Question: When was the game released in which players gamble casino chips on various possible random outcomes or combinations of outcomes?

Context articles: Random variable
Casino Kid
Sample space
Experiment (probability theory)
Jeton
Casino chip collecting
Expected utility hypothesis
Mathematics of bookmaking
Stochastic dominance
Casino game

In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are numerical outcomes of a random phenomenon.
 As a function, a random variable is required to be measurable, which rules out certain pathological cases where the quantity which the random variable returns is infinitely sensitive to small changes in the outcome.
Casino Kid is a casino video game for the Nintendo Entertainment System platform released in 1989.
 It was published and developed by Sofel.
 In Japan, the game was released as $1,000,000 Kid: Maboroshi no Teiou Hen (100万＄キッド 幻の帝王編 ) and is based on the manga series "$1,000,000 Kid" by Yuki Ishigaki.
In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.
 A sample space is usually denoted using set notation, and the possible ordered outcomes are listed as elements in the set.
 It is common to refer to a sample space by the labels "S", Ω, or "U" (for "universal set").
In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space.
 An experiment is said to be "random" if it has more than one possible outcome, and "deterministic" if it has only one.
 A random experiment that has exactly two (mutually exclusive) possible outcomes is known as a Bernoulli trial.
Jetons were token or coin-like medals produced across Europe from the 13th through the 17th centuries.
 They were produced as counters for use in calculation on a lined board similar to an abacus.
 They also found use as a money substitute in games, similar to modern casino chips or poker chips. Thousands of different jetons exist, mostly of religious and educational designs, as well as portraits, these most resembling coinage.
 (The spelling "jeton" is from the French; the English spell it "jetton".)
Casino chip collecting is the practice of intentionally taking casino chips (also called "checks") from Casino premises or trading or collecting online, or in person, for the purpose of collection.
 Casino chip collecting is a variety of exonumia, or coin collecting.
 Before it became a more serious hobby, casino chip collecting was simply a case of people keeping them as souvenirs from a casino they may visit.
 The biggest boost to the hobby came with the creation of the online auction site eBay.
 eBay has now become the most popular way to collect and trade casino chips with listings in the casino category regularly including more than 20,000 items for sale.
In economics, game theory, and decision theory the expected utility hypothesis, concerning people's preferences with regard to choices that have uncertain outcomes (gambles), states that if specific axioms are satisfied, the subjective value associated with an individual's gamble is the statistical expectation of that individual's valuations of the outcomes of that gamble.
 Initiated by Daniel Bernoulli in 1738, this hypothesis has proved useful to explain some popular choices that seem to contradict the expected value criterion (which takes into account only the sizes of the payouts and the probabilities of occurrence), such as occur in the contexts of gambling and insurance.
 Until the mid-twentieth century, the standard term for the expected utility was the moral expectation, contrasted with "mathematical expectation" for the expected value.
In gambling parlance, making a book is the practice of laying bets on the various possible outcomes of a single event.
 The term originates from the practice of recording such wagers in a hard-bound ledger (the 'book') and gives the English language the term bookmaker for the person laying the bets and thus 'making the book'.
<ref name="newsid13/33">Sidney 2003, p.13,36</ref>
Stochastic dominance is a partial order between random variables.
 It is a form of stochastic ordering.
 The concept arises in decision theory and decision analysis in situations where one gamble (a probability distribution over possible outcomes, also known as prospects) can be ranked as superior to another gamble for a broad class of decision-makers.
 It is based on shared preferences regarding sets of possible outcomes and their associated probabilities.
 Only limited knowledge of preferences is required for determining dominance.
 Risk aversion is a factor only in second order stochastic dominance.
Games available in most casinos are commonly called casino games.
 In a casino game, the players gamble casino chips on various possible random outcomes or combinations of outcomes.
 Casino games are also available in online casinos, where permitted by law.
 Casino games can also be played outside of casinos for entertainment purposes like in parties or in school competitions, some on machines that simulate gambling.