I need some Help

[lil feller]

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]

[ 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]

[ 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


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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:
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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.


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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]

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]

[ 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]

Thanks so much for that. I forwarded it to my friend, he really appreciated it.

lf

[Mr. Curious]

I found the place where this game is offered and the table was full with a waiting list [img]/images/graemlins/wink.gif[/img]

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.