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lil feller
09-26-2005, 11:35 PM
Not sure if this is the correct forum or not, but a friend of mine asked me fold help with this and i'm not qualified to do the math. At least not with confidence. Can any body help? Here's the deal.

A local casino is offer the following blackjack promotion, and my friend was curious about the EV of each bet, and the EV of the promotion as a whole. for those of you that like to flex your math muscle, here's a good opportunity to do so and help out a fellow poster.

To qualify for any of the below the player must place a \$1 "bonus" wager.

Payouts

First card A \$25
2 unsuited A's \$100
2 suited A's \$500
3 unsuited A's \$1000
3 suited A's \$2000
any 4 A's \$4500
4 all red or all black A's \$131000

Assume that to qualify you must get dealt the key cards in sequence. For example having your first card be a "K" and your next four be all black aces doesn't qualify.

Assume a fresh 6 deck shoe. Obviously the odds will change as cards get exposed.

Thanks in advance for any help.

lf

BruceZ
09-27-2005, 12:23 AM
[ QUOTE ]
3 unsuited A's \$1000

[/ QUOTE ]

Does this mean they have to be 3 different suits, or just not all the same suit? If the former, then 3 aces with exactly 2 of the same suit only wins the prize for 2 aces. Is that right?

[ QUOTE ]
any 4 A's \$4500
4 all red or all black A's \$131000

[/ QUOTE ]

Does this mean that we win both prizes if we have 4 all red or 4 all black?

For that matter, do 4 aces mean we also win the prize for 1 A, 2 aces, and 3 aces?

[ QUOTE ]
Assume that to qualify you must get dealt the key cards in sequence. For example having your first card be a "K" and your next four be all black aces doesn't qualify.

[/ QUOTE ]

Does this mean that each sequence must start with your first card and have no intervening cards?

lil feller
09-27-2005, 12:44 AM
[ QUOTE ]
Quote:
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3 unsuited A's \$1000

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Does this mean they have to be 3 different suits, or just not all the same suit? If the former, then 3 aces with exactly 2 of the same suit only wins the prize for 2 aces. Is that right?

[/ QUOTE ]

It means that they aren't all the same suit, but dont have to all be different suits.

[ QUOTE ]
Quote:
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any 4 A's \$4500
4 all red or all black A's \$131000

--------------------------------------------------------------------------------

Does this mean that we win both prizes if we have 4 all red or 4 all black?

[/ QUOTE ]

I'm not sure, but the big one is the total prize pool, so i'm going to assume that there is a "can only win one bonus" rule.

[ QUOTE ]
Quote:
--------------------------------------------------------------------------------

Assume that to qualify you must get dealt the key cards in sequence. For example having your first card be a "K" and your next four be all black aces doesn't qualify.

--------------------------------------------------------------------------------

Does this mean that each sequence must start with your first card and have no intervening cards?

[/ QUOTE ]

Thats correct.

Do you think you can help with this, i'd really appreciate it.

thanks,

lf

BruceZ
09-27-2005, 01:28 AM
The \$25 payout for 1 ace alone makes this postive EV. All the payouts together have a positive EV of \$2.68.

Since we can only win one prize, I multiplied the probability of making each hand with 1-3 aces by the probability that the next card is not an ace.

The probabilities sum to exactly 1, so we can have confidence that they are correct.

First card A \$25:

24/312*(311-23)/311*25 = \$1.78

2 unsuited A's \$100:

24/312*18/311*(310-22)/310*100 = \$0.41

2 suited A's \$500:

24/312*5/311*(310-22)/310*500 = \$0.57

3 unsuited A's \$1000:

[24/312*23/311*22/310*(309-21)/309 - P(3 suited aces)]*1000 = \$0.36

3 suited A's \$2000:

24/312*5/311*4/310*(309-21)/309*2000 = \$0.03

any 4 A's \$4500:

[24/312*23/311*22/310*21/309 - P(4 all red or black)]*4500 = \$0.11

4 all red or all black A's \$131000:

24/312*11/311*10/310*9/309*131000 = \$0.33

No prize:

(312-24)/24*(-1) = 92% * (-1) = -0.92

Total EV: \$2.68

Mr. Curious
09-27-2005, 02:05 AM
[ QUOTE ]
First card A \$25

[/ QUOTE ]

Are you positive that it is any ace? The Muck has a progessive jackpot that has this as a bonus bet, but the first payout is for your first card being a BLACK ace.

lil feller
09-27-2005, 11:10 PM
Thanks so much for that. I forwarded it to my friend, he really appreciated it.

lf

Mr. Curious
10-07-2005, 04:59 PM
I found the place where this game is offered and the table was full with a waiting list /images/graemlins/wink.gif

One thing that the OP did not mention: the table minimum is \$25. I don't think that it is enough to offset the +EV of the "Aces" bet, but it does make it harder to play for a long time if you do not have a big enough bankroll.