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Online Blackjack Games Computations

The table on the following page exhibits the 20 possible three-card subsets, their expectations, as ill as the predictions and errors of both the interactive model and simple linear approximation as ill.

As an example of the ingredients necessary for these approximations, one can easily compute the overall mean M=516, M, = 768, M2 = 636, M3 = 540, M,2 = 1080, M,3 = 885, M23 = 690. From these i get P,Z = 180, P,3 = -30, and P_3 = 120, whose average value is 90, the interactive estimate for subset 1 1,2,3 }, while P, =-744, P, =-84, and P3 = 396, the average of which is -144, the simple linear estimate for the same subset.

The multiple correlation coefficient for interactive prediction is .99 and that for simple linear prediction is .91, but a comparison of these two figures does not really do justice to the improvement in approximation afforded by the interactive model. More to the point is the fact that the proportion of squared error for the simple linear model is .1675, whereas this is reduced to .0218 for the interactive estimates.

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The Art and Science of Bluffing

Expect to lose on your bluffs so you can make money the rest of the time." This is one of the most widely misunderstood concepts in poker and has cost more players more money than almost any other "conventional poker wisdom," because actually it is not wise at all.

The reality is that in the course of making bluffs that you hope will succeed (win the pot), you will get caught/called often enough to do all the "advertising" you need. People will remember these unsuccessful bluffs, and because they are looking for excuses to play, and hate the idea of getting bluffed out of a pot, will later call you when you actually have a real hand. This means you certainly don't need to make bluffs you know will fail.