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In: Physics

In the card game Poker, a royal flush is an unbeatable hand. It is composed of...

In the card game Poker, a royal flush is an unbeatable hand. It is composed of an ace, king, queen, jack, and 10 all of the same suit. There are four possible royal flushes:

A♣️, K♣️, Q♣️, J♣️, 10♣️.
A♠︎, K♠︎, Q♠︎, J♠︎, 10♠︎.
A♥️, K♥️, Q♥️, J♥️, 10♥️.
A♦︎, K♦︎, Q♦︎, J♦︎, 10♦︎.

As you may expect, the probability of being dealt a royal flush is incredibly tiny. "Any poker player who has ever been dealt a royal flush will remember it for the rest of his or her life."

There are other hands that are less impressive than a royal flush. The least valuable hand is a bunch of unrelated numbers (e.g. not the same, not in a row) of different suits. For example, the hand

4♦︎, 3♦︎, J♥️, 2♠︎, 7♦︎.

is worth almost nothing. Let's call it a "lousy hand."

It turns out that this is a good analogy to understand entropy. A specific hand that one is dealt is a microstate. The classification of the hand ("royal flush" versus "lousy hand") is a macrostate.

Explain the difference between "microstates" and "macrostates" in this poker analogy.

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