The downside of the ‘El Farol’ bar | The science sport | EUROtoday

Regarding final week’s “bishop maze,” the reply is sure: the white rooks can checkmate the lone black king. White’s first transfer on the crowded board can solely be to maneuver the bishop from a3 or c3 to b2, and Black has to maneuver his king to b7. From there a labyrinthine chase begins through which the white bishops should attempt to make method for his or her rooks and the black king can solely undergo the white squares. Can you seize it?

Regarding the antichess downside, Salva Fuster discovered an answer in simply 15 strikes (see final remark within the earlier installment), though he thinks that maybe this system he performed in opposition to didn’t make the optimum strikes always. Can you enhance Stockfish’s technique and delay the black king’s victory?

Thursday night time fever

And talking of bizarre video games and crowded areas, a reader talked about the “El Farol bar problem,” primarily based on an actual anecdote a few bar in Santa Fe, New Mexico, and raised by economist William Brian Arthur on the flip of the century. previous. This is the issue:

On Thursday night time, all of the inhabitants of Santa Fe wish to go to the El Farol bar, so long as it’s not full, as a result of it’s a small place and it’s uncomfortable when it’s crowded. The standards for going or not going is the next:

—If lower than 60% of the inhabitants goes to El Farol, it’s higher to go to the bar than keep at residence.

—If greater than 60% of the inhabitants goes to El Farol, it’s higher to remain residence than go to the bar.

The downside is that you simply can’t know upfront how many individuals are going to go to El Farol: everybody has to make the choice to go or not go on the identical time and with out figuring out what others determine. And if everybody follows the identical standards to make their determination (so long as it’s not random, for instance, flipping a coin), the result’s a collective failure. If common standards counsel that El Farol won’t be crowded, everybody will flock and it is going to be full. If, however, common standards counsel that El Farol might be full, everybody will keep residence and the bar might be empty.

What would you do when you lived in Santa Fe? And when you have been the mayor of town, are you able to consider any proposal to resolve the issue?

An analogous downside usually arises in actual life when making an attempt to keep away from a visitors jam when there is just one different route: if the vast majority of drivers select that different route, that’s the place the visitors jam will happen.

A variant of the “traffic jam problem” arises when an exterior ingredient guides drivers’ selections. If, for instance, the General Directorate of Traffic recommends avoiding a sure street and drivers principally listen, the choice route might be congested, so in these circumstances we should take into consideration a variable that we might name the “obedience index” of the inhabitants. Paradoxically, a inhabitants very attentive to institutional suggestions would produce, in some circumstances, an impact reverse to the specified one.

The minority sport

If the issue of El Farol is predicated on an actual scenario, the situation of not figuring out what others are going to do appears unrealistic: it might be regular for the inhabitants of Santa Fe to speak with one another earlier than making the choice to go or not. . And, actually, it is a variant of the issue, though it doesn’t simplify the scenario as a lot because it might sound at first look, as a result of, amongst different issues, the individuals consulted can lie. Which brings us to the idea of “minority game”, proposed by Yi-Cheng Zhang and Damien Challet inside the framework of sport idea. But that is one other article.