Computer game Video games, also known as computer games, are electronic games that involves interaction with a user interface or input device such as a joystick, game controller, controller, computer keyboard, keyboard, or motion sensing device to gener ...

simulation A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of Conceptual model, models; the model represents the key characteristics or behaviors of the selected system or proc ...

models A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models c ...

, and

operations research Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve deci ...

programs often require a mechanism to determine

statistic A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypo ...

ally how likely the engagement between a weapon and a target will result in a satisfactory outcome (i.e. "kill"), known as the probability of kill.

Performance audit Performance audit refers to an independent examination of a program, function, operation or the management systems and procedures of a governmental or non-profit entity to assess whether the entity is achieving economy, efficiency and effectivenes ...

ing and statistical decisions are required when all of the variables that must be considered are not incorporated into the current model, similar to the actuarial methods used by

insurance companies Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to hedge ...

to deal with large numbers of customers and huge numbers of variables. Likewise, military planners rely on such calculations to determine the quantity of weapons necessary to destroy an enemy force. The probability of kill, or "P_k", is usually based on a uniform

random number In mathematics and statistics, a random number is either Pseudo-random or a number generated for, or part of, a set exhibiting statistical randomness. Algorithms and implementations A 1964-developed algorithm is popularly known as ''the Knuth s ...

generator. This algorithm creates a number between 0 and 1 that is approximately uniformly distributed in that space. If the P_k of a weapon/target engagement is 30% (or 0.30), then every random number generated that is less than 0.3 is considered a "kill"; every number greater than 0.3 is considered a "no kill". When used many times in a simulation, the average result will be that 30% of the weapon/target engagements will be a kill and 70% will not be a kill. This measure may also be used to express the

accuracy Accuracy and precision are two measures of ''observational error''. ''Accuracy'' is how close a given set of measurements (observations or readings) are to their ''true value'', while ''precision'' is how close the measurements are to each other ...

of a weapon system, known as the probability of hit or "P_hit". For example, if a weapon is expected to hit a target nine times out of ten with a representative set of ten engagements, one could say that this weapon has a P_hit of 0.9. If the chance of hits is nine out of ten, but the probability of a kill with a hit is 0.5, then the P_k becomes 0.45 or 45%. This reflects the fact that even modern guided warheads may not always destroy a hit target such as an

aircraft An aircraft is a vehicle that is able to fly by gaining support from the air. It counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines ...

missile In military terminology, a missile is a guided airborne ranged weapon capable of self-propelled flight usually by a jet engine or rocket motor. Missiles are thus also called guided missiles or guided rockets (when a previously unguided rocket i ...

main battle tank A main battle tank (MBT), also known as a battle tank or universal tank, is a tank that fills the role of armor-protected direct fire and maneuver in many modern armies. Cold War-era development of more powerful engines, better suspension sys ...

. Additional factors include the probability of detection (P_d), reliability of the targeting system (R_sys), and reliability of the weapon (R_w), to name a few. For example, if a missile operates properly ''e.g.'' 90% of the time (assuming a good shot), the targeting system operates properly 85% of the time, and enemy targets are detected at 50%, we can increase the accuracy of our P_k estimation: P_k = P_hit * P_d * R_sys * R_w For example: P_k = 0.9 * 0.5 * 0.85 * 0.90 = 0.344 Users can also specify a probability according to a class of targets, for example, it has been stated that the SA-10

surface-to-air missile A surface-to-air missile (SAM), also known as a ground-to-air missile (GTAM) or surface-to-air guided weapon (SAGW), is a missile designed to be launched from the ground to destroy aircraft or other missiles. It is one type of anti-aircraft syst ...

system has a P_k of 0.9 against highly maneuvering targets, whereas its P_k against non-maneuvering targets is much higher.

References

*A.M. Law and W.D. Kelton, ''Simulation Modeling and Analysis'', McGraw Hill, 1991. *J. Banks (editor), ''Handbook of Simulation: Principles, Methodology, Advances, Applications, and Practice'', John Wiley & Sons, 1998. *R. Smith and D. Stoner, "Fingers of Death: Algorithms for Combat Killing", ''Game Programming Gems 4'', Charles River Media, 2004. Video game gameplay Gambling mathematics

See also

References