Choix des tickets - Which tickets to choose ?

[Cedroc92]

(sorry, my English is poor. You can use on line translator)

A ma dernière partie, mon adversaire avait le choix entre :
Vancouver - Montréal 20
Winnipeg - Houston 12
Montréal - New Orleans 13

Je me demande toujours ce qu'il faut prendre dans cette configuration. Qu'auriez-vous pris ?

Plus généralement, sur 30 destinations, il y a, je crois, 4060 combinaisons différentes de 3. Il serait possible, d'avoir une liste, pour les 4060 combinaisons, d'indiquer ce que les top joueurs préfèrent. Cela existe-t-il quelque part ?
Je ne sais pas si on pourrait récupérer les données des parties jouées sur BGA, avec, par exemple, toutes les parties des joueurs de plus de 700 Elo. On aurait alors la réponse après un travail de traitement de données.

[speedypuzzlement]

I would take Montreal to New Orleans (13) and Winnipeg to Houston (12), aiming for the plan below. The plan is also compatible with several other tickets like Duluth to El Paso (10), Denver to El Paso (4), Duluth to Houston (8), etc.



In general, my opinion is that there is not always a clear answer. Sometimes the decision is obvious: Vancouver to Montreal (20), Seattle to NY (22), Boston to Miami (12). But I can also imagine situations where it turns out like rock-paper-scissors: both players are indecisive, but the decision is clear if you can predict your opponent. In such cases, the best strategy would decide randomly between 2 or more of the options (e.g. 70% ticket 1 + ticket 2, 30% ticket 2 + ticket 3). I also might make a different choice if the opponent has 200 ELO or 700 ELO. Against a weaker opponent, I would prefer ticket combinations with higher stability and lower potential.

[speedypuzzlement]

Your data processing idea is interesting. I propose a simpler approach: compute the win rates (WR) for ticket pairs (30 choose 2 = 435) with binomial proportion confidence intervals (BPCI). Below is the data from 195 games across two Experts / Masters tournaments.

