Poker Optimal Bluffing Frequency
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*Poker Optimal Bluffing Frequency Analyzer
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Bluffing in poker takes many forms and is a necessary and profitable addition to your poker strategy. Used at the wrong times or against the wrong opponents, bluffing can be very costly indeed. This article shows you how to use bluffing to maximise your poker profits and to avoid costly bluffing in poker mistakes. Optimal Bluffing Frequency Tentative Results August 25, 2013 I’ve been toying around with this situation for a while, and although I want to retain some measure of caution simply because I have a history of making mistakes with this sort of thing, I’m pretty sure I’ve determined that the optimal bluffing frequency for Hero doesn’t. Problems for Future Up: The Use of Previous: The Use of
An Example: Optimal Bluffing and Calling Frequencies
Much has been written about game theoretic optimal frequencies forbluffing, and calling a possible bluff. This serves as a nice example ofhow the underlying principles of game theory can be used as a startingpoint for a poker algorithm, but then must eventually be transcended toachieve the highest playing levels.
It can be shown that the theoretical maximum guaranteed profit from agiven poker situation can be attained by bluffing, or calling a possiblebluff, with a predetermined probability. The relative frequency of theseactions is based only on the size of the bet in relation to the size ofthe pot. To ensure the best result against perfect play, the action mustbe unpredicatable, and one way to accomplish this is by selecting aparticular range of hands to act upon, which will occur uniformly atrandom.
In the following example, we imagine two players involved in a hand ofpot-limit Draw poker (where either may bet an amount up to the currentsize of the pot). Player B has called with a one-card draw to a flush,against Player A who currently has the best hand. To simplify the math,we will assume that Player B will win the showdown if she makes the flush,but will lose otherwise. We will further assume that the probability ofcompleting the flush is exactly 0.20, or one in five. The question is howthe hand should be played after the draw.
The first principle is that Player A should not bet, because Player B willsimply fold if she missed on the draw, but will call (or raise) if shemade the flush. Since there is no profit in Player A betting, we canassume without loss of generality that Player B is first to act after thedraw. The correct strategy for Player B is to bet (the size of the pot)whenever she makes the flush, and also to bet occasionally when the drawfailed. The optimal frequency of bluffs by Player B and calls by Player Aare computed with a game theoretic analysis. For each pair of frequenciesthe overall expectation (expressed as a fraction of the total pot beforethe draw) can be calculated. Table 2 gives a sampling of these valuesover the full range of bluffing and calling frequencies.Poker Optimal Bluffing Frequency Analyzer
Table 2: Expected Values for a Four-Flush Draw: Bluffing vs CallingFrequencies
Legend:
BR = ratio of bluffs to legitimate bets
ABF = absolute bluff frequency (fraction)
Atlantic city casino specials. CFr = absolute calling frequency (fraction)
(expected values are expressed as a fraction of the total pot,
given a 0.2 legitimate betting frequency, and pot-sized bet)
If Player B never bluffs and Player A never calls, it has the same effectas having no betting round after the draw, and the expected value is 0.20of the pot for B and 0.80 for A. We can see from the table that to obtainthe guaranteed maximum, Player B should bet 30% of the time - 20% withthe flush and an additional 10% as bluffs, selected at random. Player Acan always ensure his optimal expectation of 0.70 by calling exactly 50%of the time Player B bets. The bluffing ratio of one bluff for every twolegitimate bets and the calling frequency of 50% are a general resultsfor all situations in which Player B will bet or bluff the size ofthe pot. The optimal ratios will change depending on the size of the betin relation to the pot, but are independent of other factors.Poker Optimal Bluffing Frequency Calculator
While these are optimal strategies, they are not maximalstrategies. A maximal strategy is directed toward exploiting weaknessesin the opponent, whereas an optimal strategy implicitly assumes perfectplay on the part of the opponent.
The game theoretic approach is valid if the opponent is a very strongplayer, or perhaps an unknown player, but is certainly not the way tomaximize net profit in the long run. In a typical game of poker, gametheory is not an appropriate strategy, because it also guarantees that aplayer makes no more than the expected value from the particulargame situation. This effectively ensures that the opponent also playsoptimally, regardless of her approach to the game.
As an example of maximizing strategies, we observe how a strong pokerplayer handles this type of situation. If faced with a bet from a playerwho never bluffs, a strong player will usually fold a marginal hand,knowing she cannot win. Conversely, she will often call a chronicbluffer, even with only a mediocre holding. In the role of Player B, astrong player will frequently bluff against an overly conservative player,but will seldom try to bluff a player who almost always calls. The netresult is an expectation higher than the optimal 0.3, and the tabledemonstrates just how profitable these strategy adjustments can be inpractice.
An algorithm based on game theoretic principles will provide a solid basisfor betting strategy. Nevertheless, to advance to the highest levels, aprogram must be able to understand each opponent’s playing style, and beable to adapt to the specific game conditions.
