To analyze a game mathematically, the mathematician studies the rules of the game in order to understand the inner-workings of the game, to determine winning strategies, and possibly to determine if a game has a solution.

Nim has been mathematically solved for any number of initial heaps and objects ; that is, there is an easily calculated way to determine which player will win and what winning moves are open to that player.

Delegated voting can be combined with first-past-the-post, instant-runoff, or other counting rules that determine the winning candidate.

A Langmuir probe is a device named after Nobel Prize winning physicist Irving Langmuir, used to determine the electron temperature, electron density, and electric potential of a plasma.

After winning the British Empire championship at Wimbledon, London, in 1874, the Irish Rifle Team issued a challenge through the New York Herald to riflemen of the United States to raise a team for a long-range match to determine a British-American championship.

Translation: My main purpose is to make myself commendable by a novelty of which no one was aware or perhaps was capable discovering ; this is to play the pawns well ; they are the soul of chess: it is they which uniquely determine the attack and the defence, and on their good or bad arrangement depends entirely the winning or losing of the game.

A judge may occasionally determine that the loser should compensate a winning pro bono counsel.

Points from tricks are not directly added to the players ' overall score, they are only used to determine the outcome of the deal ( win or loss for declarer ), although winning by certain margins may increase the score for that deal.

With the Royce Gracie winning three of the first four events, the UFC quickly proved that size does not always determine the outcome of the fight.

Since the bottle must be purchased to determine the message and win, people usually purchase more of the drink to increase their chances of winning.

The jury to determine the winning design was composed of:

Upon completion of each hand, teams count the points in their winning tricks to determine the scores.

The winning team received a reward, while the losing team faced a boardroom showdown with Trump and two of his associates in order to determine which team member would be fired.

Whereas the federal act states that, in the case of a referendum about the secession of a Canadian province, the House of Commons has the power to determine afterwards whether the question was clear enough and whether the obtained majority was large enough for the result to be accepted, the provincial one stipulates that Quebecers determine alone the manner in which to exercise their right to choose their political regime, and that the winning option in a referendum is whichever obtains 50 % of the votes plus one.

First round losers contest the World Group Play-offs against the four winning nations from World Group II to determine relegation / promotion for the following year's competition.

Similarly the four nations that lose their World Group II ties will face winning nations from Group I Zonal competitions, in the World Group II Play-offs, to determine relegation / promotion.

Senna and Berger both revealed at the press conference that they would not have started the race if this race didn't determine the Constructor's Championship, as the McLaren and Williams teams both went into this race with a chance of winning the championship.

Britannia Superior was one of the provinces of Roman Britain created around 197 AD by Emperor Septimius Severus immediately after winning a civil war against Clodius Albinus, a war fought to determine who would be the next emperor.

It incorporates some method of predicting what the NCAA Selection Committee will use as its Ratings Percentage Index in order to determine at-large ( non-conference winning ) teams to complete the field of 68 teams, and, to seed the field by ranking all teams from first through sixty-eighth.

Besides the winning combinations, all Cee-lo rules include certain rolls that establish a " point ," and there are situations where two or more players will roll and compare their points to determine a winner.

The votes that did not go to a winning candidate were then thrown into one national electoral district, which was then divided proportionally and used to determine the remaining 10 %, thereby going to candidates not directly elected.

To determine what artwork would be used for the Limited Edition cover, 2K games ran a contest, with the winning entry provided by Crystal Clear Art's owner and graphic designer Adam Meyer.

Before adjournment Monday afternoon, the Senate is expected to approve a study of the number of legislators allotted to rural and urban areas to determine what adjustments should be made.

An automatic number announcement circuit ( ANAC ) is a special telephone number that is meant to be used by phone company technicians and other telecommunications technicians to determine the phone number of a particular line.

To determine a number in the table, take the number immediately to the left, then look up the required number in the previous row, at the position given by the number just taken.

Classical mechanics is unable to determine this distance because of the enormous number of bombardments a Brownian particle will undergo, roughly of the order of 10 < sup > 21 </ sup > collisions per second.

" Over historical time spans there are a number of nearly constant variables that determine climate, including latitude, altitude, proportion of land to water, and proximity to oceans and mountains.

This index can be effectively used to determine the number of herbivore and mammal species numbers within a given area.

* MATLAB library function to determine condition number

For example, a court might certify a case for class treatment where a number of individual bond-holders sue to determine whether they may convert their bonds to common stock.

In its basic form, the Chinese remainder theorem will determine a number n that when divided by some given divisors leaves given remainders.

The exchange equipment interprets these dial pulses to determine the dialed number.

* Locate the central atom on the periodic table and determine the number of its valence electrons.

A mathematical calculation can determine if the number of patients is sufficient to detect a difference between treatment arms.

This formula is used to determine the number of agents or customer service representatives needed to staff a call centre, for a specified desired probability of queuing.

An advantage of ESP cards is that statistics can easily be applied to determine whether the number of hits obtained is higher than would be expected by chance.

For flow of gases, to determine whether to use compressible or incompressible fluid dynamics, the Mach number of the flow is to be evaluated.

The exact number of casualties on each side is difficult to determine, due to bias in the historical sources.

; Drivers: A one-year long study, conducted by a firm that provides statistical information to insurance companies so they can determine rates, found that drivers of H2 and H3 Hummers receive about five times as many traffic tickets as the national average for all vehicles ( standardized based on the number of violations per 100, 000 miles driven ).

For infectious diseases it helps to determine if a disease outbreak is sporadic ( occasional occurrence ), endemic ( regular cases often occurring in a region ), epidemic ( an unusually high number of cases in a region ), or pandemic ( a global epidemic ).

Contemporary chronicler William of Tyre recorded the census of 1183, which was intended to determine the number of men available to defend against an invasion, and to determine the amount of tax money that could be obtained from the inhabitants, Muslim or Christian.