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Hitting and Standing

In the column labeled "to contribute" we multiply each of the expectations by its probability; the total of this column, or "bottom line," is our expectation if we draw a card. Since a loss of 48 cents by drawing is preferable to one of 54 cents from standing, basic strategy is to draw to (T,6) v 9. Note that it was assumed that we would not draw a card to (T,6,A), (T,6,2), etc. This decision would rest on a previous and similar demonstration that it was not in our interest to do so.

Analysis of our best strategy and consequent expectation with a smaller total of possibly more than two cards, such as (5,4,3), would be based on a sort of recursive reference to previous calculations of our optimal expectation and strategy with (5,4,3,A), (5,4,3,2).... (5,4,3,9), (5,4,3,A,A), etc. All this is very tedious and time consuming, but necessary if the exact player expectation is sought. This, of course, is what computers ire designed for; limitations on the human life span and supply of paper preclude an individual doing the calculations by hand.

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Moving On Up

When is it time to move to a new limit? If you double your bankroll, it is time to consider playing higher. Just recognize that the competition generally is better the higher you go, so you shouldn't double the stakes you're playing just because you've doubled your bankroll, at least not as a long-term plan.