When Should You Split 13s?

At the 2014 Global Gaming Expo Asia, a nonstandard card deck was introduced for a game called Lucky 13s Blackjack (lucky13s.com.au). Lucky 13s was developed and marketed by the Australian firm Engaging Table Games Pty Ltd , whose credo is that new table games should follow what they call the SPA principle: Simple, Playable, and Awesome. The game was soon placed at two casinos in the United Kingdom and on Royal Caribbean cruise ships.

This game uses a single 64-card deck, with 11s, 12s, and 13s in each of the four suits added. Expanding the standard deck this way introduces the possibility that a two-card hand might bust; this is accommodated by an optional “Protection” side bet, which pays off if the total of the player’s first two cards, with aces counted as 1, exceeds 21. A protected hand busting with a total of 22-25 pays off at 5-1; if the hand busts at 26 (a pair of 13s), the payoff is 40-1. If the dealer’s upcard is a 13, these payoffs are multiplied by 5, making a 200-1 payoff on a single hand possible.

An initial hand consisting of a pair of 11s, 12s, or 13s can be split like any other pair, and so need not be an automatic loser. Unless it can be split, a hand which busts in two cards loses the main bet. This may induce players to make the Protection wager as a new form of insurance. On the other hand, given the higher busting probability with a 12 or 13, a player might choose not to split a pair of 12s or 13s against a strong dealer upcard and just take a one-unit loss rather than risking two betting units in an unfavorable situation.

To determine whether or not the Protection bet is a good wager, we begin by computing the probability that a two-card hand busts. We need to count the following combinations, which we shall call bust pairs:

Count Combinations
22        11-11, 12-10, 13-9
23        12-11, 13-10
24        12-12, 13-11
25        13-12
26        13-13

A bust pair consisting of 13-9, 12-11, 13-11, or 12-13 can occur in 16 different ways. A bust pair including a 10 has 64 possibilities, and a bust pair with two cards of the same rank has 6 possibilities. Adding gives a total of 210 possible bust pairs. The probability of a bust pair from the top of a fresh deck is then 210/2016, or approximately .1042.

The expectation for the Protection bet depends on the dealer’s upcard, which in turn depends on the composition of the bust pair. If the bust pair includes x 13s, the probability that the dealer shows a 13 is P(x) = (4-x)/62. 92 bust pairs contain no 13s, 112 bust pairs contain one 13, and 6 contain two. These last 6 are the bust pairs that receive a 200–1 payoff if the upcard is a 13.

The house advantage on the Protection bet with a single deck is 14.28%. If the game is played with a four-deck shoe, the house edge drops to 8.45%—somewhat more reasonable, but still high. In the infinite deck approximation, the house edge only decreases to 6.45%. This is protection you can do without.

In the play of the game, certain important rules have been changed in light of the new high-value cards:

• The dealer must stand on hard 16 rather than 17. Soft 16s must be hit.

• A 21 consisting of an 11 and a 10, 12 and 9, or 13 and 8 is a hard 21, not a natural.

• Insurance is not offered when the dealer’s upcard is an 11.

The 11s, 12s, and 13s also lead to a new basic strategy chart, which may be viewed at http://lucky13s.com.au/ETG-Brochure.pdf. Of particular interest to players is what to do against a dealer 11, 12, or 13. With these upcards, a dealer two-card bust is a possibility, so this is a time to consider putting more money in play if the risk in doing so is not too great. Toward that end, the following actions are called for:

• Double down on hard 11 or lower against a 12 or 13, including hands as low as a hard 5. The slight risk of busting a hard 9, 10, or 11 is more than balanced by the dealer’s increased chance of busting. The dealer busts with a 10; you do not.

• Double down on any soft hand of 19 or lower against a 12 or 13. Here, the only risk of busting comes when drawing a 13 to an ace/8 hand.

• Except for 10s and 4s, split all pairs against a 12 or 13. Split any pair from 6-8, 11–13, or aces against an 11.

Pairs of 11s, 12s, or 13s should almost always be split, with only the following four exceptions, which are akin to surrendering (an option not available in Lucky 13s Blackjack):

• Bust a pair of 13s against a dealer 9, 10, or ace.

• Bust a pair of 12s against a dealer ace.

If you have made the Protection bet, busting these hands still leaves you with a net profit. If not, you are in the long run cutting your losses by giving up one bet instead of doubling your stakes with a high chance of busting in two cards against a strong dealer upcard. Given an initial pair of 13s against a dealer ace, the probability of busting after splitting the pair is approximately .6122.

Read more about the mathematics of gambling in Mark Bollman’s Basic Gambling Mathematics: The Numbers Behind The Neon, available from CRC Press or at amazon.com.

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