Here are some equity calculations pertinent to the discussion of continuation bets with missed hands.
*If we bet 1/2 of the pot postflop, we break even on the move if villain folds 1 of every 3 times (33%).
*If we bet 3/4 of the pot on the flop, we need villain to fold 3 of 7 times (42%) to break even.
*If we bet pot on the flop, we need villain to fold 1 of every 2 times (50%).
These assume situations where we do not want a call on the flop. We do see some added equity from the times we do not get raised on the flop, and are able to take the pot with a later bet or win at showdown. So the first hurdle, determining proper bet size for continuation bets without a made hand, leads us to believe that something around 3/4 pot is correct - enough to get them to fold regularly, but not so high that we need an unreasonable chance of success.
The other side of the coin is building the pot when we have a monster hand. Here we want to bet enough that we will be able to get our entire stack in by the river, if possible, without making overbets (bets that exceed the size of the pot). Assuming only one bet on each street (no raises at any point), betting pot-pot-pot on each street enables us to get 13 times the preflop pot in by the river. In other words:
You raise to 5 BB preflop and get a call. Ignoring the blinds, the pot is 10 BB before the flop. If you bet pot on the flop and get called, the pot is 30 BB. If you bet pot on the turn and get called, the pot is now 90 BB. You are then able to bet 90 BB on the river, for a total of 130 BB of bets after the flop (or 13 times the preflop pot).
Half-pot bets on each street yield the following results: (Preflop pot 10 BB) flop bet 5 BB, turn bet 10 BB, river bet 20 BB. You've only managed to bet 35 BB (3.5 times the preflop pot) with this line. Three-quarter pot bets yield (preflop pot 10BB, rounding up bet sizes) flop bet 8 BB, turn bet 20 BB, river bet 49 BB. This line results in betting 77 BB.
Given that most online poker cash games are played with a maximum of 100 BB buyins, the 77 BB result is pretty close to where we want to end up, but still leaves a lot of money behind in the case of monster hands. Ideally, we should be able to get our entire stack in the pot when we want to without overbetting.
There's another argument in favor of betting larger on the flop - it's easier to get calls on the river for bets that are significantly smaller than the pot, since the expressed pot odds for our opponent will be so big. If we bet pot on the flop, and bet pot on the turn, we can induce more calls on the river if our all in bet is something smaller, perhaps half the pot. Sometimes a player with a decent pair plus a missed draw will look us up.
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