house edge match the dealer bonus

Hi, I need help on calculating the house edge of this bet.

One or both of the players original two cards of the hand will match the dealers up card.

2 suited matches 25:1
1 suited + 1 non suited match 20:1
1 suited match 9:1
2 non suited matches 9:1
1 non suited match 4:1

i'm not going to do a complete analysis, but this is a rough start to give you some idea

probability of one card matching the dealer's = 7.7%
(note this includes the suited match payout so you will want to divide this by 3/4)

probability of at least one of the player's card matching the dealer's = 15% (again includes the the suited)
probability of both cards matching the dealer's = .6%


In order to calculate return you multiply the payout by the probability of it hitting

Quote: Runlikegod777

Hi, I need help on calculating the house edge of this bet.

One or both of the players original two cards of the hand will match the dealers up card.

2 suited matches 25:1
1 suited + 1 non suited match 20:1
1 suited match 9:1
2 non suited matches 9:1
1 non suited match 4:1

How many decks are used in this game? Also, are the decks regular or Spanish?

Assuming eight regular decks, taking out the dealer's up card there are 415 cards in the shoe, 31 cards of the dealer's up card's rank, and 384 cards not of the dealer's up card's rank. There are 7 cards that are of both the dealer's up card's rank and suit, and there are 24 cards of the dealer's up card's rank but of a different suit.

The number of ways for 2 suited matches is 7× 6 / 2.

The ways for 1 suited + 1 non suited is 7 × 24.

The ways for 1 suited match is 7 × 384.

The ways for 2 non suited matches is 24 × 23 / 2.

The ways for 1 non suited match is 24 × 384.

And the ways for no matches is 384 × 383 /2.

To find the house edge multiply each of the above numbers by its payout (the payout of no matches is -1.) Then divide the sum by the sum of the above numbers of ways, which should be 415 × 414 / 2.

For eight regular decks, I get a house edge of 7.11%.

sorry i forgot to include this is regular decks, they use 8 decks, but the penetration is to about 6 decks.


appreciate the responses so far, but can anyone confirm the approximate 7 percent being correct? i just need the ballpark # within a percent

Quote: Runlikegod777

sorry i forgot to include this is regular decks, they use 8 decks, but the penetration is to about 6 decks.


appreciate the responses so far, but can anyone confirm the approximate 7 percent being correct? i just need the ballpark # within a percent

ChesterDog used the parameters you later confirmed, to come up with HE 7.11%. Penetration doesn't matter for this calculation. I think you have an accurate answer already.

Quote: beachbumbabs

ChesterDog used the parameters you later confirmed, to come up with HE 7.11%. Penetration doesn't matter for this calculation. I think you have an accurate answer already.

And I agree. You check yourself by going to http://miplet.net/blackjack/ and download the appropriate file. You can then edit the pay table and deck composition.