly higher than 1/4. This in total results in a ~0.3 point difference in average, and ~2% chance of having a total of 24 HCPs or more as I have also checked the numbers with the second method.

 

Now that we sort this out, it is clear to me that BBO uses the deal-and-throw-away method. It should be stated clearly somewhere as there is a real difference.

 

I thank those who suggested me to look at previous records since they can't be sure about the details in my program and thus my trustability. However, for those who suggests a program like this can go wrong in many ways I think they should either check their own programming ability or stop their ignorance.

[kenrexford]

Now that we sort this out, it is clear to me that BBO uses the deal-and-throw-away method. It should be stated clearly somewhere as there is a real difference.

I find it rather frightening that anyone would adjust some aspect of their bridge game to account for the slight difference between the apparently assumed method and the deal-and-throw-away method.

[cherdanno]

However, for those who suggests a program like this can go wrong in many ways I think they should either check their own programming ability or stop their ignorance.

Says the person who

- first had to "stabilize his random generator" until it was working properly, and

- missed the obvious difference between the two possible ways of ensuring that South has at least as many hcp as everyone else.

[allfail]

To my own defense, my number was never off more than a standard deviation so even the not-so-good random generator works ok. In fact, what I changed was just from using the global random number to newing a class member in the RandomLib. I don't really know the difference between the two. But as so much as that it is the only perceptible difficulty in writing such a dealing program.

 

In addition, I hope I did present all the necessary details of what I did in this post so the "obvious" differences in the result between the two possible ways was not really obvious to all the responders on this post and you may be the only exception. If you think this is obvious why don't you be so kind and let us know instead of just replying a "nope"?

 

I acknowledged that you verified the 44.3% percentage in previous posts but I just couldn't figure it could be the same person who just responded a "nope" up there. Frankly speaking, why not just bypass the post if you don't want to share your knowledge?

 

On the other hand, strategy-wise these two method does have some impact. To begin with, we all recognize in a time-limited, total point game, the overall strategy would be to ignore as much partials as possible. Therefore, one might open quite heavily; for example, myself (previously) open only 16+ any shape any vul. and 19+ when nonvel, 3rd or 4th seat. This action can be interpreted as choosing to open with a threshold of game possibility.

 

However, why doesn't one just open when game is almost certain? The reason behind, of course, is that there is a cost of not bidding. The cost is not quite the time spending passout, instead is that every few boards even if you pass your opps might open. This, although mostly ending up in partials, costs a lot of time (maybe as much as 1.5 mins?) as GiB plays slower in partials. So to maximize the games in a given time period we have to open some number of hands provided that a game is somewhat likely.

 

Now we compare the two distributions. Note in the current method you would have twice to thrice as many of those tied hands compared to the first method, in which if you don't open your opps might. This reduces the optimum threshold of game possibility for one to open. I am not sure how large an effect this is, but among 20-25 boards I played in a tournament I would encounter, maybe 1/4 to 1/3 of the boards to be in the situation that I want it to pass out but some opp opened. Factoring in that there has to be a tie for us to have a difference, it's maybe like 1-2 boards per round.

 

I am not sure if this is an observable effect, but I do sense this kind of thing happened more often to me after the end of January... Is it even possible that BBO had changed the dealing policy by then?