Blackjack side bet

There is casino in Manila offering blackjack side bet : over/under 13 player's first 2 cards. Correct bet pays even money. Ace as 1 . The wizard 's had mentioned this in his blackjack side bet analyzed but did not give us the mathematical calculation about how many over 13 and how many under 13 on the average hand. He mentioned the house edge of 10% on under 13 and 6% on over 13 .
Any body can help me on this? Thanks.

Quote: Francisco

There is casino in Manila offering blackjack side bet : over/under 13 player's first 2 cards. Correct bet pays even money. Ace as 1 . The wizard 's had mentioned this in his blackjack side bet analyzed but did not give us the mathematical calculation about how many over 13 and how many under 13 on the average hand. He mentioned the house edge of 10% on under 13 and 6% on over 13 .
Any body can help me on this? Thanks.

I get the following probabilities depending on how many decks are used:

decks	4	6	8
prob.(under 13)	0.4496	0.4497	0.4497
prob. (13)	0.0832	0.0831	0.0830
prob. (over 13)	0.4671	0.4672	0.4673

You can calculate these probabilities easily. In an 8-deck shoe, there are 32 cards of each rank ace through nine, and there are 128 tens. You would calculate the number of ways of getting each total. The total of 6, for example, can be made by getting dealt A/5, 2/4, 3/3, 4/2, or 5/A So, the number of ways of getting 6 is 32*32 + 32*32 + 32*31 + 32*32 + 32*32 = 5088. To find the number of ways of getting under 13, for example, just sum the numbers of ways of getting 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. And to convert this to a probability, divide this number by the total number of ways of getting dealt two cards, which is 416 * 415.

And to convert these probabilities to player EVs, use this formula: EV = ( odds + 1 ) * prob. - 1 , where odds for under is 1, over is 1, and 13 is 10.

Thank you. Mr. ChesterDog.

If you are a Counter:
With Good Penetration Counting the Over/Under 13 Bet is a better proposition using the appropriate Counting System than Counting the main BJ Bet.