![]() ![]() And these are often based on, you have a sum of a large number of games, and then the real question in terms of playing a game decently is which one to play in. Are not optimum but are actually computable and in some sense, within a bound of being optimum, that is they're not necessarily optimum strategy, but they're guaranteed to be not too bad. Like a number and as n gets large k is, doesn't depend on n so k is small relative to n, so as n gets large this approximation gets better and better at least relatively, this is called the mean value term and, analysis of this together with, with an actual construction of, of, of the calculation of this mean value called the thermograph allows us of, of to have a number of strategies that. So, so large numbers of copies of G played together behave approximately. Such that when you add up Gn times that this minus n times the mean value if this is whether a bound which doesn't depend on n over multiple of the mean value. Such that oh, when a number K independent of N. And so given again there's a number M of G called the mean value of G. although not the same one as in calculus. There's actually a theorem behind all this. If this is the game g, and you play g plus g plus g, if you played sums of these, they behave just like numbers, or very much like numbers, or close to numbers. By, when you played sums of these games, people grabbed the games. And in these games, people want to play it. Mean values one thing we look at a little while ago at least in some of the extra problems were these games, for instance, like uh, these, up, and these are games called check games, cashing checks. ![]() So and if you have a Japanese dictionary, you can look up the last two terms. Games Without Chance, and week seven, and we want to talk about mean values, hot, cold, sente, gote. ![]()
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