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Last Updated: October 12, 2016

Effect of Card Removal in Blackjack

Introduction

The following table shows the effect on the player's expected value by removing one of each given card from a six-deck shoe. These numbers were based on these rules: Double on any two cards, double after split allowed, split anything only once, and strategy adjustments for the changed deck composition.

Effect of Removal — Six-Deck Shoe

Card Stand
Soft 17
Hit
Soft 17
2 0.069% 0.071%
3 0.082% 0.086%
4 0.110% 0.117%
5 0.141% 0.143%
6 0.079% 0.084%
7 0.041% 0.038%
8 -0.008% -0.010%
9 -0.040% -0.045%
10 -0.091% -0.097%
Ace -0.094% -0.084%


The source for this table is the amazing Composition Dependent Combinatorial Analyzer at bjstrat.net.



  • Blackjack main page.
  • Appendix 1:Total dependent expected return table for an infinite deck.
  • Appendix 2a:Dealer probabilities after dealer peeks for blackjack.
  • Appendix 2b:Dealer probabilities before dealer peeks for blackjack.
  • Appendix 3a:Composition dependent exceptions to single deck basic strategy where the dealer stands on soft 17.
  • Appendix 3b:Composition dependent exceptions to double deck basic strategy where the dealer stands on soft 17.
  • Appendix 3c:Composition dependent exceptions to single deck basic strategy where the dealer hits a soft 17.
  • Appendix 4:Details on the standard deviation in blackjack.
  • Appendix 5:Infinite deck expected return according to player hand and dealer up card.
  • Appendix 6:Fine points of when to surrender.
  • Appendix 7:Effect of card removal.
  • Appendix 8:Analysis of some popular blackjack side bets includingSuper Sevens, Streak, Royal Match, and a tie.
  • Appendix 9:Composition dependent expected returns for 1, 2, 4, 5, 6, and 8 decks.
  • Appendix 10:The effect on the house edge of the continuous shuffling machines vs. the cut card.
  • Appendix 11: Value and strategy for 678 and 777 bonuses.
  • Appendix 12:Risk of ruin statistics.
  • Appendix 13:Probabilities in the first four cards. May be used to test for the number of decks in online blackjack.
  • Appendix 14:Value of each initial player card.
  • Appendix 15:House edge using total dependent vs composition dependent basic strategy
  • Appendix 16: Basic strategy when dealer exposes both cards.
  • Appendix 17: The Ace-Five Count. Possibly the easiest way to count cards.
  • Appendix 18: Basic strategy exceptions for three to six cards.
  • Appendix 19: Blackjack splitting strategy when a back-player is betting.
  • Appendix 20: Blackjack doubling strategy, when doubling after splitting aces is allowed.
  • Appendix 21: Details on the Wizard's Simple Strategy.
  • "21" Movie — Truth and Fiction : My comments on the movie "21."
  • Australian Blackjack: Rules and odds for blackjack down under.
  • Introduction to Card Counting
  • Rule Variations: The effect of just about every known blackjack rule change.
  • Automatic Winner Charlie Rule in Blackjack.


Written by: Michael Shackleford

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