Cards are dealt to all players at the table....
Situation #1 - A player looks at his/her cards and notices that they have 3 cards and has not acted.
Situation #2 - Players looks at his/her cards and places a bet. Flop comes out and a player now notices that they have 3 cards.
Hi Jim. In Situation 1, according to TDA rules,
it depends on whether substantial action (SA) has occurred or not. See 2011 TDA Rule 31 "Misdeals" (number will change in the 2013 rules no doubt). Rule 31 is not intended to be an exhaustive list of misdeal conditions as those are covered extensively in the conventional rules, hence "...misdeals include but are not necessarily limited to...". A very commonly recognized misdeal condition is when a hand has more cards than it should; see RRoP Section 3, Misdeals, 2-e for example.
Back to TDA Rule 31: "If substantial action occurs, a misdeal cannot be declared and the hand must proceed." This is the main point of the rule:
after SA happens the hand must proceed. SA is then defined in the next rule (32: Substantial Action) as any two actions, one of which puts chips in the pot, or 3 actions without chips.
In your OP you say that all cards have been dealt out, but you do not say whether any action has occurred, only that the player with 3 cards hasn't acted.
Bottom line: The correct ruling under TDA 31 is to declare a misdeal if SA hasn't occurred, or to kill the hand if SA has occurred.
I have ruled the following.
Situation #1 - Since the player has not acted this is a misdeal, all bets are returned and the hand is restarted.
Situation #2 - This hand is dead, all chips placed into the pot remain in the pot and action continues.
According to TDA, the correct decision factor is not whether the player has acted, but whether SA has occurred at the table or not.
I make these rulings on 2 theories.
Situation #1 - Most players do not look at their cards until it is their turn to act, and until a player realizes that they have 3 cards before they act they do not have liability to the misdeal.
This is actually the rule in some venues, that SA will not be declared until the bet has gone fully around the table one time, in order to "give players a chance to look at their cards in turn". It was considered for discussion at the 2013 TDA Summit, however there are several conceptual problems with it. 1) Nothing precludes players from looking at their hand before action comes to them, it's just a practice they choose; 2) They don't have to look at the face of their cards to see they have a different color back or in the case in the OP, an incorrect number of cards; 3) Not locking in the deal after SA allows for some unlikely but possible angle shots that a player who knows a misdeal condition exists might choose to keep quiet about, play their hand in some fashion, then bring attention to the misdeal if they don't like the way the betting is going before it returns to the BB (in holdem for example).
The Association re-affirmed the misdeal and SA language as-is at Summit VI in 2013.
Thanks for the great question Jim. Listing more misdeal and fouled-hand conditions may be subjects for Summit VII.