Aces Cracked Promo: Value per hour?

[carddown]

Two local card rooms offer "Aces Cracked" promotions, and one of them is expanding their offer to several days a week. One place rewards $100 and the other pays $60 for Aces Cracked. Surely, there is a formula to determine the estimated value per hour of this promotion, but I'm unable to find it. The promo is for any game, but realistically, we're talking here about a 3/6 limit Hold 'Em game. I guess you can use the results for any game if you figure out a value of the promotion independent of your pot investment.

Another statistics question: I know how often I'm likely to get pocket Aces, but how often am I supposed to be playing against them at a full table? Is it still 1 in 221, or is it number of players/221?

[Acey]

# of players/221?

[dippy111]

It's more complicated than that. You have to use the binomial formula. Assuming you dont hold an ace:
Let P be the probability of AT LEAST 1 person having aces
A will be the prob of EXACTLY 1 person having aces.
B will be the prob of EXACTLY 2 people having aces
n=number of OTHER players at table

A=(n!/(n-1)!).(1/221).(220/221)^(n-1)
B=A.((n-1)!/(n-2)!).(1/1225).(1224/1225)^(n-2)
P=A+B

I think this is right, but I can't solve it b/c I don't have my calculator.

[jesse8888]

You'll be playing against pocket aces ABOUT # of players/221 (it's a little less than that because the events are dependent, but that's good enough for government work).

Assuming 31 hands per hour, you should get aces about once every 7 hours. Assuming standard 3/6 players, you'll be up against lets call it 4 opponents. How often will one of them outdraw you? I'd say getting them cracked about 50% of the time sounds reasonable, although it could vary greatly. So you'll get aces cracked once every 14 hours and receive 100 dollars for your effort.

If you adjust the cracking percentage, you obviously can change this quite a bit.

[jesse8888]

For the record, one of the most frustrating experience I ever had was a session where I bet top pair very aggressively all the way to the river 3 times, only to be shown aces by a saddened villain who just wanted his 100 bucks.

[pzhon]

[ QUOTE ]
For the record, one of the most frustrating experience I ever had was a session where I bet top pair very aggressively all the way to the river 3 times, only to be shown aces by a saddened villain who just wanted his 100 bucks.

[/ QUOTE ]
Be happy he didn't realize he could have raised safely on the river. He's ahead of your calling range, and no hand better than AA would fold very often.

[carddown]

Thanks for the input. My math skills were bad before they atrophied, so check me on this:

Assuming 25 hands per hour, chances of you getting AA about 11.3%
estimate losing with AA (calling only) 55%,
taking our bonus chances per AA to 6.21%.

Aces Cracked pays $100, promotion worth $6.21 per hour
Aces Cracked pays $ 60, promotion worth $3.71 per hour
Aces Cracked pays $ 40, promotion worth $2.48 per hour

This is estimate is for the bonus only and doesn't take into account what you have invested in the pot.

The value for the promotion is likely greater than the above numbers indicate, as you benefit even when the bonus is awarded to another player. More money is pumped into the game, but I have no idea on how to estimate a value for that.

[chillrob]

This logic all sounds correct, but I just find it hard to believe it could possibly be true! Would a casino really offer a promotion that pays every player over $6 per hour?
That would be one big bet an hour in a 3/6 game and could turn some losing players into winning ones. It just seems unlikely that a house would get enough value from the promotion that they would be willing to pay that much for it.

FWIW, I only played one time at a place with an Aces Cracked promotion going that day, and at my table it was hit once in about 5 hours of play. I know my single experience isn't statistically valid, but that would only amount to about $2 per hour per player.

[p4594spa]

I think you are missing the real reason that the casinos offer the promotion. In the case of Cache Creek in N. CA,
they only offer the Aces crack on week days during the day. Real objective is to draw people in during the low periods of the day. This isn't too different from why most Casinos do their tournaments in off hours. When the players get busted, they then sit down and play poker at the regular tables. So Casinos can actually lose money, for the promotion (be it tournaments or Aces cracked), and make money long term by getting seats at their tables.

[Tom Ames]

[ QUOTE ]
This logic all sounds correct, but I just find it hard to believe it could possibly be true! Would a casino really offer a promotion that pays every player over $6 per hour?
That would be one big bet an hour in a 3/6 game and could turn some losing players into winning ones. It just seems unlikely that a house would get enough value from the promotion that they would be willing to pay that much for it.

FWIW, I only played one time at a place with an Aces Cracked promotion going that day, and at my table it was hit once in about 5 hours of play. I know my single experience isn't statistically valid, but that would only amount to about $2 per hour per player.

[/ QUOTE ]

The Aces Cracked Promo is funded from the bbj fund--not the casino's profits. It costs them nothing extra and puts butts in the chairs.