In fact, I think the entire idea of using the ways of thinking discussed here so far, are out of line when looking at things from the players perspective and I was trying to make that point.The correct strategy for any game is the one that maximizes your expectation. In the case of Craps, the only correct strategy is not to play, because there is no strategy with a positive expectation.The only way to determine this is through using the concept of mathematical expectation. I find this concept immensely useful from the perspective of a player. I am also dumbfounded that you are arguing against the use of this concept from the same perspective.Casinos make money because their customers do not understand this concept, let alone employ it in their decision making.But you have to have a huge number or samples to make that happen. I, as individual player *never* enter that universe.In which case, you have no way of determining what correct strategy is. But I take issue with your statement that you "never" enter the universe.For example, how do you decide which bets to place on a Craps table? If your decision is based in any way upon your expectation, then you have indeed entered that universe, because you have made a decision based upon a long-run assumption.Now, you may not be concerned with maximizing the amount of money you win. You may only play for entertainment, and that's fine. I play strictly for the money, and to do so it's necessary to enter the abstract universe of infinite trials, because correct strategy can only be determined through that perspective.heihojin
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