Okay, let's unpack this.
Let's say you're on the button.
You raise about 7BB's to get only 1 caller. Head's up.
If villain does not have pocket pair, but just 2 overcards,
The odds of V hitting the flop is 1/3 = 33%
The odds of V missing the flop is 2/3 = 67%
So, most of the time, V has missed and you want to C-bet to take the pot.
7BB is a huge raise and totally unnecessary as well as counterproductive. You might succeed in stealing the blinds more often but your success rate will have to be too great to make up for the losses.
Let's say with a normal size raise like
3x you get through both blinds
50% of the time and win
1.5bb's and get called the other
50% and lose
3bb's for a combined EV of
-1.5bb's or
-.75bb/hand. Look at that, raising only
3x is losing me money. Maybe if I raise more I'll get more folds. Let's try raising to 7x. Now you're getting through
55%, great, but you're risking
2.33 as much for only a
5% increase in fold equity and you're EV drops to
-2.32bb's/hand. (BTW, I'm not just making these numbers up, they come right out of my database unfiltered for active player).
So you see the value in late position raises doesn't come from stealing the blinds but rather from getting called in position and outplaying you're opponent post flop either by continuation betting of value betting.
Your numbers on the likelihood of V. hitting or missing the flop are about right but your odds of taking it down with a CB don't correlate exactly as many bottom and middle pairs will fold to overcards and many draws will call. That's why again, the CB success rate is only about
53% but that slight advantage along with the overlay makes all the difference in the world.
What if you get 2 callers to your PF raise?
Odds of BOTH MISSING the flop is 2/3 * 2/3 = 4/9 = 45%
Odds of ONE of them hitting the flop is (1/3 * 2/3) + (2/3 * 1/3) = 2/9 + 2/9 = 4/9 = 45%
Odds of BOTH of them HITTING the flop is 1/3 * 1/3 = 1/9 = 10%
So, with 2 callers, odds are that someone has paired the board.
Basically, coin flip is someone hit the board.
C-bet will not be as effective, unless you have TP, etc.
Is this good so far?
This is getting a little more involved than I had intended. I should have just started a thread on Button steals. Still might.
So both blinds call and you go to the flop 3 ways. You're equity as a percentage of the pot now decreases considerable but the same principles as above apply. You're obout
7% less likely to win the pot with a CBet but the additional overlay. That said you need to start being cautious about what boards you decide to continue on. Basically the more coordinated the flop is the less likely you should be to continue without a battle hand. The best flops to CBet are
unconnected monotone or rainbow, the worst are
2 tone connected. An Ace on the flop is usually a good thing but with both blinds calling I might consider delaying or shutting it down all together. That's not based on data just my opinion.
Next let's talk about C-bet size.
V's odds of hitting TP after the missed flop are 6 outs for 12% pot equity in the next card.. You want to bet enough that villain overpaid to see the next card, if he calls.
If I bet 25% of pot, he is getting 5:1 or 17% pot odds.
If I bet 50% of pot, he is getting 3:1 or 25% pot odds.
If I bet 100% of pot, he is getting 2:1 or 33% pot odds.
So, I only really need to C-bet 25% to 50% of the pot for V to either fold, or make a bad call.
Hmm, you seem to be putting him on a range of overcards to the board. I see you mentioned that above but where did that assumption come from? So far all he's done is call and check the flop. His range hasn't been further defined. As far as you're concerned he still has 2 almost random cards. (he probably didn't call with 7-2o). You really can't put him on a range at this point so bet sizing is pretty much a guessing game.
At this point your cards don't matter much either. Sure it's nice to know what you have so you can sharpen things up a bit but for the most part you're just hoping to induce a folding error. My CBets are usually around
1/2 pot but lately (at $1/$2, $2/$5 live) it seems I've been seeing just as many folds to 1/4-1/3 pot sized bets as 1/2 - 2/3. Your average recreational player doesn't base their decision to call or fold on the sized of the bet but rather on how pretty their cards are. They're not thinking about pot odds or implied odds, they're thinking,
"me have pair" "Me have flush draw" "Me have gutshot" So my advice is to just bet the least amount you can get away with without looking like a 90lb weakling waiting to get sand kicked in his face.
If we are short stacked, and he might go all in, then I will consider the next TWO cards. This gives V 24% pot equity. In this case, only betting 50% of pot makes it a coin flip. So, I want to bet more than 50%, maybe more like 75% to 100% of pot, s V is overpaying.
Is this good so far?
Ah, so now we're getting into
SPR, a subject I'm just now starting to take seriously. So the larger the effective stack sizes are in relation to the pot the lighter both you and V. should be calling down with and the less likely you should be to Cbet without a value hand. If the pot is $20 bucks and V. only has $10 behind he's never going away with any pair or draw, the size of the bet won't matter. But in that case you shouldn't have walked down this road to begin with. The smaller the stacks the less leverage you have and the less ability to outplay you're opponents post flop. The magic behind blind steals comes from the power of position which is severely hobbled when effective stacks are small. So you can see how important it is to be aware of the stack sizes around you, and also how much value you're losing by not topping off when you drop below the max.
Time to hit the Gym. GL