Going to attempt an analysis: please chime in with critiques! Still in the learning phase...
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Hero has T T
UTG raises to 3 BB, fold, fold, Hero calls 3 BB, fold, fold
Happy with this, I find the 3x a little weak as there are antes meaning V is really only betting pot at this point, widens V's range imo
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Flop: (8.6 BB, 2 players) 3 Q K
UTG checks, Hero checks
While I think V's got weak holding according to pre-flop bet, K & Q are definitely in there given his position.
At this point I'm finding V' range to be too wide to assign, obviously AA-TT, Ax, Kx, KQ, & maybe some suited connectors. Since Hero isn't the aggressor I find checking here to be fine.
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Turn: (8.6 BB, 2 players) 2
UTG checks, Hero checks
With him checking the up to this point, I'm putting him on a weak A, Q, or K, AA, JJ, or <99. There is also the possibility he's got KK & QQ but based on his weak open, I'm discounting these hands.
I personally think a bet around 3-6BB here would be appropriate to A) build a pot if you're ahead & B) give an indication to where you stand. Granted the issue is you have to decide what you'd do if he check/raises. Dependent on the c/r size I would still probably say call.
V's either folding or calling imo. If V's folding it's probably a draw and you're happy to charge/win, if V's calling you at least know V's hit something, and a re-raise you can assume strength.
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River: (8.6 BB, 2 players) T
UTG bets 6.2 BB, Hero raises to 24.4 BB, UTG raises to 61 BB, fold
AP I say a call would be best, I would think most of the time you're ahead. Not sure I'd re-raise because if V is slow playing KK or QQ you're done. The T also brings the possibility of AJ/J9 into the hand, w/o reads or stats I would say J9s/o is not in UTG open range but AJs/o is. Without betting the turn and giving a free card the possibility of AJ imo is much greater.
But all that is beating you right now is KK, QQ & AJ of which there are only something like 35 combos of? I'm not great with the in depth EV calculations but I think you're likely ahead still.
My confusion (and I find myself doing this in the moment to) is that you re-raise what I'm perceiving as a thin value bet and then fold. So my question why did you raise in the first place, what did you expect the outcome to be and did you even fathom V'd re-raise? In the moment, I have a ton of trouble thinking through hand possibilities so I usually don't hit that many levels
Just my two cents, now to find out how poor my skills are...