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A. "We want to emphasize playing hands which have a high amount of equity against our opponent’s betting and calling range. Hands which only have a high amount of equity against those hands our opponent will frequently fold by the river are much less useful"
Ouch my english is not that great, another way to say that could be what I wrote below?
We can't play only hands that have a huge advantage over Villain's holdings, so we should play more marginal hands
You misunderstand it. What he's saying is that you want hands which do well when your opponent is betting or calling on the river. For example, when you check-raise the flop, if your opponent is never stacking off with TPTK, and only 2-pair+, then it might not be best to raise with an overpair. Instead it would be better to check-raise with a set because you can be confident to be ahead if all the money goes in by the river.
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B. “Hand signaling” occurs when our hand tells us whether or not we should try to see additional cards to make the best hand by the river. For instance, after seeing a flop with a suited connector, we’ll almost always know exactly what we need in order to make the best hand, and we’ll usually want to see a turn card if we flop a pair, straight draw, flush draw, or three to a flush and three to a straight. Since we only fold suited connectors on the flop and turn if our hand has little equity, if we don’t see a river card, it’s unlikely we would have outdrawn our opponent on the river anyway.
Pretty embaressed about that, I don't understand the last sentence
He's saying that when you have a hand like 7h 6h that you're going to fold it on a Ac Tc 2d board because it's signaling to you that it has little chance of outdrawing your opponent because it would likely need to runner runner a two-pair. On the other hand, the same hand on a Ac Tc 5h board plays differently because the hand is signaling that it has two-back door draws. And if it hits one of those backdoor draws on the turn it can continue, and it'll be easy to tell if it does.
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C. About the grey area between value betting and bluffing
I read this chapter and a question come into my mind, while your considerations are pretty strong, I think we need to decide if a bet is for value or bluff, in order to keep the things simple especially at the tables. At the tables, if we are questioning about what type of bet we are making, we could get confused. I think what you stated is good, but maybe it could help us away from the table. What do you think? If you don't agree with me, when you are at the tables, what you are asking yourself instead "why I'm betting?
It's not that you will really be confused. Think of it this way, when you have a flush draw on the flop and the flush comes in, then you're going to be able to value bet it and will need to balance that with a bluff. On the other hand, when the flush doesn't come in, then you can use the same hand as a bluff.
Let's look at it in terms of value to bluff ratios. Let's say that your flush draw hand has roughly 33% chance of being able to bet it as a value hand (if the flush comes in). So one out of three times, it will be a value hand. Furthermore, let's assume that your value to
bluff ratio should be 1:2, so one value hand for every two bluffs -- ie 33% of your hands should be for value. This is the exact same frequency that your flush draw will be able to be bet as a value hand. Therefore, when you're betting your flush draw, you DON'T need to count it as a bluff because it will be able to be bet as a value hand at a high enough frequency that it makes up for all the times that it'll will be need to be bet as a bluff, when the flush doesn't come in.
At the end of many sections, Matt gives a step by step process on how to think at the tables. But to answer your question, "Why am I betting?" Matt gives a few different reasons throughout the book. Bet for value, bet as a bluff, bet to get high equity hands to fold, bet to charge draws.