Game Theory 101: The Complete Textbook on Amazon: https://www.amazon.com/Game-Theory-101-Complete-Textbook/dp/1492728152/
http://gametheory101.com/courses/game-theory-101/
For a player to be willing to mix between two strategies, he must be indifferent between them. Put differently, he must expect to earn exact the same amount by choosing either strategy in expectation.
As a result, we must be very careful when we write mixed strategies. Although we commonly write 1/3 as .33, those two numbers are not equal to one another. This lecture shows why using decimals can be problematic. In general, you should always play it safe and write numbers as fractions, not decimals.
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