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Effect of Removal on Dealer's Bust Probability

Surprise is often expressed at the anomalous fact that removal of a seven makes hitting 16 vs. Ten less favorable. it can be verified that proper strategy with a sevenless deck is to stand in this situation and a thought experiment should convince the reader that as we add more and more sevens to the deck we will never reach a point where standing would be correct: suppose four million sevens are mixed into an otherwise normal deck. Then hitting 16 will win approximately four times and tie once out of a million attempts, while standing wins only twice (when dealer has a 5 or 6 underneath) and never ties! (Calculations assume the occurrence of two nonsevens is a negligible second order possibility.) The addition of a seven decreases the dealer's chance of busting to more than offset the player's gloomier hitting prognosis.

in the following table we may read off the effect of removing a card of each denomination on the dealer's chance of busting for each up-card. The last line confirms that the removal of a seven increases the chance of busting a ten by .60%, which is a more extreme change than that produced by any other card.

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Mixed Games
These very high limit games usually are $200-$400 and up, so they aren't something you'll encounter anytime soon. Such a game requires a bankroll in excess of $50,000. Participants play rotation games to keep specialists from dominating. For example, a world champion hold'em player might want to sit in, but if the players know that his triple-draw game is not very good, they will be sure to throw that into the mix.

Because a beginner is not going to play at such high levels for quite a while, you can choose to specialize without fear; add other games after you are comfortable with one.
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