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The Spectrum Of Opportunity

Gwynn's simulation study shoid no statistically significant difference in basic strategy expectation among the first seven hands dealt from a full pack and only three times in 8,000,000 decks was he unable to finish four hands using 38 cards. Thus, as a matter of practicality, i may assume the first several hands have the same basic strategy expectation.

Although it may seem contradictory, it is also true that no particular subsequent hand, before it is dealt, would have the same set of conditional probabilities attached to it as the first hand from a full deck. This realization leads us to consider what Thorp and Walden termed the "spectrum of opportunity" in their paper The Fundamental Theorem of Card Counting wherein they proved that the variations in player expectation for a fixed strategy must become increasingly spread out as the deck is depleted.

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Just One Round
Players should be consistent, though. A player who pleads for doubled stakes one week while losing should not object on another occasion when he is winning.

Usually, the player who has pleaded for the increased stakes to get even loses even more during that last period. If this regularly happens, particularly to someone who cannot afford the loss, you need to decide just how serious you are. Whether or not you have a moral duty to look out for another player's best interests really depends on whether the game truly is a "friendly" game, or whether, as is often the case in poker, everyone is trying to maximize his own winning chances.

If your game is truly friendly, even though for serious stakes, it makes sense to help a player protect himself from his short-term bad judgment. Most of the time, even when the players like one another, everyone is presumed to be "a grown-up" and must protect himself. In such situations, you may still want to protect a player from himself, figuring that you can shear a sheep many times, but only kill him once. It is often better to ensure the longevity of the game than worry about temporary unhappiness of one player.
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