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I'm still a beginner, but I think this advice applies.
An acknowledged standard for pre-flop raise sizes is this: 3-4bb + 1bb per limper. In the case of CO posting because he's fresh to the table he counts as a limper. In this hand this would suggest a standard raise size of 7-8bb. If you consider the action alone, this is what you should come up with.
Now, you could also consider the stack sizes. UTG+1 has 42bb. If UTG+1 were to call an 8bb raise from you he would have 34bb behind and there would be 19.5bb in the pot. Because KK is a hand that has a lot of equity pre-flop and on many flops it would be interesting to get 42bbs in the pot against UTG either pre-flop or on the flop if you had reason to think you would be playing against him. If you thought you'd be up against UTG+1 I could see an argument for raising to 13bb instead so he has 29bb behind and the pot is 29.5bb on the flop at which point you can open shove to commit him.
UTG on the other hand has you covered, so effective stack sizes against him are 143.5bb. This means you cannot play to get the money in pre-flop or on the flop while your KK is in good shape. If you end up being called by UTG you need to be prepared to play poker on all four streets.
Not knowing whether you'll end up playing against UTG or UTG+1 and with people left to act in the hand I would go for the standard raise size without trying to adjust it further to conditions. $0.15 seems reasonable.
On the flop: You really need to work out what it means to relate a bet and/or a raise to the size of the pot. Let me help a bit.
The central concept here is pot odds. In plain terms it is the odds offered by the pot on your bets. A big pot and small bet gives you great pot odds, a small pot and big bets give you bad pot odds. To really understand the concept you have to mentally shift back and forth between bettor and caller several times.
If the pot contains $1 and someone bets $1 into it, I need to call $1 to have a chance to win the $2 we say that I get 2-1 odds to call.
From the bettors perspective I bet $1 into a $1 pot laying 2-1 odds to the caller. A pot sized bet (PSB) lays/gets 2-1 odds. A half pot sized bet lays/gets 3-1 odds.
When you are making a raise you want it to be an effective bet. This means that you want to lay odds to the caller which are in the same sort of realm as if you were doing a half pot sized bet or pot sized bet or whatever you think is appropriate for the situation. This means that the raise in general needs to be much larger than one would intuitively suspect.
A $1 pot sees a $1 bet and the action is on you. This is a PSB, and you want to make a raise that is also a PSB. You calculate how much to raise in this way:
1) Complete the 'call' bit and calculate what the interim pot size is then. You 'call' $1 making the interim pot $3.
2) Make a PSB. Interim pot is $3 so you bet $3 into it to lay 2-1 odds on the caller.
3) Add up the 'call' and the 'PSB' to get the size that you should raise to. You add $1 'call' to $3 'PSB' in your head - the actual action in the hand is: Pot is $1. Villain bets $1. Hero raises to $4.
The pot is $0.49 and he bets $0.49. To make a 'PSB' size raise you would need to raise to $1.96. if you raise to anything less you are offering him better odds to call than he was offering you in the first place (not that that is necessarily a bad thing) - but raising to $1.02 is definitely too small. A raise to $2.79 (your stack) is a bit of an overbet, but not unreasonable.
What does it mean when he does a PSB on this board?
It's rainbow so flush is unlikely to be a factor. To finish this thought, if he was playing 7s6s he would have 8 outs to finish his straight and although he would need running spades to finish a flush that is similar to approximately 2 outs. In that way a flush is a possible factor in the villain's considerations, but it is unlikely to factor in.
A big bet can mean many things. It can mean strength or weakness both. Sometimes people take a hand that is vulnerable but which has potential and bet big on it, considering a fold a good result. Sometimes a big bet means simply a big hand - other times big hands bet small to keep people calling so they can drag more money out of you. Robb's recent post on beginners first 20k hands or something does a good job (in lesson 2) of describing some beginner level considerations when it comes to flop bet sizing.
When deciding what to do on the flop we have to consider what he's holding - and we make educated guesses (referred to as hand reading) by considering his past actions.
He limped UTG - then called a small raise (good odds) when the pot was already 4 way - 5 way with him and potentially going up to 6 way.
On the flop, second to act with 3 people behind him he makes a PSB.
When making educated guesses you should always start by asking which hands an intelligent and skilled player would have played in this way - and then worry about adjusting to known weaknesses or stupidity if it applies afterwards. And you should always consider unknowns intelligent and skilled until proven otherwise - it tends to save you money.
Which hands would he limp UTG with? On the surface he wants to see a cheap flop. He could have a low to medium pair, or suited connectors hoping to flop big. If this table doesn't normally have a lot of re-raising pre-flop it might be reasonable for him to expect to get in cheaply with that type of hand.
When it comes around to him with 4 people already in, him making it 5way to the flop - which hands would he call with? The exact same type of hand that he would limp with UTG I'd think - a small/medium pair hoping to set or a suited connector that plays very well in a multiway pot.
What does it mean when he fires a PSB second to act with 3 people to act behind him (one of them being the pre-flop aggressor)? It could mean: "I have a big hand - call me and pay me" or it could mean: "Go away". I would be tempted to suspect that he doesn't have a made straight or set but rather something along the lines of TT or T9 for a made pair with good draw potential.
If he has something like Ts9s he would have effectively 14-15 outs to beat your KK. (four sevens, four queens, two nines, three tens and one to two outs for runner runner spades - less than 2 in this case because some of the spades complete some of the other hands that beat you).
If he has something like Ts9s and you go all-in on the flop as played it is entirely possible that he will think he is behind and will fold - even though it would actually be correct for him to call. People at these stakes sometimes don't properly understand the strength of their hand. I mention this to underline that it's not wrong to play a KK hand aggressively in this spot and have someone fold - you may just have had someone fold the better hand.
That said - 88, 99 and 89s and J9s are certainly also in his range.
On the flop I would tend to agree with your assertion that he's probably on a draw or a single pair with a draw and just go all-in with the kings here.
About the turn: There's $2.53 in the pot and you have $1.77 behind. If you have any reason to think you're ahead (such as if he checks) you're all-in. The pot is offering such attractive odds at this time that I'm not sure you can get away from it regardless.
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