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A game of snakes and ladders or any other game whose moves are determined entirely by dice is a Markov chain, indeed, an absorbing Markov chain. This is in contrast to card games such as blackjack, where the cards represent a 'memory' of the past moves. To see the difference, consider the probability for a certain event in the game.
Instead of defining to represent the total value of the coins on the table, we could define to represent the count of the various coin types on the table. For instance, X 6 = 1 , 0 , 5 {\displaystyle X_{6}=1,0,5} could be defined to represent the state where there is one quarter, zero dimes, and five nickels on the table after 6 one-by-one draws.
The possible values of X i form a countable set S called the state space of the chain. [ 1 ] Markov chains are often described by a sequence of directed graphs , where the edges of graph n are labeled by the probabilities of going from one state at time n to the other states at time n + 1, Pr ( X n + 1 = x ∣ X n = x n ) . {\displaystyle \Pr(X ...
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An additive Markov chain of order m is a sequence of random variables X 1, X 2, X 3, ..., possessing the following property: the probability that a random variable X n has a certain value x n under the condition that the values of all previous variables are fixed depends on the values of m previous variables only (Markov chain of order m), and the influence of previous variables on a generated ...
An addition-subtraction chain for n, of length L, is an addition-subtraction chain such that =. That is, one can thereby compute n by L additions and/or subtractions. (Note that n need not be positive. In this case, one may also include a −1 = 0 in the sequence, so that n = −1 can be obtained by a chain of length 1.)
The New Orleans Recovery School District adopted school choice version of TTC in 2012. ... Top Trading Cycles and Chains (TTCC). [14 ... Toggle the table of contents ...
The class of stochastic chains with memory of variable length was introduced by Jorma Rissanen in the article A universal data compression system. [1] Such class of stochastic chains was popularized in the statistical and probabilistic community by P. Bühlmann and A. J. Wyner in 1999, in the article Variable Length Markov Chains.