Flush Fever -- Nevada Variant
In my third in a series, I've found a new video poker game called Flush Fever. This is not to be confused with a game of the same name found in Oregon. To help avoid confusion, or perhaps cause it, I'll call the Oregon game the Oregon variant and the one seen in Vegas the Nevada variant.
The concept is simple. For an optional sixth coin bet the player will be guaranteed a winner if he draws to four to a flush. This is achieved by the game burning through the other 47 cards in the deck until a win is found. There is also a progressive feature, that goes up by a coin for every burned card.
For all the details, please see my new page on Flush Fever -- Nevada variant.
A problem arises in declaring the return of the game because it is progressive. So far I've just analyzed one pay table, 8-6 double double bonus. Here are three returns I'm dealing with:
- 95.15%: This is my return without considering the progressive feature. In other words a 4,000 coin royal.
- 97.18%: This is my return considering the progressive feature and assuming an average royal win, which would be 7870 coins. I did not factor in the $99,999 progressive growth cap in this figure, as this would be mathematically complicated and the average return would vary depending on denomination.
- 97.07%: This is a return given to my by IGT. I do not know what IGT assumed about the average royal or denomination behind this figure. I've tried to ask them about such questions, but have been unable to make myself clear as they keep telling me things I already knew in their replies.
The way I have addressed progressive games in the past is to indicate the lowest return at the re-seed amount and an adjustment factor based on the meter amount. For example, "The return is x% plus an additional y% for each z coins in the meter beyond 4,000.
I haven't posted my an analysis section. For now, I welcome all questions, comments, and especially corrections based on the rules and example that I have posted.
Looks like there will be some chances for 100% opportunities here.
On a side note: Did you ever find a new game in a casino just to come back home and realize, "Oh, I had already analyzed that 2 years ago."
Quote: DRichDoes the progressive go up one coin or one cent for every burned card. In your picture it shows the progressive one coin higher but you made it sound like it burned through more than one card before the Jack of Diamonds came up.
Good catch! I guess I remembered incorrectly and there was just one burned card before I got that flush, as evidenced by the fact that the meter is 5 cents higher. Thank you.
Quote: BozDid you figure how many times the 5th card would give you a Straight Flush when coming up with the payback number?
Yes.
Quote: CanyoneroWhere did you find it?
The Rampart casino in Summerlin, the closest casino to my house.
Quote:On a side note: Did you ever find a new game in a casino just to come back home and realize, "Oh, I had already analyzed that 2 years ago."
Yes, lots of times. Most recently with the game Change It, which I saw at the Fremont. I was part of the way through an analysis of it when I vaguely recalled working on such a game before. Sure enough, I found a spreadsheet for the game I did over ten years ago. Just goes to show how long a game inventor has to stay at it to get his game out there.
Quote: DRichDoes the progressive go up one coin or one cent for every burned card. In your picture it shows the progressive one coin higher but you made it sound like it burned through more than one card before the Jack of Diamonds came up.
Good point. But without a big progressive, the bonus bet is probably a loser, unless there is a math goof.
Edit: Wiz verified it was just one burn.
So, I now have no idea why I'm coming up 0.11% higher than IGT.
The way I think I'll express my results for this game is something like this, using 8-6 double double bonus as an example.
Base return at 4,000 coin royal = 95.16%
Additional return per 1,000 additional coins in meter beyond 4,000 = 0.52%.
Breakeven meter = 13,266 coins.
Probability of each royal cycle reaching positive EV = 0.03%.
Unfortunately, if this was missed, it actually makes the return calculations further apart.
Quote: AyecarumbaI note that the Flush returned 30 coins with the sixth coin inserted instead of the 25 in the five coin table, while the other payouts (except the progressive) were the same. The write up says that all the payouts are standard with the sixth coin inserted, but this doesn't seem to be case.
Unfortunately, if this was missed, it actually makes the return calculations further apart.
Good catch, I didn't see that either.
The biggest question the results ask is does enabling the feature decrease the expected return of the game? Every other IGT feature game I've seen increased the return or had no effect. I ask this because the base return of a 5 coin 8-6 DDB is 97.9% which is higher than the wizard's or IGT's analysis.
Quote: Wizard
Probability of each royal cycle reaching positive EV = 0.03%.
Considering the average royal value you calculated, I don't see how this is possible. And shouldn't royals be more likely in this game? You get redraws on 4 to a royal right?
Quote: TortoiseThe flush fever game at my local casino increases the payouts for the flush and straight flush when playing the sixth coin. For example there's a 9-5 JOB pay table when betting 5 coins that increases to 30 for 1 on the flush and 350 for 1 on the straight flush when betting 6 coins.
The biggest question the results ask is does enabling the feature decrease the expected return of the game? Every other IGT feature game I've seen increased the return or had no effect. I ask this because the base return of a 5 coin 8-6 DDB is 97.9% which is higher than the wizard's or IGT's analysis.
But if you look at his pictures, he shows 7/5 JoB and the paytable moves up to 7/6 with the 6th coin. So it's likely this would be an 8/5 DDB game if you only bet 5 coins.
Quote: PokeraddictThere is also a Flush Fever on VLT machines in South Dakota that isn't either one of these games. One would think IGT could come up with a unique name.
