first ace and hi-tie bet

We all know side bets are for suckers but there are some dealers who are sloppy cutters and when sitting at first base you can take advantage of this. Supposing you are on a table with the Hi-Tie side bet and KNOWING that your first card from a fresh shoe is going to be an ace, what is the player edge on this bet. We will use an 8 deck shoe and the pay-offs on the side bet are as follows:

50-1 hi-tie
15-1 suited pair
10-1 suited bj
6-1 bj
3-1 pair

Also, some places reverse the pays on the suited pair and suited BJ

I dont think it matters but just in case, the bj house rules are:

H17
double anything
split to 4 hands
double after split

Ibeatyouraces,

First, for the player to get a BJ, his 2nd card must be an X (ten or face). The 8-deck shoe has 8*16 = 128 X's, and since the first card is an Ace, the shoe contains 52*8 - 1 = 415 other cards. Thus, the probability of a player BJ is

Player BJ Prob = 128/415 = 0.3084...

or nearly 31%. Of these BJ's, one-quarter will be suited, and the other three-quarters will not be suited.

To get a High Tie, the player needs the dealer to also have a BJ. Given that the player has a BJ already, the probability of the dealer having an ace + X (in either order) is given as follows:

Ace + X: [(4*8 - 1)/414]*[(16*8 - 1)/413] = 0.02302...
X + Ace: [(16*8 - 1)/414]*[(4*8 - 1)/413] = 0.02302...
Total = 2*0.02302... = 0.04605...

High Tie probability = (Prob of player BJ)*(Prob of dealer BJ) = 0.01420...

Return of High Tie (50) payout = 0.71019...

By the way, the probability of the dealer NOT having a BJ when the player DOES is simply 1 - 0.04605... = 0.9539...

Suited BJ: here, the player must have a suited BJ with the dealer NOT having a BJ. This probability is given as

(1/4)*(0.3084...)*(0.9539...) = 0.07355...

Return of Suited BJ (15) payout = 1.1033...

Unsuited BJ: Here, the player needs an unsuited BJ with the dealer NOT having a BJ. This probability is given as

(3/4)*(0.3084...)*(0.9539...) = 0.2206...

Return of Unsuited BJ (6) payout = 1.3240...

Suited Pair: Here, the player needs one of the seven remaining suited Aces, so the probability is given as

(7/415) = 0.0168...

Return of Suited pair (10) payout = 0.1686...

Unsuited Pair: Here, the player needs one of the 24 remaining suited Aces, so the probability is given as

(24/415) = 0.0578...

Return of Unsuited pair (3) payout = 0.1734...

Total Win Probability = 0.01420... + 0.07355... + 0.2206... + 0.0168... + 0.0578... = 0.3831...

Total Lose Probability = 1 - 0.3831... = 0.6168...

Total Lose Return = -1*0.6168... = -0.6168...

Total Return = 0.71019... + 1.1033... + 1.3240... + 0.1686... + 0.1734... + -0.6168... = 2.8626...

Thus, given that your first card out of the shoe will be an Ace, you have a whopping 186% edge on the High Tie bet.

Go for it! ;-)

Dog Hand

Thanks for the math Dog. We knew it would be huge but couldn't figure in the probabilty with the dealers hand. As for knowing the ace, Some dealers are sloppy and some tip you off :)

Nice to have friends in high places ;)

Table max, here I come!!

Knowing this info I may never count again in my life haha. Been hole carding alot of three card poker anyway lately

Hopefully they will stay friendly when you guys will share a cell... Tipping the next card to a player is called: collusion. In most jurisdiction this is good for jail time.