Seattle to New York, Vancouver to Montreal: 4/5
Denver to Pittsburgh, Vancouver to Montreal: 3/4
Chicago to Santa Fe, Los Angeles to Chicago: 3/4
Calgary to Phoenix, Seattle to New York: 3/4
Calgary to Salt Lake City, Helena to Los Angeles: 2/4
Denver to El Paso, Vancouver to Santa Fe: 2/4
Calgary to Phoenix, Calgary to Salt Lake City: 2/4
Sault St. Marie to Oklahoma City, Winnipeg to Houston: 2/4
Montreal to New Orleans, Sault St. Marie to Nashville: 1/4
Portland to Nashville, Toronto to Miami: 3/3
Duluth to Houston, Helena to Los Angeles: 3/3
Duluth to El Paso, Winnipeg to Houston: 3/3
Los Angeles to Miami, San Francisco to Atlanta: 3/3
Duluth to Houston, Los Angeles to Chicago: 3/3
Sault St. Marie to Oklahoma City, Vancouver to Montreal: 2/3
Vancouver to Montreal, Winnipeg to Little Rock: 2/3
Denver to El Paso, Vancouver to Montreal: 2/3
Los Angeles to New York, Seattle to New York: 2/3
Denver to El Paso, Duluth to Houston: 2/3
Calgary to Salt Lake City, Denver to Pittsburgh: 1/3
Calgary to Phoenix, Los Angeles to Miami: 1/3
Los Angeles to Chicago, Portland to Phoenix: 1/3
Kansas City to Houston, Los Angeles to Miami: 1/3
Sault St. Marie to Nashville, Vancouver to Montreal: 1/3
Los Angeles to Miami, Portland to Phoenix: 0/3
Los Angeles to Chicago, San Francisco to Atlanta: 0/3
Duluth to Houston, Los Angeles to Miami: 2/2
Montreal to Atlanta, Seattle to New York: 2/2
Helena to Los Angeles, Vancouver to Montreal: 2/2
Denver to El Paso, Sault St. Marie to Oklahoma City: 2/2
Duluth to El Paso, Helena to Los Angeles: 2/2
Helena to Los Angeles, Winnipeg to Houston: 2/2
New York to Atlanta, Sault St. Marie to Nashville: 2/2
Calgary to Salt Lake City, Portland to Phoenix: 2/2
Duluth to Houston, Vancouver to Montreal: 2/2
Chicago to Santa Fe, Vancouver to Santa Fe: 2/2
Chicago to Santa Fe, Duluth to El Paso: 2/2
Kansas City to Houston, San Francisco to Atlanta: 1/2
Duluth to El Paso, Portland to Phoenix: 1/2
Calgary to Salt Lake City, Winnipeg to Little Rock: 1/2
Montreal to Atlanta, Montreal to New Orleans: 1/2
Helena to Los Angeles, Los Angeles to Chicago: 1/2
Portland to Nashville, Sault St. Marie to Nashville: 1/2
Calgary to Phoenix, Denver to Pittsburgh: 1/2
Calgary to Phoenix, Los Angeles to Chicago: 1/2
Calgary to Phoenix, Vancouver to Santa Fe: 1/2
Chicago to New Orleans, Seattle to New York: 1/2
Portland to Nashville, Seattle to New York: 1/2
Calgary to Salt Lake City, Kansas City to Houston: 1/2
Sault St. Marie to Oklahoma City, Winnipeg to Little Rock: 1/2
Kansas City to Houston, Vancouver to Montreal: 1/2
Kansas City to Houston, Winnipeg to Houston: 1/2
Los Angeles to Chicago, Vancouver to Santa Fe: 1/2
Dallas to New York, Duluth to El Paso: 1/2
Calgary to Phoenix, Portland to Phoenix: 1/2
Los Angeles to Chicago, Portland to Nashville: 1/2
Duluth to El Paso, Kansas City to Houston: 1/2
Winnipeg to Houston, Winnipeg to Little Rock: 1/2
Calgary to Salt Lake City, Vancouver to Santa Fe: 1/2
Denver to Pittsburgh, Duluth to El Paso: 1/2
Toronto to Miami, Winnipeg to Houston: 1/2
Calgary to Phoenix, Helena to Los Angeles: 1/2
Portland to Nashville, San Francisco to Atlanta: 1/2
Calgary to Salt Lake City, Portland to Nashville: 1/2
Los Angeles to New York, Montreal to New Orleans: 1/2
Seattle to Los Angeles, Seattle to New York: 1/2
Duluth to El Paso, Winnipeg to Little Rock: 1/2
Denver to El Paso, Kansas City to Houston: 0/2
Duluth to Houston, Sault St. Marie to Oklahoma City: 0/2
San Francisco to Atlanta, Winnipeg to Houston: 0/2
Calgary to Phoenix, Chicago to New Orleans: 0/2
Duluth to El Paso, Seattle to Los Angeles: 0/2
Los Angeles to Miami, Portland to Nashville: 0/2
Helena to Los Angeles, Los Angeles to New York: 0/2
Vancouver to Montreal, Vancouver to Santa Fe: 0/2
Los Angeles to New York, Toronto to Miami: 0/2
Chicago to Santa Fe, Seattle to New York: 0/2
Chicago to Santa Fe, Portland to Nashville: 1/1
Duluth to El Paso, Los Angeles to New York: 1/1
Calgary to Phoenix, Winnipeg to Houston: 1/1
Dallas to New York, Los Angeles to New York: 1/1
Denver to El Paso, Duluth to El Paso: 1/1
Calgary to Salt Lake City, Los Angeles to Chicago: 1/1
Duluth to El Paso, San Francisco to Atlanta: 1/1
Duluth to El Paso, Vancouver to Santa Fe: 1/1
Kansas City to Houston, Seattle to New York: 1/1
Chicago to Santa Fe, Sault St. Marie to Oklahoma City: 1/1
Chicago to New Orleans, Montreal to New Orleans: 1/1
Portland to Nashville, Winnipeg to Little Rock: 1/1
Chicago to Santa Fe, Helena to Los Angeles: 1/1
Helena to Los Angeles, Winnipeg to Little Rock: 1/1
Montreal to New Orleans, Winnipeg to Little Rock: 1/1
Los Angeles to Chicago, Los Angeles to Miami: 1/1
Portland to Nashville, Seattle to Los Angeles: 1/1
Calgary to Phoenix, Winnipeg to Little Rock: 1/1
Chicago to Santa Fe, Duluth to Houston: 1/1
Seattle to New York, Winnipeg to Little Rock: 1/1
