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Approximating Variation

The numbers are derived by multiplying the effect of removing a single card from the full 52 card pack (on the player's basic strategy expectation) by -51. To assert that these are "best" estimates under the criterion of least squares means that, although another choice might work better in occasional situations, this selection is guaranteed to minimize the overall average squared discrepancy betien the true expectation and our estimate of it.

How do i use them? Suppose i're considering the residue [2,4,6,7,9,T] mentioned earlier and we want to estimate the basic strategy expectation (which we already know to be -6.67%). i add the six payoffs corresponding to these cards -19.4-28.0-23.4-14.3+9.2+26.0=-49.9andthen divide by six, to average: - 49.9/6 = -8.32 (in %). it is the ensemble of squared differences betien numbers like -6.67%, the true expectation, and -8.32%, our estimate of it, which least squares minimizes.

The estimate is not astoundingly good in this small subset case, but accuracy is much better for larger subsets, necessarily becoming perfect for 51 card decks. A subsequent simulation study mentioned in page Four indicates the technique is quite satisfactory in the first 2/3 of the deck, where it is of most practical interest, considering casino shuffling practices.

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Poker Lore
Most of the time, the ante in a \$5-10 game will fall somewhere between those extremes and as you gain experience, you'll get a feel for what hands are playable at what ratio of antes-to-bets.

Finally, you should remain aware of your opponents' styles. Some players routinely play any ace or king doorcard as if they have a pair when the odds are certainly against that being the case on any given occasion. Against such aggressive players you can continue playing when you have a smaller pair, even though every once in a while you will get trapped when the aggressor really has the goods.