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So the first is, that in principle Pi(Si) could be zero.
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Just because I'm playing a mixed strategy,
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it doesn't mean I have to involve all of my strategies.
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I could be playing a mixed strategy on two of my strategies
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and leave the other one with zero probability.
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So, for example, again in rock, paper, scissors,
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we could think of the strategy (?, ?, 0).
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In this strategy I assign, I play rock half the time,
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I play paper half the time, but I never play scissors.
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So everyone understand that?
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And while we're here let's look at the other extreme.
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The probability assigned by my mixed strategy