Download e-book for iPad: Harrington on Cash Games, Volume II: How to Play No-Limit by Dan Harrington

By Dan Harrington

ISBN-10: 1880685434

ISBN-13: 9781880685433

Fresh replica in usual used situation with common shelf put on. No writing/highlighting. monitoring quantity supplied on your account with each order. A component to the proceeds is donated to neighborhood libraries.

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Extra resources for Harrington on Cash Games, Volume II: How to Play No-Limit Hold 'em Cash Games

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Feedback Control and Dynamic Programming The key ingredient in the dynamic programming approach to optimal control is Bellman's 35 36 Principle of Optimality. Assume that u*(t) is the optimal control function and that x*(t) is the associated optimal state trajectory. Let v = u*(0) denote the optimal action to be taken at the initial moment, with the initial state being x(0) = c = x*(0). Then the Principle of Optimality states that the part of the optimal trajectory starting at time t = ∆ from the state c + f(c, v, 0) ∆ is also the optimal trajectory for a problem that begins not at time t = 0 in the state c, but at time t = ∆ in the state c + f (c, v, 0) ∆.

A mathematical framework is then developed within which the particular example of a point in space is seen to be just a very special case of a much broader structure, say a point in three-dimensional space. Further generalizations then show this new structure itself to be only a special case of an even broader framework, the notion of a point in a space of n dimensions. And so it goes, one generalization piled atop another, each element leading to a deeper understanding of how the original object fits into a bigger picture.

Thus, the function u(t) accounts for our uncertainty about the true dynamics and for whatever stochastic effects may be influencing the state. It is clear that, on the one hand, we want to choose u(t) so that the state follows a trajectory reasonably close to that dictated by what we think the state dynamics actually are (given by the vector field f). On the other hand, we don't want our estimate of the state to depart too wildly from what has actually been observed (the function y(t)). So we need to choose the control function to optimally trade off these two costs.

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Harrington on Cash Games, Volume II: How to Play No-Limit Hold 'em Cash Games by Dan Harrington

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