by Kardi Teknomo

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Monte carlo Simulation for Adaptive Learning

Let us start with an example of a simple game. We want to make a game to improve the ability of user to memorize the 48 basic Japanese Hiragana syllables . Conventional game without learning is basically showing the 48 characters randomly. The algorithm to show the syllable randomly is explained as follow.

To give equal chance to each syllable, we use random number generated by computer, which is also called a uniform distribution . Since it has 48 syllables and each syllable have equal chance, we say that the probability of each syllable would be Monte Carlo . I use notation Monte Carlo to represent the probability distribution of each syllable Monte Carlo . The probability distribution and cumulative probability distribution is shown in the table below.

Syllables

a

u

i

e

o

ka

ku

...

ro

wa

o

n

Probability

1/48

1/48

1/48

1/48

1/48

1/48

1/48

1/48

1/48

1/48

1/48

Cumulative

1/48

2/48

3/48

4/48

5/48

6/48

7/48

45/48

46/48

47/48

48/48

To show the syllable with equal probability, we generate random number using computer and use the inverse cumulative distribution . The random number computer generate is between 0 and 1 inclusively Monte Carlo . Suppose the random number generated by computer is denoted by Monte Carlo , then

Show syllable a if Monte Carlo

Show syllable u if Monte Carlo

Show syllable ka if Monte Carlo

Show syllable ku if Monte Carlo

Show syllable wa if Monte Carlo

Show syllable o if Monte Carlo

Show syllable n if Monte Carlo

The process to show the syllables randomly above is called Discrete Monte Carlo algorithm.

Next section is about Adaptive Learning Game

See Also: Monte Carlo Simulation Tutorial

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Preferable reference for this tutorial is

Teknomo, Kardi (2015) Learning Algorithm Tutorials. http:\\people.revoledu.com\kardi\ tutorial\Learning\

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