Applications - A Guide to MATLAB for Beginners and Experienced Users - page 156

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− 200 − 100 0 100 200 300 400 500 600

Though the chances of a loss after 10,000 games is quite small, the
possibility cannot be ignored, and we might judge that the house should not
rule out being behind at some point by 100 or more units. However, the
overall upward trend seems clear, and we may expect that after 100,000
games the casino is overwhelmingly likely to have made a profit. Based on
our previous observations of the growth of the spread of outcomes, we expect
that most of the time the net profit will be within 1000 of the expected value
of 2000. We show the results of 10 trials of 100,000 games below.

profits(100000, 10)

ans =
Columns 1 through 6
2294 1946 2652 2630 1872

2078
Columns 7 through 10
1984

1552 2138 1852

Population Dynamics

We are going to look at two models for population growthof a species. The
first is a standard exponential growthand decay model that describes quite
well the population of a species becoming extinct, or the short-term behavior
of a population growing in an unchecked fashion. The second, more realistic