three-bet
(v) raise a raise, that is put in the third bet; often followed by the name of a person. "He opened, I raised, and he three-bet me." "I opened, Sue raised, and Willie three-bet the pot."
I guess the terminology applies more to limit than no-limit.
However, in no-limit the first bet is just a "bet", not a raise. Right?
So in this case UTG+1 is not "raising a raise". I.e. he's only 2betting.
A 3-bet is a reraise, so your example is a 3-bet (the big blind counts as the first bet). Terminology comes from limit originally where it's more intuitive.
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I kinda go along with 13Cards here (I think)... It is my understanding that the term, 2 bet, 3 bet, apply only to Structured Limit, not NL. My way of thinking and ALL I have ever heard playing Casino NL in Niagara, Vegas or Atlantic City is raise or re-raise or re-raise again (This last raise means AA or KK, lol). If we were trying to retrofit the term 2 bet or 3 bet into NL to me a 2 bet would be the 1st raise, a 3 bet the 2nd raise.. But that's just me...
If we are trying to re-invent the wheel here than please....go ahead and debate this. If you are trying to understand proper terminology for either limit or no-limit games here it is:
Pre-flop: BB is the first bet. A raise is the 2nd. re-raise is the 3rd.
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