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The minimum raise would actually be to $18, not $20.

Making it $10 to go is an $8 raise. So you can re-raise $8 more to $18.

As far as your question is concerned, I am not sure, however I do not believe the 3rd player is allowed to raise because the 2nd players all in was 16 and not 18. I could be wrong though.

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The third player should still be allowed to do what he wants as he has had no action in the pot, yet. If the 3rd player calls, the 1st player's only choices are to call the additional $6 or to fold. He will not be allowed to reraise in order to force the 3rd player out.