I want to apologize for sounding harsh in my previous post.
Mario has this exactly right. This is a great lesson on bet sizing and also a perfect example of asking those questions: what hands better than us are folding and what hands worse than us are calling?
In any given hand, Villain has hands in his range that fall into 1 of 4 groups.
Group A: hands ahead of us that are not folding.
Group B: hands ahead of us that he should, could or at least might fold.
Group C: hands behind us that should, could or at least might call.
Group D: hands behind us that he is definitely folding.
By looking at board texture, Villain's line/story and Villain's tendencies, we put him on a range of hands and then sort those hands into the 4 groups.
If group A is large and group B is small or non-existent, we do not want to
bluff.
If group B is fairly large and group A small, this is a bluff spot.
If group C is fairly large, or at least larger than group B, this is probably a value spot.
If group D is large and the other groups small or non-existent, then we are left with equity denial or just check it back due to reverse implied
odds.
Now before we discuss that flop jam, let's look at the pre-flop. In a pro game a standard opening size is usually 2.25x bb. At low and micro stakes this is a little small. We probably want to use 2.5 or 3x. In a freeroll we are more likely to use 3x as a minimum open. Why larger at low stakes? Because players call way more at lower stakes so we need to bet a little bigger to get some folds pre-flop. Furthermore, the more limpers in the pot before we open, the larger we need to open raise. So we might use 2.5x plus an extra half-bb for each limper. Many profitable micro grinders even add 1 whole BB per limper.
So if we are in a freeroll on the BT with 3 limpers, we could conceivably open 6x or 7x. But we are not. We're in a target tournament which presumably has a decent stake buy-in, so as we can see 7x is HUGE! This is an error. Why? Because only strong hands will call and so-so hands will all fold. Now it's okay to open TT a little larger so long as our sizing doesn't tip off a smart player (and most Villains are dumb, just saying), since TT needs a little more protection given that it only has 2 outs to improve and hates overcards, but 7x is massive. What is calling? High pocket pairs, AK, maybe AQ, AJ, and some suited broadways.
So now that we have been called for 7bb and flopped a set on KT9 (we'll assume rainbow so we can ignore flushes and keep it simple) we look at how many hands are in ...
Group A: KK (3combos), QJ (4 combos suited if Villain is tighter or all 16 combos if he is loose).
Group B: nothing.
Group C: AA (6 combos), 99 (3 combos), AK (12 combos), Qx, Jx (multiple combos but many of them would not call 7x pre), KT (3 combos because we block it hard), K9 (9 combos), we'll include QQ and JJ in Qx and Jx because they are gut draws the same just with a couple more outs. We can add in 87s (4 combos) because it's the only open-ended draw (although very unlikely to call 7x pre).
Group D: some lower pocket pairs, probably not too many at 7x pre just depending how loose Villain is.
Looking at groups A and B there are no hands ahead of us that will fold so we cannot bluff.
Group C looks pretty good though, so this is a strong value situation. In particular due to the 7x pre we should target AA overpair, AK top-top, AQ or AJ gut draw. When sizing for value, we use the largest size that Villain will call. We might get away with something as large as pot here, but half-pot is probably fine, maybe 3/4-pot? Of course there are straight draws in our Villain's range but they are all gut draws (we will ignore 87, very doubtful to be there) so gut draws fold much easier. When making say and open-ended draw pay, we need to be bare minimum 40% pot, maybe 75%, but with a gut draw it's a lot less, so half-pot might even fold that out. But I think we are more likely to see AA AK here (due to the 7x pre) and get paid, so I'd probably start with half-pot. Remember that a gut draw has about 15% chance to complete with 2 cards to come. It's 85% (!!) in favor of 2nd set TT. There is not much equity to deny.
Instead we jam for 55b, or roughly 3.7 times pot!! So almost nothing in group C is calling. We're not getting paid! Furthermore, group B is empty so there is nothing better than us that will fold to this.
See why this bet is such an error? Villain either folds and we win 15bb (of which 7bb is ours) with 2nd set (we could have won quite a bit more), or we get called by KK or QJ and felt. NOTHING can go well with this bet unless Villain is a complete bum whale and calls us with a low pocket pair or K-rag!
Now, also look at the pot size. 15bb on the flop which is about 30% of our stack. We're very close to pot committed ourself here. If we bet 2/3rd pot or 10bb on flop and get called, the pot is now 35bb and our stack behind is only 45bb. That's getting worrisome. If we had opened 3x pre instead of 7x, the pot would be 6 or 7 bb and we are totally playable the rest of the way. And even then, if we wish to bet large for equity denial as we did (which I believe is a mistake in a pretty obvious value situation - but let's just say) we could bet something like 12bb and if we get snap-called or raised we can put the brakes on and still have just under 50bb.
In this particular hand, we were getting coolered by QJ, a group A hand. There is nothing that we can do to beat group A hands other than to get super lucky on the turn or river. These hands will not fold, so it is all about our poker senses and exercising caution. Often we are just going down in flames even when we play it well. Also, there is nothing we can do about group D hands. They are junk that is folding no matter what, so when we flop quads and no one will call, we just won't get paid. We did nothing wrong. It's the group B and group C hands that we face that will make the difference in our win rate. If we can get group B hands to fold and group C hands to call (mostly group C hands to call), we will be a winning player. That is the zen.
So the next time that we flop 2nd set on a connected board, think of all of the value hands worse than ours that could call, and bet to keep them around. Don't knee jerk to equity denial "... so the villain wouldn’t have a chance to catch up," especially on a gut draw.