The Importance of Marginal Value Betting from the perspective of theory of games, Jon Ettinger

The translation of this week is about the best game in game theory. However, it is not so much apply game theory to NLHE, but to understand its concepts to understand why our bets depending on which rank ... It is impossible to overstate the value of a good ability to read hands in No Limit Hold'em. The more precisely you can understand the range of hands of the villain, the better your decisions on every street, every hand you play. One of the most egregious situations to take advantage of precise capabilities of reading is worth the marginal bid (NT: just translate "thin value bet") in the river. Value bet third pair, top kicker on the river can be something old and for veterans of Limit Hold'em, but understanding the range of your opponent well enough to make that bet in No Limit is a different story. Analyzing the specific case of value bet on the river in no limit when it comes hand in passing, we can develop a more nuanced understanding of the importance of thin value bets within a balanced game plan against opponents who think.

In particular, analyze the situation from the perspective of game theory can help players better understand advanced thin value bets do is important, when to do it taking into account the full range of hands of the self in the river and how reading hands can become equity on the boat. This scenario I'll use something abstract. Imagine you're on the river in a boat and go heads-up to you. Everything is normal except that you're in a world of game theory optimal opponent playing against game theory (abbreviated to GTO, for optimal game theory). Your opponent knows GTO the way you play well and know your exact rank in the river given the previous action and texture of the board. More specifically, you know that you have the following types of hands with the following frequencies: - Clean Air 40% (failed projects, two barrels of bluff) - The nuts 20% (sets, two pair másximas, etc, depending on the board ) - Hands of mean force: 40% (various partners) He knows your rank because he plays comes from the world GTO and GTO. However, you read mediocre hands, so while you know your opponent is never going to be tricky with the nuts, do not know what hand you can bet for value with profitability of the category average gray hands.

It is essential to note that your opponent always knows how often bets. In our example, the hand of your opponent to win only your range of air, his hand is good only 40% of the time. Assume that there is $ 100 in the pot, with another $ 100 cash back stack and the only size you can do is bet all-in (prize if you have to prove why you would not want to do any other kind of bet in this situation ). If you pass, your equity on the boat will be just $ 40 (40% * 100 $). In fact, if only bets the nuts and you check for 80% of the time, he will retire every time you bet, and its equity is just $ 40. Although you can not read hands as he, at least know the value of bluffing and often have a perfect bluff your opponent GTO can not gamble. Let's step back and see what are the two ways of being "exploited? in this scenario. One would be bluffing too much. In this case, your opponent can call profitably, on average, every time you bet (albeit obvious, sometimes you will get the nuts and value).

How often is too often? Well, as your opponent has a 2 to 1 odds to call on the river, if you bluff more than 33.33% (if not understand this, considering the odds) of the time you are betting against a rival GTO too. Against a regular rival retires maybe your strategy of bluffing too much more can be exploited, but a rival GTO, by definition, can not be exploited. Likewise, if you were bluffing less than 33.33% of the time, your opponent with a 2 to 1 odds to call on the river never paid. If only 10% of your bets are bluffs, then you're giving up money on the table and your opponent will exploit you retire forever.

Even if you are good at reading hands, you know perfectly bluff with a relatively balanced or optimal frequency range of your value bet. Your rank to gamble is worth 20% of your total range, and since your opponent will have a 2 to 1 odds on the river bluff your optimal frequency is 1 for every two times you bet for value, or 10% of the time you spend (1 / 2 * 20%, that is, your value bet frequency). With this relationship about value bet bluffing, your opponent has to be indifferent to pay or retire to your all-in, although by virtue of the argument, assume you will always fold (if ever paid, pay 20% of the time or pay the 74.3% of the time, would be the same from a mathematical point of view). What is your new equity on the boat taking into account all the times you bluff? Previously we saw that if you spent all the time, or just value bet and never bluff, your equity would be about $ 60. Now, however, 10% of the time it happens, we and our rival GTO bluff "is that? to retire.

10% of the time we would have missed the boat for $ 100 we will have won with the lantern. In this way our equity increases to $ 70! ($ 60 + 10% * 100 $). Putting the pieces of the puzzle, how to increase the value of our position showdown over the natural equity of 60%, or $ 60 because the pot of $ 100, is to bet more frequently. And the only way to bluff more often GTO against an opponent who knows exactly how your range is formed, and our (balanced) bet often given board texture and earlier street action is to increase our range of bets by value. If we start holding bluff over the same range of value bet, our opponents could exploit by call every time. The ratio of 2 to 1 on bluffs must be maintained. In this simplified scheme, we can use our "palm reading? to increase our range of value bet, reducing the range of our rival, or in this specific case, realizing that some 40% of our range is medium strength hands, can be bet for value. GTO In this example, the value actually gained by these marginal value bets is entirely due to our ability to increase our frequency of bluffing.

To illustrate this, we follow the same example. Our hand, when we win 60% of the time. Before we were betting 20% ​​of the time and only those who were close to the nuts, but we had the best hand 40% of the time. Magically increase our ability to read hands, and now we can value bet 40% of our best hands instead of 20%, realizing that our opponent's hand is weaker than we thought. Keeping our frequency of bluffing and betting value based on pot odds, bluffing can now bet 20% of the time that happens to us, and our opponents still would have to retire (in fact, is indifferent) all times. Now we are winning the pot 80% of the time. Our thin value bets has given us an extra $ 10 of equity. To further clarify the point I'm getting at, imagine that the opponent's hand is face up. We know that our range is exactly 60% of the time in front of him (and he knows it too), and obviously we're going to bet every time we have better hand.

Now we could bluff 30% of the time in addition to the 60% who bet for value and our opponents are still unable to call, our equity up to $ 90. It goes without saying that the real poker is much more complicated than this example. You can vary the size of the bet, your opponent can check / call with strong hands (especially if you know that your range is narrower than your range of value bet) and, more generally, you can not expect your value bets have 100% of equity when they are paid. The showdown value is not always so clear, and adding the possibility of bluffing checkraise when the stacks are big that can prevent marginal value bets. Also, you should base your play on how you think your range is perceived and not how it really is. Of course, once we left the game theory and return to the real world, the optimal frequencies of the theory loses its significance and becomes a level playing scene. Your rank and your value bet bluffing frequency should depend on your reading and be designed to exploit your opponent, just as your opponent calls will heroic heroic or folds based on their perception of how you play.

He is hardly going to be "indifferent? to your bet. Still, I think that the better one understands the fundamental concepts of hold'em, removed from game theory, the more you'll realize how important one is and how applicable are the one game. Without such a concept map, having a "balanced range? is just an abstract concept. Understand why you can not bluff in certain positions is something left to intuition and experience against the fundamental logic. As you level up and play more sophisticated, more balanced and less exploitable against rivals, these ideas can only grow in importance. I am the first to admit that the whole game theory applied to the No Limit Hold'em is unreal, and though plausible, is not the most profitable way to play. However, the next time you make that sexy value bet with bottom pair on the river waiting to pay you AK high, remember why your bets rebuild marginal value sense. It comes down to frequencies of lanterns and win pots when you have the weakest hand may be able to bet that your opponent knows you're doing bet for value with a wide range.

Source: 2 +2 Magazine.

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