I talked to Jeffage about this hand, but I wanted to post my ideas to see if they had any validity for the group.

Jeffage capped pre-flop so it's presumed he has large pocket pair or AK suited.

When flop AA3, sb (who had 3 bet) bets out, bad limper/cold caller calls, Jeffage should re-raise. Sure an Ace would slow play and go for the re-raise on the turn, but KK or QQ would have to raise here to see what's happening in the hand or put sb on defensive. AK can call so he's announcing he's got KK, QQ, or JJ, but that's fine.

If sb 3 bets and bad player cold calls 2 bets again Jeffage knows he's in trouble and can fold. Not just from the 3 bet, which could be a bluff 3 bet because Jeffage announced he probably doesn't have an A, but because of the cold caller. But, it's still 19 small bets in the pot at that point to Jeff at the cost of one small bet to see a card. Fold to any bet on the turn unless a J comes off.

If sb 3 bets and bad player folds, Jeffage can call to see one more card and fold to a turn bet. At that point there are 18 small bets and it costs him only 1 small bet to see the turn.

If sb has an A, wouldn't he prefer an overcall from bad player than reraise and take the hand right there? He might call, hope for the overcall and then bet out to guarantee a bet goes in on the turn.

If sb just calls, so will bad player. So Jeffage is in good shape for a check through on the turn potentially because he's shown strength, unless sb has an ace. He can value bet the river, if checked through again, or call one bet.

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When the A comes on the turn everyone has to either fear or represent an A in this situation.

If Jeffage's raise on the flop was the last bet it is likely checked to him. He can check and bet the river for or call one bet on the river.

If sb 3 bet and bad player called 2 bets cold and then there is a bet and call on the turn, Jeffage has to fold.

If sb 3 bet and bad player folded and sb bets out Jeffage probably still has to fold. But, if he made quads would he bet out after putting Jeffage on KK, QQ, or JJ? I doubt it. Jeffage has to fold to a turn bet with 3 aces and this action. sb would prefer to check and see if Jeffage made his nut boat or full of Qs or Js. He could then check raise or let Jeffage bet his hand to ensure the maximum action.