Next: Problems for Future Up: The Use of Previous: The Use of Poker Optimal Bluffing Frequency Examples& Schaeffer
Thu Feb 12 14:00:05 MST 1998
Register here: http://gg.gg/vcblt
https://diarynote-jp.indered.space
Next:
*Poker Optimal Bluffing Frequency Analyzer
*Poker Optimal Bluffing Frequency Calculator
*Poker Optimal Bluffing Frequency Examples
Bluffing in poker takes many forms and is a necessary and profitable addition to your poker strategy. Used at the wrong times or against the wrong opponents, bluffing can be very costly indeed. This article shows you how to use bluffing to maximise your poker profits and to avoid costly bluffing in poker mistakes. Optimal Bluffing Frequency Tentative Results August 25, 2013 I’ve been toying around with this situation for a while, and although I want to retain some measure of caution simply because I have a history of making mistakes with this sort of thing, I’m pretty sure I’ve determined that the optimal bluffing frequency for Hero doesn’t. Problems for Future Up: The Use of Previous: The Use of
An Example: Optimal Bluffing and Calling Frequencies
Much has been written about game theoretic optimal frequencies forbluffing, and calling a possible bluff. This serves as a nice example ofhow the underlying principles of game theory can be used as a startingpoint for a poker algorithm, but then must eventually be transcended toachieve the highest playing levels.
It can be shown that the theoretical maximum guaranteed profit from agiven poker situation can be attained by bluffing, or calling a possiblebluff, with a predetermined probability. The relative frequency of theseactions is based only on the size of the bet in relation to the size ofthe pot. To ensure the best result against perfect play, the action mustbe unpredicatable, and one way to accomplish this is by selecting aparticular range of hands to act upon, which will occur uniformly atrandom.
In the following example, we imagine two players involved in a hand ofpot-limit Draw poker (where either may bet an amount up to the currentsize of the pot). Player B has called with a one-card draw to a flush,against Player A who currently has the best hand. To simplify the math,we will assume that Player B will win the showdown if she makes the flush,but will lose otherwise. We will further assume that the probability ofcompleting the flush is exactly 0.20, or one in five. The question is howthe hand should be played after the draw.
The first principle is that Player A should not bet, because Player B willsimply fold if she missed on the draw, but will call (or raise) if shemade the flush. Since there is no profit in Player A betting, we canassume without loss of generality that Player B is first to act after thedraw. The correct strategy for Player B is to bet (the size of the pot)whenever she makes the flush, and also to bet occasionally when the drawfailed. The optimal frequency of bluffs by Player B and calls by Player Aare computed with a game theoretic analysis. For each pair of frequenciesthe overall expectation (expressed as a fraction of the total pot beforethe draw) can be calculated. Table 2 gives a sampling of these valuesover the full range of bluffing and calling frequencies.Poker Optimal Bluffing Frequency Analyzer
Table 2: Expected Values for a Four-Flush Draw: Bluffing vs CallingFrequencies
Legend:
BR = ratio of bluffs to legitimate bets
ABF = absolute bluff frequency (fraction)
Atlantic city casino specials. CFr = absolute calling frequency (fraction)
(expected values are expressed as a fraction of the total pot,
given a 0.2 legitimate betting frequency, and pot-sized bet)
If Player B never bluffs and Player A never calls, it has the same effectas having no betting round after the draw, and the expected value is 0.20of the pot for B and 0.80 for A. We can see from the table that to obtainthe guaranteed maximum, Player B should bet 30% of the time - 20% withthe flush and an additional 10% as bluffs, selected at random. Player Acan always ensure his optimal expectation of 0.70 by calling exactly 50%of the time Player B bets. The bluffing ratio of one bluff for every twolegitimate bets and the calling frequency of 50% are a general resultsfor all situations in which Player B will bet or bluff the size ofthe pot. The optimal ratios will change depending on the size of the betin relation to the pot, but are independent of other factors.Poker Optimal Bluffing Frequency Calculator
While these are optimal strategies, they are not maximalstrategies. A maximal strategy is directed toward exploiting weaknessesin the opponent, whereas an optimal strategy implicitly assumes perfectplay on the part of the opponent.
The game theoretic approach is valid if the opponent is a very strongplayer, or perhaps an unknown player, but is certainly not the way tomaximize net profit in the long run. In a typical game of poker, gametheory is not an appropriate strategy, because it also guarantees that aplayer makes no more than the expected value from the particulargame situation. This effectively ensures that the opponent also playsoptimally, regardless of her approach to the game.
As an example of maximizing strategies, we observe how a strong pokerplayer handles this type of situation. If faced with a bet from a playerwho never bluffs, a strong player will usually fold a marginal hand,knowing she cannot win. Conversely, she will often call a chronicbluffer, even with only a mediocre holding. In the role of Player B, astrong player will frequently bluff against an overly conservative player,but will seldom try to bluff a player who almost always calls. The netresult is an expectation higher than the optimal 0.3, and the tabledemonstrates just how profitable these strategy adjustments can be inpractice.
An algorithm based on game theoretic principles will provide a solid basisfor betting strategy. Nevertheless, to advance to the highest levels, aprogram must be able to understand each opponent’s playing style, and beable to adapt to the specific game conditions.
Next: Problems for Future Up: The Use of Previous: The Use of Poker Optimal Bluffing Frequency Examples& Schaeffer
Thu Feb 12 14:00:05 MST 1998
Register here: http://gg.gg/vcblt
https://diarynote-jp.indered.space
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