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Strategic Efficiency

A noteworthy observation is that, if the ace is to be counted zero, improvement in the second decimal cannot be achieved beyond level three. Also, bigger is not necessarily better; the level four system narrowly edges the level five system. For the evaluated systems all decisions are made on the basis of a single parameter, the average number of points remaining in the deck. Evidently the maximum efficiency possible for strategic variation with a single parameter system is of the order of 70% and one can come quite close to that without going beyond the third level.

Some other interesting evaluations follow. Considering the difficulty and likelihood of error in, for instance, trying to associate four points with five spots on the card and one point with seven spots on the card, it is extremely questionable whether a price tag of $200 for a less than optimal level four system is a bargain. Although the Ten Count, when parameterized as a point count, uses the numbers 4 and -9, it is certainly not at the 9th level of mental gymnastics-one keeps track of the proportion of tens by counting off the tens and non-tens as they leave the deck.

Two other methods of evaluation, based on the mysterious infinite deck, included pair splitting and doubling down on any two cards as options. They gave very similar relative results for all the systems' strategy gains reported here, with only an occasional interchange of the order of two systems whose efficiencies differ only in the third digit after the decimal point.

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Considerations Involved in hanging the Stakes
Before changing stakes, make sure that everyone in the group is comfortable with the change and doesn't feel trapped by peer pressure. If Fred is already losing enough each week to jeopardize his home situation and the game changes from $5-10 to $10-20, Fred may need to drop out even if he doesn't want to say so in front of everyone. But if the game just seems no fun because the stakes are too low for everyone but Fred, talk it over as a group and, if appropriate, take a vote.

It doesn't have to be unanimous, but seriously consider how much the lone objector contributes to the ambience and dynamic of the game. If everyone really likes Fred, or if Fred is the game's biggest regular loser and doubling the stakes will mean Fred will drop out, raising the stakes could prove much costlier to the remaining players than it initially appears. Instead of winning twice as much, good players may actually win less.

Discussions about permanent stake changes don't happen too often in a poker game: Once a year is a lot. The second kind of stake-changing happens quite often in private games, though.
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