|
I am having a hard time understanding the beginning of your answer
"That equation is so simple because once someone is all-in, there can be no more betting. Furthermore, the value of Hero folding is exactly 0, so plays no role in the final equity we calculate. We completely ignore the term, as it cannot contribute to your winnings if you fold, but it doesn't cost you anything to fold, either."
I understand that its easier on the river because there will be no more betting rounds, so you do the calculation to see the equity you need to call and decide from there. When we are on the flop what math dictates our decision to call after checking without a made hand?In the example we are way ahead even without a pair and if villain bets us his bluffing range is huge, but do we need to do equity calculations on the flop like this or not so much more or less on the river?
Sorry about that. Let's break it up.
"That equation is so simple because once someone is all-in, there can be no more betting."
The equation for calling an all in is simplified because there are no later bets. Once someone is all-in, there cannot be any other bets in the pot. That means the success of this bet is not contingent on any future events other than the dealing of the cards, which was predetermined before the hand started.
This simplifies things.
"Furthermore, the value of Hero folding is exactly 0, so plays no role in the final equity we calculate."
When we calculate the equity of a decision, we have to calculate the value of all possible outcomes of that decision. Then we sum the value of each outcome by the frequency of that outcome occurring. The total EV of a decision is
{probability of outcome A}*{value of outcome A} + {probability of outcome B}*{value of outcome B} + ...
With the constraint that all the probabilities alone would sum to 100%, meaning we've accounted for every possible outcome.
We take the sum of terms, each of which is a product. If any part of the product is 0, then the product is 0, and we don't have to account for it in our sum. (accepting that the total probability of all events will still sum to 100% if we double check that)
"We completely ignore the term, as it cannot contribute to your winnings if you fold, but it doesn't cost you anything to fold, either."
Since the cost of a fold is 0, and the reward for a fold is 0 (you do not win the pot 100% of the time when you fold), the value of a fold is 0. So no matter the probability of folding, a fold contributes 0 EV to the total.
|