[Free]

The problem with taking averages is that 50 hands is way too few to draw any conclusions. Pretty much every tournament you will ever play, one side will have more HCP than the other, even with hand dealt cards or a true randomizer. It's like flipping a coin 50 times: the chance that you flip exactly 25 times heads is rather small.
20.80HCP on average is not that big a difference.

What made me stop playing moneybridge is the fact that we keep changing sides. Although it has no influence on the long run average, I got the impression there were huge streaks of HCP either for me or for my opponent. In fact, I even calculated it once, and not switching sides would've resulted in an average closer to 20HCP. And this happened every single time. NS gets 25HCP 2 deals in a row while we're sitting EW, you expect EW to get some HCP soon and what happens: you were right but you also switched sides, so another game for your opponent. And vulnerabilities are also cruel: you have streaks where you're Vul 75% of the time (great, but then your opponent leaves) but you also have streaks were your opponent is Vul 75% of the time while you stay NV 75% of the time. One should expect to be Vul 50% of the time and NV 50% of the time and the same for opponent, and it's not even difficult to force this. But having NV-NV, NV-V, V-NV and switched sides, V-V is simply unfair to one of the players. I don't know if this "switching sides" has be changed, but there were no ears when I previously mentioned this on the forums so I guess not.

[BunnyGo]

han said:

I don't know why this is actually interesting, but when somebody starts posting incorrect mathematics I feel a strong urge to correct them before anybody gets harmed.

I too have this impulse.

Free, on 2011-September-13, 02:00, said:

The problem with taking averages is that 50 hands is way too few to draw any conclusions. Pretty much every tournament you will ever play, one side will have more HCP than the other, even with hand dealt cards or a true randomizer. It's like flipping a coin 50 times: the chance that you flip exactly 25 times heads is rather small.
20.80HCP on average is not that big a difference.

True. There are tables that you can look at (or calculate yourself) that will tell you how much bigger than 20 HCP is "significant" for a given number of hands.

Quote

What made me stop playing moneybridge is the fact that we keep changing sides. Although it has no influence on the long run average, I got the impression there were huge streaks of HCP either for me or for my opponent.

This. Even with long run averages being "equal", one can expect that streaks of arbitrary long length will occur.

Quote

In fact, I even calculated it once, and not switching sides would've resulted in an average closer to 20HCP. And this happened every single time. NS gets 25HCP 2 deals in a row while we're sitting EW, you expect EW to get some HCP soon and what happens: you were right but you also switched sides, so another game for your opponent. And vulnerabilities are also cruel: you have streaks where you're Vul 75% of the time (great, but then your opponent leaves) but you also have streaks were your opponent is Vul 75% of the time while you stay NV 75% of the time. One should expect to be Vul 50% of the time and NV 50% of the time and the same for opponent, and it's not even difficult to force this. But having NV-NV, NV-V, V-NV and switched sides, V-V is simply unfair to one of the players. I don't know if this "switching sides" has be changed, but there were no ears when I previously mentioned this on the forums so I guess not.

Not this. In fact, you too seem to have drawn conclusions from too few observations. When you switch sides, you are just as likely to have joined NS and get lots of points as you are to have left EW when they start to get points.

[helene_t]

last week, I had had (my guess) an average of 12 HCPs per hand in the club mitchell. Apparently the cards were in favor of East. Last two rounds were arrow-switched so if I had been superstitious I might have expected bad cards now that I was North. I got 21 points on the first of the remaining boards and also opening strength on two others.

Maybe our dealer software is skewed but I would need much, much, much stronger evidence to take such a suspicion seriously. I would expect standard random number generators to have been tested on millions if not billions of samples before being released. So I wouldn't second-guess them just because I found a p-value of say 0.001 when testing some random null hypothesis on bridge hands. Much less if it was just a vague feeling not based on a formal statistical test.

If there is a real skew in in bridge hands then I would guess that it would be due to a data management flaw or (less likely) a flaw in the bridge part of the dealer software. That it could be related to a flaw in the underlying random number generator is not plausible.

[Free]

BunnyGo, on 2011-September-13, 02:55, said:

Not this. In fact, you too seem to have drawn conclusions from too few observations. When you switch sides, you are just as likely to have joined NS and get lots of points as you are to have left EW when they start to get points.

I admit that my decision is based on a few observations. Frankly, it's my money, so I don't care...

Random direction and random deals shouldn't make much difference. However, you can't deny the fact that it's simply ridiculous to randomize something as simple as the vulnerability and claim that it's ok because in the long run the variance will cancel out. There's no reason to add vulnerability and direction to the luck factors.

Perhaps an interesting problem: does anyone know how many deals you need to play before you can speak of "the long run"? Does it change if your direction is randomized as well? And what about changing vulnerability?

[hrothgar]

Free, on 2011-September-13, 07:40, said:

Perhaps an interesting problem: does anyone know how many deals you need to play before you can speak of "the long run"? Does it change if your direction is randomized as well? And what about changing vulnerability?

This does strike me as vaguely interesting
If no one beats me to it, I'll throw together a quick sim later in the week.

FWIW, I'd bet dollars to donuts that introducing directions and vulnerabilities will increase the number of samples that one needs, however, I'm not sure how quickly things will converge.

[helene_t]

My guess would be that the vulnerable player has a slight edge so to make the game fair, the vulnerability should be equal throughout.

Then again, you can't make the dealer neutral and presumably the dealer has an edge (however, someone once posted some weird statistics showing that when Jack plays against itself, the dealer is actually disadvantaged). Maybe it should always be w/r for dealer to neutralize dealer's advantage?

Not sure if making the vulnerability deterministic (as in real bridge) is better than random. Someone who perceives (say) red colours to be best could game the system by leaving prior to a w/r board.

Edit: it was Cascade who did the Jack study. http://www.bridgebas...in-1st3rd-seat/