Calgary to Salt Lake City, Seattle to New York: 1/1
Sault St. Marie to Nashville, Winnipeg to Little Rock: 1/1
Seattle to New York, Toronto to Miami: 1/1
Chicago to New Orleans, Los Angeles to Miami: 1/1
Vancouver to Santa Fe, Winnipeg to Little Rock: 1/1
Sault St. Marie to Oklahoma City, Seattle to New York: 1/1
Denver to El Paso, Seattle to Los Angeles: 1/1
Montreal to New Orleans, Vancouver to Montreal: 1/1
San Francisco to Atlanta, Toronto to Miami: 1/1
Duluth to El Paso, Los Angeles to Chicago: 1/1
Chicago to Santa Fe, Denver to Pittsburgh: 1/1
Los Angeles to Chicago, Seattle to Los Angeles: 1/1
Calgary to Phoenix, Seattle to Los Angeles: 1/1
Calgary to Phoenix, Duluth to Houston: 1/1
Sault St. Marie to Oklahoma City, Vancouver to Santa Fe: 1/1
Chicago to New Orleans, Toronto to Miami: 1/1
Seattle to Los Angeles, Vancouver to Santa Fe: 1/1
Los Angeles to Chicago, Vancouver to Montreal: 1/1
Boston to Miami, Montreal to New Orleans: 1/1
Los Angeles to Miami, Toronto to Miami: 1/1
Denver to Pittsburgh, Los Angeles to Chicago: 1/1
Denver to El Paso, Portland to Nashville: 1/1
Dallas to New York, Kansas City to Houston: 1/1
Kansas City to Houston, Sault St. Marie to Oklahoma City: 1/1
Toronto to Miami, Vancouver to Montreal: 1/1
Los Angeles to Chicago, Winnipeg to Houston: 1/1
Calgary to Phoenix, Duluth to El Paso: 1/1
Denver to Pittsburgh, Los Angeles to New York: 1/1
Los Angeles to Miami, Winnipeg to Little Rock: 1/1
New York to Atlanta, Vancouver to Montreal: 1/1
Helena to Los Angeles, Portland to Nashville: 1/1
Denver to Pittsburgh, Seattle to New York: 1/1
Helena to Los Angeles, Seattle to Los Angeles: 1/1
Chicago to New Orleans, Duluth to Houston: 1/1
Denver to Pittsburgh, San Francisco to Atlanta: 1/1
Calgary to Phoenix, Sault St. Marie to Oklahoma City: 1/1
Kansas City to Houston, Los Angeles to Chicago: 1/1
Duluth to Houston, Winnipeg to Houston: 1/1
Denver to Pittsburgh, Helena to Los Angeles: 0/1
Denver to Pittsburgh, Portland to Nashville: 0/1
Portland to Phoenix, Vancouver to Santa Fe: 0/1
Calgary to Salt Lake City, Los Angeles to New York: 0/1
Chicago to New Orleans, Chicago to Santa Fe: 0/1
Sault St. Marie to Nashville, Vancouver to Santa Fe: 0/1
Denver to El Paso, Los Angeles to Chicago: 0/1
Boston to Miami, Montreal to Atlanta: 0/1
Portland to Phoenix, Seattle to Los Angeles: 0/1
Chicago to New Orleans, Portland to Phoenix: 0/1
Denver to Pittsburgh, Sault St. Marie to Oklahoma City: 0/1
Seattle to Los Angeles, Winnipeg to Little Rock: 0/1
Calgary to Salt Lake City, Vancouver to Montreal: 0/1
Duluth to Houston, Vancouver to Santa Fe: 0/1
Chicago to New Orleans, New York to Atlanta: 0/1
Denver to El Paso, New York to Atlanta: 0/1
Calgary to Phoenix, Los Angeles to New York: 0/1
Chicago to New Orleans, Duluth to El Paso: 0/1
Portland to Nashville, Portland to Phoenix: 0/1
Chicago to New Orleans, Vancouver to Montreal: 0/1
Los Angeles to New York, Vancouver to Santa Fe: 0/1
Dallas to New York, Sault St. Marie to Oklahoma City: 0/1
Chicago to Santa Fe, Kansas City to Houston: 0/1
Los Angeles to New York, Portland to Nashville: 0/1
Denver to Pittsburgh, Montreal to Atlanta: 0/1
Helena to Los Angeles, Sault St. Marie to Oklahoma City: 0/1
New York to Atlanta, Toronto to Miami: 0/1
Dallas to New York, Montreal to Atlanta: 0/1
Seattle to New York, Vancouver to Santa Fe: 0/1
Portland to Nashville, Sault St. Marie to Oklahoma City: 0/1
Boston to Miami, San Francisco to Atlanta: 0/1
Boston to Miami, Seattle to New York: 0/1
Helena to Los Angeles, Seattle to New York: 0/1
Boston to Miami, New York to Atlanta: 0/1
Seattle to Los Angeles, Winnipeg to Houston: 0/1
Montreal to New Orleans, Toronto to Miami: 0/1
Calgary to Salt Lake City, Duluth to El Paso: 0/1
Denver to Pittsburgh, Los Angeles to Miami: 0/1
Denver to El Paso, Montreal to Atlanta: 0/1
Portland to Phoenix, Winnipeg to Little Rock: 0/1
Duluth to Houston, Sault St. Marie to Nashville: 0/1
Dallas to New York, Vancouver to Montreal: 0/1
Portland to Phoenix, Sault St. Marie to Oklahoma City: 0/1
Denver to El Paso, Los Angeles to New York: 0/1
Montreal to New Orleans, New York to Atlanta: 0/1
Denver to Pittsburgh, Vancouver to Santa Fe: 0/1
Los Angeles to Chicago, Sault St. Marie to Oklahoma City: 0/1
Los Angeles to Chicago, Seattle to New York: 0/1
Sault St. Marie to Nashville, Seattle to Los Angeles: 0/1
Chicago to Santa Fe, Sault St. Marie to Nashville: 0/1
Calgary to Salt Lake City, Los Angeles to Miami: 0/1
Duluth to Houston, Kansas City to Houston: 0/1
Vancouver to Santa Fe, Winnipeg to Houston: 0/1
Denver to Pittsburgh, Portland to Phoenix: 0/1
Sault St. Marie to Nashville, Winnipeg to Houston: 0/1
Chicago to Santa Fe, Toronto to Miami: 0/1
Chicago to Santa Fe, Vancouver to Montreal: 0/1
Los Angeles to Miami, Seattle to Los Angeles: 0/1
Duluth to El Paso, Sault St. Marie to Oklahoma City: 0/1

