Casino Nassau

13 Hi Low
Some casinos have the option to play an added game on top of the hand that is dealt to the player, commonly known as 13 Hi Low or Hi Low 13. As in the diagram below, above the box where the bets are placed, there is a separate section above with the number 13 and + and - sign.
How this is played is that the player has to guess if the first two cards total is above or below 13. Sounds simple?
Well, if you guess that the first two cards total for this round will be more than 13, you place your bet in the circle with the +. And if you get dealt a 9 and 10, the total is 19, you win. Payment is 1:1.
Many people think that this is easy money because with the 4 out of 13 cards are 10 value cards (10, J, Q, K), the likelihood of been dealt a more than 13 total is very high. This is a big, big mistake.
Do you think the casino will invent a game to let people win money from them?
The casino has a huge advantage in this game. In the long run, the casino has the edge. Because there is a catch in this game, Aces are counted as 1 and not 11. Hence if you get dealt a 4 and Ace, it is counted as only 5.
However, this is not the advantage that the casino has. The real casino advantage is this, if the first two card total is 13, it is NOT a draw; you will lose your bet.
Question for thoughts
Do you have any idea the probabilities of the first two cards total to be equal to 13?
Do you have any idea what is the distribution of the cards are like for the first two cards total?
Is there a high likelihood that the total will be more than 13?
What are your winning chance in this game?
Well, do not believe a word I say. See the math yourself
Yes, it is true that there is a higher likelihood of been dealt a hand of more than 13. But the probabilities are not significant enough for the player to have an edge and win. A more interesting thing to take note is the number of time the first two cards total add up to exactly 13. Out of a possible 169 combination, the distribution is as follows.
Card total of more than 13, is 79 out of 169
Card total of  less than 13, is 76 out of 169
Card total of exactly 13, is 14 out of 169
As we can see in the three tables above, in a random distribution, the number of time the first two cards adds up to more than 13 is 79 out of 169 (46.7%), number of times less than 13 is 76 out of 169 (44.9)% and 14 times (8.3%) when it will total up exactly 13.
Looking at the odds, you will see that these odds are no better than any other game in the casino. You will lose money in the long run.