Probability question: names in hats

[Whateverist]

Yes, that's exactly what I'm saying.

Once we enforce the rules of the game, there is a probability of 1/2 that player 1 picks number 3. He can pick either 2, or 3.

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Once he has picked that number, player 2 is left with numbers 1 and 2. He can't pick his own number, so he must pick number 1. And then player 3 must pick number 2.

So half the time, player 1 picks number 3. Every time that happens, we always get 3, 1, 2

But if player 1 takes the number 2 instead (the other half of the time), there are two equally likely possibilities:

2, 3, 1

And

2, 1, 3

So those two share the probability. They get 1/4 each.

This is a very nonstandard puzzle!

But why are you keeping track of mis-draws?  A player's turn isn't over until he draws a strip he can keep.  I'm saying the sample space should only keep track of allowable draws.  Whenever any other draw is made it is essentially just noise but of no consequence. The probability should not be tracking the number of times a player draws a strip, only the number of times he draws an allowable strip.

And with that I'm off to work on the roof today.  We've had record rains which led to leak in my closet coming from the skylight above the bathroom in the next room.  I've got to get some flashing and paint to make sure that does't happen again when the rains return.