Great, now we not only have the Oregon and Nevada variants but South Dakota as well. Do you know the thrust of the SD version?
Quote: AyecarumbaI note that the Flush returned 30 coins with the sixth coin inserted instead of the 25 in the five coin table, while the other payouts (except the progressive) were the same. The write up says that all the payouts are standard with the sixth coin inserted, but this doesn't seem to be case.
Unfortunately, if this was missed, it actually makes the return calculations further apart.
My math accounted for the more generous pay table for six coins bet. I will add to the rules that the sixth coin also bumps up the pay table a bit.
Quote: AyecarumbaDid your calculation assume the player would always hold four to a flush, even if playing five coins or less? If a player has a pair of aces, and no straight flush draw, is drawing to a flush always the best play?
I only analyzed the game for a max-coin bet. The way I did it was to consider every way the player could hold four to a flush, including sacrificing a dealt flush, as well as all other possible plays, and went with the one with the greatest expected value. For the four-flush holds, it iterated through the other 47 cards in the decks and took an average win among all the winning cards.
Quote: Wizard...The way I did it was to consider every way the player could hold four to a flush, including sacrificing a dealt flush, as well as all other possible plays, and went with the one with the greatest expected value...
I didn't consider that a strong play on this game is to drop the non-sequential card in a dealt five card flush to go for the straight flush.
Could your use of average win vs. running every single permutation account for the difference?
Quote: AyecarumbaI didn't consider that a strong play on this game is to drop the non-sequential card in a dealt five card flush to go for the straight flush.
Could your use of average win vs. running every single permutation account for the difference?
It's better than that. If you're dealt a flush with 0 or 1 high cards you discard a card just to raise the royal flush jackpot, knowing you're guaranteed to draw a flush.
Maybe thats the difference in Wiz's and IGTs calc? Discarding currently equal EV flushes to just increase the progressive more?? Maybe IGT missed that? I would be shocked if that added 0.11% though.
Edit: With some rough math...yeah it could possibly make that much of a difference. I dunno the royal probability...
Quote: AyecarumbaCould your use of average win vs. running every single permutation account for the difference?
My code does consider every permutation. It considers all 2^5 ways to play the hand ordinarily, plus the up to 5 ways to play it by holding a four to a flush with the win guarantee. In all cases it cycles through all the ways the replacement card could come out.
I'm 99.54% sure there isn't anything wrong with the methodology of scoring the hand by hand EV, but that doesn't mean I didn't make a coding error somewhere.
When I did the analysis I just assumed the 4,000 coin royal. My return would only go up if I made strategy changes as the royal got larger. Since my return is already higher than IGT's, I don't think that is the issue.
This brings up an interesting issue if one wanted to do a perfect analysis, based on a growing royal. Would you calculate the house edge as the optimal play one hand at a time, or consider playing the machine an infinite period of time by sometimes taking a lower EV now in return for a bigger royal later.
Quote: WizardThis brings up an interesting issue if one wanted to do a perfect analysis, based on a growing royal. Would you calculate the house edge as the optimal play one hand at a time, or consider playing the machine an infinite period of time by sometimes taking a lower EV now in return for a bigger royal later.
This seems to be similar to the ideas that come up when vulturing Ultimate X comes up. I'm not saying the ideas are exactly the same, but I do see some similarities there.
Qs-Ks-Js-3s-5d
7/6 Jacks, EV: 1.482886
The KQJ is slightly better than 10JQ.
Now, if you hold Qs-Ks-Js-3s-5d, and the only possibilities are a Flush or High Pair, then:
(9/18 * 6) + (9/18 * 1) = 3.5
So, clearly you hold the Four Flush and it's not close.
I'm interested, Wizard, how does the overall probability of a Royal in your analysis compare to .000025? Does the increase of Royals due to Four-to-a-Royal draws being more likely to hit make up for how often three to a Royal is discarded in favor of a Four-Flush?
I think I would definitely play this game on Three-Play or Five-Play, on single-hand, meh.
I assume the best play is to always go for the best hand. Building a progressive and actually having the time and bankroll to collect it are two very different things.Quote: Wizard...This brings up an interesting issue if one wanted to do a perfect analysis, based on a growing royal. Would you calculate the house edge as the optimal play one hand at a time, or consider playing the machine an infinite period of time by sometimes taking a lower EV now in return for a bigger royal later.
Of course, I have yet to hit a royal, so my view may be askew...
Quote: AyecarumbaI assume the best play is to always go for the best hand. Building a progressive and actually having the time and bankroll to collect it are two very different things.
I agree. In this case, I think it is appropriate to assume an impatient player whose goal is to maximize the win of the current hand. For Ultimate X, that may be a different story, because you don't have to wait 40,000 hands to realize the benefit of making a sacrificial play now.
In other news, I just added lots of tables to my Flush Fever page, including return tables for 34 games as well as information on the value of each extra 1,000 coins in the meter and when any given pay table becomes positive.
I spent the good part of this week working on it, so I hope my readers will appreciate the effort, but probably won't. Usually the things I work the hardest on get the least attention.
Finally, I'd like to say happy birthday to Laura Ingalls Wilder.
I would be expecting the game to be over 100% about 30% (a little less than 1/e) the time since the average payout is near 100% but it's worst payout is sub 98%.