As you can see, the sample size is not big enough - some pairs are never encountered and even the most decisive results have weak statistical power. Examples:

3/3 (WR 1.000, 95% BPCI 0.292 to 1.000)
4/5 (WR 0.800, 95% BPCI 0.284 to 0.995)
3/4 (WR 0.750, 95% BPCI 0.194 to 0.994)

In other words, winning 3/3 with a ticket pair suggests that the true win rate of that ticket pair is between 29.2% and 100% with a confidence level of 95% - not very useful since we would assume a win rate of 50% by default. Perhaps it is worth organizing a community effort among top players, e.g. in the 2-player League by @Sysyphus, or asking admin permission to web-scrape replay logs.

The 435 pairs may also raise the problem of multiple comparisons: a confidence level of 95% may be insufficient, but raising it to something like 1 - 0.05 / 435 > 99.98% (Bonferroni correction) would widen the confidence interval further and make the results even less useful. As an example, suppose you've won 18 out of 20 games with a certain ticket pair. How certain are you that the ticket combo is better than average?

18/20 (WR 0.900, 95% BPCI 0.683 to 0.988)
18/20 (WR 0.900, 99.98% BPCI 0.463 to 0.999)

Finally, players having the ability to choose their tickets may make such a database less accurate. Unpopular pairs will have fewer samples, making the confidence interval of their win rate larger, making them less popular - a vicious cycle. Furthermore, players will be less familiar with unpopular pairs, making their win rates lower, making them even less popular - another vicious cycle.

[Cedroc92]

Nice answer !

Do you think it is possible to ask for web-scrape replay logs ? I think many players should be interested in !

Then, we will have a data base with opening moves.
May be the game would be less fun if you know for each combination what is "best" good pair...

[speedypuzzlement]

Good question! I asked in the main discussion forum whether game logs can be quoted from BGA. I think the best approach is to make a collection of game logs, volunteered by trusted community members, which can be analyzed in aggregate. This ensures the highest standard of data quality. And of course the database would not be perfect. The community might say a pair is weak when you have a secret weapon prepared .