21 Burn Blackjack

Introduction

21 Burn Blackjack is a blackjack variant offered by Betsoft, which is a software provider for Internet casinos. The game is like conventional blackjack except the player may burn his second card for a random card. To burn, the player must make Burn wager, equal to half his original bet. Also, blackjacks pay even money only.

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Rules

Following are the rules:

Six decks.
The dealer hits a soft 17.
Dealer peeks at the hole card for blackjack. This happens before the player has any chance to play his cards. As in conventional blackjack, the player may make an insurance wager if the dealer has an ace up.
A winning blackjack pays even money.
Player may double on any two cards, including after splitting.
Player may split once only.
No surrender.
After seeing his initial hand and the dealer up card, the player may make the Burn bet. The burn bet must be equal to exactly half the original wager. When the player makes the Burn bet, his second card will be burned and replaced with a random card.
The pay table for the Burn bet is shown below.
An ace and 10 after burning a card shall be treated as a blackjack.
The player may not burn after splitting.

Burn Bet Pay Table

Burn Card	Pays
Ace of spades	7 to 1
All other aces	2 to 1
All other cards	Loss

Strategy

The burn wager, by itself, is highly negative. To be specific, the player can expect to lose 67.31% of whatever he bets on it, before considering any benefit to the blackjack wager. Given that the player must bet half his original bet on the Burn wager, the player should only invoke the Burn option when he stands to improve the value of his blackjack wager by 67.31% * 50% = 33.65%. The following strategy shows specifically when the value of burning is greater than 33.65%, in which case the player should invoke the burn option.

Burn if the first card is a 7, the second card is an 8 or 9, and the dealer up card is a 7.
Burn if the first card is an 8, 9, 10, or ace according to the following table.
Do not burn in all other situations.

Next, the play strategy is the same as conventional blackjack, as follows:

Analysis

Based on an infinite number decks and infinite re-splitting, I get a house edge of 0.64%. Based on conventional blackjack, the house edge is 0.1% less in a six-deck game, compared to infinite decks, so I approximate the actual house edge to be 0.54%. This means that for every initial dollar bet, the player can expect to lose 0.54 cents.