[onoway]

The last IAC team matches we had 8 teams playing in a round robin series with 12 boards per match. At the end of the series, we had two teams tied, not only with VP's but also in imps.
It seems that this has to be highly unlikely. Anyone have an idea? I have no clue how to go about calculating the odds.

[hanp]

I am fairly confident that you are correct.

[jdonn]

About 0.034% by my calculations. Not likely at all.

[onoway]

thanks

[Echognome]

Anything that is used as an estimate is really nothing more than an educated guess. The mathmaticians can assure that the calculations are correct given the assumptions, but the assumptions here would be very subjective. You have to assume the process by which imps are generated and then you could use a VP scale and calculate the odds. Of course imps are not generated randomly, so when you model them as a random process you will lose some accuracy.

Anyway, probably just as easy to use logic or look at the occurences in our collective experience and say it is quite rare.

[helene_t]

If I recall correctly the residual SD (residuals relative to the predictions from the models Gerben, Cascade, I and probably countless others invented) is about 4 IMP per board, meaning an SD on the difference between the total IMPs of any two teams to be 4*sqrt(2*7*12) ~= 52. The probability that two exactly equally strong teams get the same number of IMPs is then approximately the probability that a normal distributed variable with SD=52 is between -0.5 and 0.5. This is 0.007671849 or about 20 times more than what Josh said.

Then again I haven't taken into account that the VPs also need to be the same and that probably no two teams are really exactly equally strong. I just made some simulations that shows that if two teams get tied IMP-vise the probability that they are tied VP-vise is appr. 10%. So now we are at about 0.077% or about twice Josh's estimate. I suppose Josh has used a more complex model that takes into account that there will in practice not be two teams that are exactly equally strong.

[hanp]

Quote

Anything that is used as an estimate is really nothing more than an educated guess. The mathmaticians can assure that the calculations are correct given the assumptions, but the assumptions here would be very subjective.

Exactly, which is why I hope that Josh was joking.

[jdonn]

hanp, on Mar 19 2009, 02:34 PM, said:

Quote

Anything that is used as an estimate is really nothing more than an educated guess. The mathmaticians can assure that the calculations are correct given the assumptions, but the assumptions here would be very subjective.

Exactly, which is why I hope that Josh was joking.

No, I used my pocket abacus.

What's funny about you not being sure if I was joking is that I thought it was obvious I was, but I couldn't tell if onoway's "thanks" was a joke.

[hanp]

I've seen your math skillz Josh, I stopped making assumptions.

[onoway]

I am an innocent in calculating odds so happilly believed that in some arcane way ( don't you work in Vegas?) you had divined something approximating the odds. It sounded plausible, so my thanks were quite sincere

[Lobowolf]

This thread is starting to remind me of Asimov's Foundation books.

In another bulletin board I belong to, someone asked for help in calculating the odds of surviving the Titanic wreck, including a convoluted series of event including not only being aboard the ship, but also the odds on having been born.

[jdonn]

I just read Helene's post too and that was even funnier. Maybe it wasn't as obvious as I thought. I just made up a meaningless number and pretended it meant something. My model was to pull a number from my butt.

[Cascade]

helene_t, on Mar 20 2009, 08:33 AM, said:

If I recall correctly the residual SD (residuals relative to the predictions from the models Gerben, Cascade, I and probably countless others invented) is about 4 IMP per board, meaning an SD on the difference between the total IMPs of any two teams to be 4*sqrt(2*7*12) ~= 52. The probability that two exactly equally strong teams get the same number of IMPs is then approximately the probability that a normal distributed variable with SD=52 is between -0.5 and 0.5. This is 0.007671849 or about 20 times more than what Josh said.

Then again I haven't taken into account that the VPs also need to be the same and that probably no two teams are really exactly equally strong. I just made some simulations that shows that if two teams get tied IMP-vise the probability that they are tied VP-vise is appr. 10%. So now we are at about 0.077% or about twice Josh's estimate. I suppose Josh has used a more complex model that takes into account that there will in practice not be two teams that are exactly equally strong.

I actually usually get a slightly higher standard deviation than this when I have empirically tried to estimate the standard deviation.

In the past I have done this based on world championship finals and semi-finals results as well as with my own results. I don't have those figures available for easy access.

I just did a quick estimate based on 140 boards that I played in a tournament (teams) recently and our standard deviation was slightly more than 6 IMPs per board (6.09 2dp).

[Cascade]

Lobowolf, on Mar 20 2009, 01:10 PM, said:

This thread is starting to remind me of Asimov's Foundation books.

In another bulletin board I belong to, someone asked for help in calculating the odds of surviving the Titanic wreck, including a convoluted series of event including not only being aboard the ship, but also the odds on having been born.

It is relatively unlikely that I was born in time to survive the Titanic.

[barmar]

Lobowolf, on Mar 19 2009, 07:10 PM, said:

This thread is starting to remind me of Asimov's Foundation books.

In another bulletin board I belong to, someone asked for help in calculating the odds of surviving the Titanic wreck, including a convoluted series of event including not only being aboard the ship, but also the odds on having been born.

It reminds me of shows like Star Trek, where Vulcans and androids habitually report the odds of things like surviving an attack to multiple decimal places.

[Fluffy]

helene_t, on Mar 19 2009, 07:33 PM, said:

I suppose Josh has used a more complex model that takes into account that there will in practice not be two teams that are exactly equally strong.

I was about to laugh at this, but I guess I am too late .

I actually though Josh put several numbers before coming to that number, not that it took him more than a minute, but at least he tried something

[helene_t]

Cascade, on Mar 20 2009, 01:19 AM, said:

I just did a quick estimate based on 140 boards that I played in a tournament (teams) recently and our standard deviation was slightly more than 6 IMPs per board (6.09 2dp).

OK, that would bring my estimate for the probability at 0.051%. Getting closer to Josh's figure.

[FrancesHinden]

jdonn, on Mar 19 2009, 08:07 PM, said:

hanp, on Mar 19 2009, 02:34 PM, said:

Quote

Anything that is used as an estimate is really nothing more than an educated guess. The mathmaticians can assure that the calculations are correct given the assumptions, but the assumptions here would be very subjective.

Exactly, which is why I hope that Josh was joking.

No, I used my pocket abacus.

What's funny about you not being sure if I was joking is that I thought it was obvious I was, but I couldn't tell if onoway's "thanks" was a joke.

I thought it obvious you were, but what do I know?