Black Jack Cards

You probably think I’m a bit manic publishing two blog articles on card counting blackjack side bets in one day. Truth is, that’s kind of right. It’s either math or some other obsession, so it might as well be math, right? Well, my other obsessions (right now) are hiking (took a 4 mile hike into the mountains this morning with my dog), music (my band is playing tonight) and Tai Chi (I just can’t move in slow motion right now, could you?). My wife is out-of-town. The bottle is empty. So, this is what you get.

The Upcard Luck (UL) blackjack side bet is a bit wacky to describe. Payouts are based on the dealer’s up-card together with the two cards the player is dealt. In this sense, it is similar to both Lucky Lucky and 21 + 3. There would certainly be intellectual property issues if this bet made it big. Right now, though, it has very few placements.

Here’s how it goes. The player receives two cards and the dealer receives his two cards, with one of the cards (the dealer’s up-card) face up, as usual. If the dealer’s up-card is not a 2, 3, 4, 5, 6 or 7, then the player automatically loses the UL bet. Otherwise, the player’s hand is considered. The player then needs either a total of 9, 10, 11, 18, 19, 20, 21 or he needs two suited Aces, to win UL. Note that Aces always count 11 in figuring out the player’s two card total, so that a total of 21 is the same as blackjack.

The game developer believes this game does have a theme. Players love it when the dealer has a crappy up-card. Players love it when they get a good starting hand. This wager requires both good things to happen in order to win the bet. In other words, if either the player’s starting hand sucks, or the dealer’s up-card is good, the player loses his UL wager. Good compounds good and bad compounds bad. The problem is, for the player there is a lot more bad than good.

The following are the payouts for the most common pay table. These payouts assume the dealer’s up-card is a 2, 3, 4, 5, 6 or 7. Recall that Aces count 11.

• Player has two suited Aces, pays 60-to-1
• Player has blackjack, pays 10-to-1
• Player has a total of 9, 10 or 11, pays 5-to-1
• Player has a total of 18, 19 or 21, pays 2-to-1
• Player loses all other hands, including all hands where the dealer’s up-card is an 8, 9, T, J, Q, K or A.

The following table gives the combinatorial analysis for UL with the pay table above when the game is dealt from a six-deck shoe:

In particular,

• The house edge is 5.8894%
• The standard deviation is 2.6342
• The hit frequency is 18.6667%

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