smoothgrh
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October 26th, 2018 at 11:17:42 AM permalink
Fantastic Fives video poker by IGT is boring in my opinion—but it seems to be a rare game, so there's some novelty in that. I'm trying to figure out how many hands I should expect to play to even get any quad 5s. I looked at the Wizard's "Royal Sevens" page, in which the probability is .000231 to get Four Sevens. The probability should be the same, right? So that's expected to be about 2 occurrences in 10,000 hands?

smoothgrh
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October 29th, 2018 at 2:47:28 PM permalink
OK, please help my feeble math brain.

I see from the Wizard of Odds site that the odds of getting any four of a kind is 1 in 3,430.

The probability of a specific four of a kind appears to be 0.0002 — is that the same as 2 in 10,000?

If so, is that the same as 1 in 5,000?

If so, how is it that the odds of any four of a kind is 1 in 3,430, but a specific four of a kind is 1 in 5,000?

Finally, the Ask the Wizard page says the expected number of four of a kinds to get at least one of all 13 four of a kinds is about 41.3 — so does that mean I can expect an average of (41.3)(3,430) = 141,659 hands until I'm statistically expected to get my stupid quad 5s?
HugoSlavia
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October 29th, 2018 at 6:10:11 PM permalink
Quote: smoothgrh

If so, is that the same as 1 in 5,000?

If so, how is it that the odds of any four of a kind is 1 in 3,430, but a specific four of a kind is 1 in 5,000?

Finally, the Ask the Wizard page says the expected number of four of a kinds to get at least one of all 13 four of a kinds is about 41.3 — so does that mean I can expect an average of (41.3)(3,430) = 141,659 hands until I'm statistically expected to get my stupid quad 5s?


For 8/5 Jacks, quads of any rank come at a rate of about 1 in 423. So if you're looking for a specific rank, I think you could multiply by 13 to get a very rough estimate of 1 in 5,500.

The big 141,659 number is for accumulating all 13 ranks, which is a lot more difficult.

I've never seen the Fantastic Fives game before, but it doesn't look like a good one. The extra payoffs only occur in very rare scenarios. You need quad 5s with specific kickers, and the kickers only play in positions 1 or 5.

It would be a fun enhancement to a 9/6 Jacks game, but 8/5 Jacks is only 97.3% base.
smoothgrh
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October 29th, 2018 at 10:06:28 PM permalink
Yeah, that the kickers need to be in the 1 or 5 positions makes the game insane. It's quite a mountain to climb to get that award.
tringlomane
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October 29th, 2018 at 11:09:05 PM permalink
Some quick and dirty math shows it adds about 0.7% when you don't make any strategy changes at all. But you obviously will in some cases, especially holding 555A in position. I would think 55A in position would be a hold as well since it's like 3 to a Royal.
AxelWolf
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October 30th, 2018 at 3:07:01 AM permalink
Quote: HugoSlavia



The big 141,659 number is for accumulating all 13 ranks, which is a lot more difficult.

.

That can't be right. ??????
♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
HugoSlavia
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October 30th, 2018 at 4:59:07 AM permalink
Quote: AxelWolf

That can't be right. ??????


Thanks, you're correct. I knew it was a big number, but didn't look at it carefully.

Wizard says 1 in 17,893 for a generic game with no strategy adjustments:

https://wizardofodds.com/games/video-poker/tables/power-quads/

Smoothgrh mentioned that you need 41 quads on average to catch all 13 ranks, then you would multiply 41 by the 423 cycle for quads.

Quote: tringlomane

Some quick and dirty math shows it adds about 0.7% when you don't make any strategy changes at all.


Thanks. I would have guessed lower than that.
HugoSlavia
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October 30th, 2018 at 5:17:59 AM permalink
By the way, the Power Quads link also shows the relative probabilities for ranks. The high card ranks are around 0.000195 (1 in ~5100), while the low cards are only 0.000175 (1 in ~5700).

Fives are listed at 0.000175832 = 1 in 5,687.

That's for a 9/6 Jacks game, but 8/5 Jacks would be similar.
Wizard
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October 30th, 2018 at 7:53:33 AM permalink
My video poker program that handles sequential hands is 1,334 lines of code and I haven't used it in a while. It would take some customizing for this game. I will put it on my "to do" list, but it's rather low down.
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smoothgrh
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October 30th, 2018 at 8:44:47 AM permalink
Thanks everyone.

I would call this a "failed" game, but in a way, that's what makes it interesting.
gordonm888
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October 30th, 2018 at 12:11:46 PM permalink
Quote: Wizard

My video poker program that handles sequential hands is 1,334 lines of code and I haven't used it in a while. It would take some customizing for this game. I will put it on my "to do" list, but it's rather low down.



The need for Quad 5s kickers to be in 1st or last position will complicate the analysis a little bit - at least for the techniques that I use. Do any other VP games use position-dependent bonuses like this? (Is position dependence what is meant by "sequential hands"?)
Last edited by: gordonm888 on Oct 30, 2018
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DRich
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October 30th, 2018 at 12:23:15 PM permalink
Quote: gordonm888

The need for Quad 5s kickers to be in 1st or last position will complicates the analysis a little bit - at least for the techniques that I use. Do any other VP games use position-dependent bonuses like this? (Is position dependence what is meant by "sequential hands"?)



A-C-E-S Bonus poker is position dependent.
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GaryJKoehler
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October 31st, 2018 at 11:58:59 AM permalink
As you guessed, the Sequential Royal games are position dependent. As noted above, A-C-E-S Bonus poker is another. So is Double Bonus Poker Plus and, to a lesser extent, Pick'em Poker.
Wizard
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October 31st, 2018 at 1:58:17 PM permalink
There are 57,407,703,889,536,000 possible permutations in positional video poker games. It takes a lot of short cuts to get the run time in terms of minutes as opposed to years. Every different game requires different short cuts. This is the first game I've seen where a win for a four of a kind with a kicker depended on the position, so I would have to figure out how my code worked before (because I never document) and then tweak it for this game.
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tringlomane
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October 31st, 2018 at 2:08:13 PM permalink
Quote: smoothgrh

Yeah, that the kickers need to be in the 1 or 5 positions makes the game insane. It's quite a mountain to climb to get that award.



Looking back at my 516 documented quads in the last 5 years, I've got it at least once unintentionally in another game.



Quote: smoothgrh

Thanks everyone.

I would call this a "failed" game, but in a way, that's what makes it interesting.



Yeah Double Bonus Plus is a "failed game" too. I'm not too sure why positional dependent games haven't caught on that much. But of course the math is a lot more complex, so maybe IGT also avoided creating them. Why work a lot harder for a mildly exciting gimmick?
DRich
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October 31st, 2018 at 2:19:12 PM permalink
Quote: tringlomane

. I'm not too sure why positional dependent games haven't caught on that much.



My gut feeling is that players don't really like them because it is disappointing to get the four of a kind but in the wrong position most of the time.
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RealizeGaming
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October 31st, 2018 at 2:38:16 PM permalink
Quote: smoothgrh

Fantastic Fives video poker by IGT is boring in my opinion—but it seems to be a rare game, so there's some novelty in that. I'm trying to figure out how many hands I should expect to play to even get any quad 5s. I looked at the Wizard's "Royal Sevens" page, in which the probability is .000231 to get Four Sevens. The probability should be the same, right? So that's expected to be about 2 occurrences in 10,000 hands?



I'm curious as to where this game is located. I have no idea if I'd be interested in playing it, but I do find these types of games to be different and fun.

I'm also assuming you could do the same game, but change the fives to some other value?
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