A floor call I had never seen

[PantsOnFire]

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The other problem with this is the players up front often start playing before the dealer is done dealing so the existence of a bet and raise does not mean he wasn't on top of it to speak up the moment he didn't get get his fourth card.

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If this is the case, then I would say give button the burn card if he stopped action in a reasonable amount of time after he realized dealer wasn't going to give him his fourth card.

Usually two actions is sufficient time to call a stop in play. Early actions by UTG and UTG+1 should not count as actions for this type of ruling.

If this is the case, I hope you gave button the flop burn card.