A-C-E-S Bonus Poker cycle calculation

Wondering if someone ever calculated the mathematical cycle for getting the 4 aces in the proper sequence in the ACES Bonus Poker game. I just got back from Vegas and hit this hand at one of the downtown casinos. I would think it would be significantly rarer than The Royal Flush. I did it on a full-pay 8/5 machine. Humorous part is I did not even realize I hit the hand until the "call attendant" message flashed on the screen. I got to admit though that it was much more exciting than a Royal. As luck would have it some days, I hit a Royal in the same casino later that evening.

Quote: oldbudman

Wondering if someone ever calculated the mathematical cycle for getting the 4 aces in the proper sequence in the ACES Bonus Poker game. I just got back from Vegas and hit this hand at one of the downtown casinos. I would think it would be significantly rarer than The Royal Flush. I did it on a full-pay 8/5 machine. Humorous part is I did not even realize I hit the hand until the "call attendant" message flashed on the screen. I got to admit though that it was much more exciting than a Royal. As luck would have it some days, I hit a Royal in the same casino later that evening.

Nice run! No idea on the ACES math except it's 1/x x 1/13 rarer than a random 4oak, where x is all including out of order. 2/x if it counts either backwards or forwards. Now I have to try it...thanks.

Edit: So, I get 24 ways to display 4 aces. 1 spells ACES, the others out of order. There's a 5th card in there somewhere, though I don't know if it matters on that game (whether they have to be on consecutive reels, or the 5th card can be interspersed ). If the 5th card is ignored, it's just 1/24 x 1/13 x likelihood of any 4oak.

If the 5th card placement counts, the above would need another multiplier of 2/5, making it rarer yet.

I'm not calculating how many hands it can appear, though I think it would be 47/y, where y is all possible hands. A Royal is only 4/y, so still less likely than ACES by a factor of about 12.

Otoh, order matters in the ACES, and doesn't on the RF, or generally when counting y, so with order counting, perhaps ACES is rarer than a RF.

Not a math guy. I look forward to someone who is running thru it if they're interested.

IIRC, it's something like 300k or 500k hand cycle. If I have a minute later I'll do the math.

EDIT: I got 297,221.93609 for the cycle. Yes, I did the math free hand.



Sidenote: It does have to be ACE$- or -ACE$, meaning you can't have the non-ace in positions 2, 3, nor 4. The non-ace has to be in position 1 or 5.

Quote: oldbudman

Wondering if someone ever calculated the mathematical cycle for getting the 4 aces in the proper sequence in the ACES Bonus Poker game...

Here's the Wizard's page about your game.

Using the Wizard's permutations in his table, you can get a cycle of about 297,222, which is 99,666,152,586,000 / 335,325,696.

As RS recollected, it's about 300K.

Cool. Thanks, guys.

I guess the lesson reinforced here, is when faced with an option of playing 2 almost identical video poker machines (8/5 Bonus Poker or 8/5 ACES Bonus Poker) always play the one with the slightly higher return even if the odds of hitting the bonus jackpot are astronomical. Thanks for doing the math.

Quote: oldbudman

I guess the lesson reinforced here, is when faced with an option of playing 2 almost identical video poker machines (8/5 Bonus Poker or 8/5 ACES Bonus Poker) always play the one with the slightly higher return even if the odds of hitting the bonus jackpot are astronomical. Thanks for doing the math.

sure since it basically the same game and its not costing you anything extra for playing it.

but im not doing the extra coin ($1) for the $60k dealt royal bonus for the game im playing.
1 in 650k

Another way to look at it is that 1-in-60 quad aces hands qualifies for the bonus. the only hand you play differently is aces full , for example AAA55 --- and only then if the three aces are in the correct position.

Would someone be interested in telling me where these machines are located? Would like to try my hand at them.

Quote: rsactuary

Would someone be interested in telling me where these machines are located? Would like to try my hand at them.

I have played the 8/5 paytable at the M Resort and a number of Station properties. Of course the 7/5 paytable is out there, so be sure to check before you play.

Quote: Keeneone

I have played the 8/5 paytable at the M Resort and a number of Station properties. Of course the 7/5 paytable is out there, so be sure to check before you play.

The pic noted that they played "downtown", so was looking for information on that. I have seen the 7/5 paytables around.....

Quote: Keeneone

I have played the 8/5 paytable at the M Resort and a number of Station properties. Of course the 7/5 paytable is out there, so be sure to check before you play.

After a recent visit, I noticed the M Resort lowered the few machines they had to 6/5. Boo!
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Had a chance (at a Stations property):