[cardcounter0]

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What is the houses edge against a player using basic strategy on six deck shoe?

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It depends. Does the dealer Hit or Stand on Soft 17? Can you double down on any two cards? How many times can you split? Can you double down after split? Can you re-split Aces? Can you surrender? Late or Early? All these rule variations, and others, effect the House Edge.

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What is the edge of the house/player counting cards on a six deck shoe?

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See above. What count system are you using? How far into the shoe is the dealer dealing before shuffling? What is the ratio of your small bet to your large bet? Are you playing every hand? How many hands at a time are you playing? How many playing indexes are you using? Are you using a side count? All these things would effect your edge.

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What is the dealers edge v. a player using basic strategy against an infinite deck?

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Pretty close to an 8 Deck shoe, after 8 Decks adding more decks doesn't effect things that much.

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What is the dealers edge v. a player counting against an infinite deck?

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If there is an infinite number of decks then counting would be useless, since an infinite number of decks implies that the next card is just as likely as any other, despite how many cards have been dealt just like it.