Appendices
1: Total dependent expected return table for an infinite deck
2a: Probabilities of dealer blackjack after peek
2b: Probabilities of dealer blackjack before peek
3a: Exceptions to single-deck S17 basic strategy
3b: Exceptions to double-deck S17 basic strategy
3c: Exceptions to single-deck H17 basic strategy
4: Blackjack standard deviation details
5: Infinite deck expected return by player hand and dealer upcard
6: Fine points of when to surrender
7: Effect of card removal
8: Analysis of blackjack side bets
9: Composition-dependent expected returns for 1 to 8 decks
10: Continuous shuffling machine vs. cut card
11: Value and strategy for 678 and 777 bonuses
12: Risk of ruin statistics
13: Probabilities in the first four cards
14: Value of each initial player card
15: House edge using total-dependent vs. composition-dependent basic strategy
16: Basic strategy when dealer exposes both cards
17: The Ace-Five card counting method
18: Basic strategy exceptions for three to six cards
19: Blackjack splitting strategy when a back-player is betting
20: Blackjack doubling strategy when doubling after splitting aces is allowed
21: Details on the Wizard\’s Simple Strategy
Miscellaneous
My comments on the movie "21"
Australian Blackjack
Introduction to Card Counting
Rule Variations
Blackjack "Charlie" Rule
Rummy (Blackjack variant popular in Costa Rica)
External Links
Macau Blackjack rules
Simple Blackjack Explanation
Dealer Exposes Both Cards
Introduction
Sometimes either accidentally or as part of a promotion the dealer will expose both cards. This is not to be confused with double exposure, in which ties lose. The following is the basic strategy, based on an infinite number of decks, when both dealer cards are exposed and the dealer stands on soft 17.
The player advantage of this game is about 10.1%, give or take a little depending on the specific rules.
I get asked a lot why this strategy calls for hitting 11 against a total of 10, when in regular blackjack the player should double. In blackjack, we can assume the dealer does not have an ace as his hole card. That increases the expected value of doubling. In double exposure, there is no such guarantee the dealer does not have an ace as his third card, giving him a 21, making doubling more risky.
Internal Links
Blackjack Side Bets
Introduction to Card Counting
The Hi-Lo Count
The Wizard's Ace-Five Count
When to Surrender in Blackjack
Value of a Free Ace
Dealer Exposes Both Cards
Splitting Strategy for the Back Players
Double after Splitting Aces Allowed
Continuous Shuffling Machines
Cut Card Effect
Variance in Blackjack
678 and 777 Bonuses in Blackjack
Risk of Ruin in blackjack
Total Dependent vs. Composition Dependent Basic
Expected Returns with Infinite Decks
Dealer Odds in Blackjack under U.S. Rules
Dealer Odds in Blackjack under European Rules
Effect of Card Removal in Blackjack
Blackjack Expected Values
Estimating Number of Decks in Online Blackjack
Composition-Dependent Strategy for Single Deck and Dealer Stands on Soft 17
Composition-Dependent Strategy for Single Deck and Dealer Hits on Soft 17
Composition-Dependent Strategy for Double Deck and Dealer Stands on Soft 17