. ^g Extreme 21

Last update: February 1, 2005

Introduction

Extreme 21 is a blackjack variant in which the players play one at a time and the dealer keeps hiting until he beats the player or goes bust trying. Other rules are also made in the players favor. As of this writing (January 2005), the game can be found at the Imperial Palace in Las Vegas, John Ascuaga's Nugget near Reno, and various casinos in Alberta, Canada.

Rules

Following are the rules for Extreme 21.

Any number of ordinary decks may be used but I believe 6 is the norm.
The game is played individually between each player and the dealer. The players must take turns playing.
Play begins with the player making a bet.
After all players have made a bet the dealer deals one card to each player.
In turn, the dealer deals each player a second card and the dealer 1 up card.
Blackjacks have no special significance and are treated as any other 21-point total, thus there is no need for the dealer to take a hole card.
All cards are valued as they are in blackjack: 2 to 9 are counted at their pip value, tens and face cards count as 10, and aces count as 11 unless that would bust a hand, in which case they count as 1.
Doubling is allowed on any number of cards, including after splitting. In addition, the player may hit and double again after doubling.
Splitting is allowed on the first two cards if they are the same point value. Resplitting is allowed an unlimited number of times, except on aces, which may only be split once.
If the player gets to exactly 21 points it is an automatic winner and the player is paid 1 to 1 immediately.
If the player did not bust or reach exactly 21 points then the dealer will play out his hand by hitting until he either beats the player or busts. For example, if the player stands on 17 points then the dealer must keep hitting until he either has 18 or more, or busts.
If the player splits then the dealer will play against each hand individually, starting with the same face-up card in each hand.
A winning player bet is paid 1 to 1.

Rule Variants

Doubling allowed on first two cards only, including after splitting.
Doubling allowed on any number of cards, including after splitting, but redoubling not allowed.

Strategy

The following table shows the basic strategy for Extreme 21 if redoubling is allowed.

The next table shows the basic strategy for Extreme 21 if redoubling is not allowed.

Key to table:

H: Hit
S: Stand
D: Double
P: Split

House Edge

Doubling allowed on any number of cards, including redoubling: 0.63%
Doubling allowed on any number of cards, but no redoubling: 0.90%
Doubling allowed on first two cards only (including after splitting): 1.16%

The version practiced in Las Vegas and Reno is the latter version with a 1.16% house edge.

Methodology

This analysis was conducted in Excel as well as C++ assuming an infinite number of decks. I feel the number of decks is not as significant as it is in blackjack and no adjustment has been made for a 6-deck game.