Flushes Gone Wild now at PH - any insights?

So Bally's Flushes Gone Wild went live at Planet Hollywood sometime last week. I spent a little time watching on Saturday before I had to run, and unfortunately the dealer wasn't much help as it was her first five minutes on the game and she fully admitted she didn't know exactly what was going on after her crash course of instruction.

https://www.ballytech.com/Table-Products/Table-Games/Specialty-Games/Flushes-Gone-Wild

Seems like a direct High Card Flush competitor, although with community cards and the added factor that deuces are wild. Anyone spend any time playing this yet and are there any other installs?

This game was part of the Coventry showcase in May - I had a quick look at it before the show started but took few notes (so can't remember the details of the ante,blind,raise).

Adding wild twos and the two-card board makes it a more interesting game. I didn't work out a strategy but it was fun to play.

Obviously there's a technical issue with counting the twos (in other words if players know there aren't any left, then they should play more often).

Can you specify the rules a little bit more such as payouts when you beat the dealer. If the dealer doesn't have at least a 2 card flush, does that mean he doesn't qualify?

Quote: Avincow

Can you specify the rules a little bit more such as payouts when you beat the dealer. If the dealer doesn't have at least a 2 card flush, does that mean he doesn't qualify?

FWIW, it's not possible for the dealer NOT to have a 2 card flush. But I don't know anything more than what was on the Ballytech page above, so I can't answer your question about paytables for sure. Watching the video, I gathered the following:

There is no "dealer qualifies with.." language on the insurance circle, and it was not mentioned in the narrative, so I think there's no qualifier.

From what I could see on the felt, this appeared to be the Flush Rush (sidebet) paytable (it was a little blurry, so I may have the amounts wrong):

7 card natural flush 250:1
7 card wild flush 100:1
6 card natural flush 50:1
6 card wild flush 10:1
5 card natural flush 6:1
5 card wild flush 3:1
4 card natural flush 1:1

This bet pays regardless of whether the player wins or loses against the dealer, and is optional.

The Ante and Play bets pay 1:1 when you win regardless of length. The blind (required bet) pays on odds of by how many cards your flush beat the dealer's cards. Again, the video was a little blurry, but here's what it appeared to say:


0-1 Push
2 2 to 1
3 5 to 1
4 25 to 1
5 200 to 1

If this paytable is correct, in the first hand the dealer appears to pay the 5 card flush (4 diamonds plus a wild deuce) 2:1 on the Blind, when the dealer has a 3 card Spade flush as best hand. Dealer also has a 3 card Club flush using the community cards, but the same-length Spade flush outranks their Club flush, so that's the one the players compete with.

I think it's pretty interesting that you have to bet without seeing the Community cards. I'd be interested in the numbers and optimal strategy on this. I don't think you can count on community cards improving your hand, and should probably fold on a rainbow with no wilds, possibly fold with 2 - 2 card flushes and no wild (perhaps if one of them includes an Ace or both have Face or better you should stay; not sure), must stay with any deuce in hand, must stay with any 3 card or better flush hand regardless of rank, because of the possibility of deuces in the community cards. I could be wrong, easily.

Edit: I also think the strategy vs. optimal strategy on HCF (play with 3 card flush J or better) is heavily affected by 2 things: on this game, your ante bet is 2x (on HCF it's 1x unless you want to go up with 5 card flush or better); and you only know 5 of your cards before you have to bet 2x your ante.

There's also the Blind bet to consider, which you lose every time you lose, but you only win when your hand has 2+ more length (and otherwise pushes); at a rough guess, you're going to lose the blind bet 60% of the time (disregarding ties) because of folding, push it 30% of the time, win 2:1 maybe 8% of the time, win more 2% of the time.

Still wondering about OS: in the Bally video, the person who folds their hand in example 1 had Kx of one black suit, Qx of the other, and a red card, with no wilds. So they folded that hand (which I thought might be one worth betting as I said above), and then the community cards put 2 more clubs up there, which resulted in a 4 card club suit that would have beaten the dealer, had they stayed. With their faces, even if only 1 suit had caught 1 of the 2 community cards, they still would have won (dealer had Jxx spades for their high hand). And yet, I don't think Bally would post a demo video where their players didn't play optimum strategy. I don't know. Any thoughts?

2nd edit: Washington State approved the game for play with these rules. I think that should answer most of your questions. Note, however, that in the video, the Blind pay for 2 more cards than the dealer was 2:1. In the WA state rules, the game is 3:1. That has to have a pretty big effect on the HE - the WA game w/ 3:1 the HE is listed at 2.81%, but I bet the 2:1 in the video adds 2-3% to that. The sidebet HE is listed at 8.58%. I corrected both tables above to reflect the WA values, except for the 2:1 vs. 3:1 Blind pay as shown in the video. No guarantee that the other values shown on the felt in the video match the WA values.

In my opinion (only), a game that requires a $20 bet minimum (assuming a $5 ante, and not including the sidebet), the 2.81% HE is more than enough to pay for it. I think it's a little greedy of PH to play the game with a higher HE using the 2:1 payoff, if that's the paytable they're using for the Blind and all the other amounts are the same.

I saw this at PH a week or so ago, grabbed a rack card, and wrote down the paytables. I spent some time playing it today actually, and it's a lot of fun.

Here are some things I learned:

Wilds are played the same as Pai Gow Poker, where they take the place of the highest card not already part of your hand. For example, AcTc2d is treated as AKT of clubs.

As compared to HCF, you choose whether or not to play, but you don't discard. Because of this, there are plenty of times where you win with a suit you hadn't planned on. For example, play a hand with Kh Th 9c 4d 2s, then catch a Qc Jc shared board for a AQJ9 of clubs.

I would be curious about optimal strategy too. Intuitively it seems that any hand with a deuce is playable and any 3 card natural would be as well. Not sure beyond that.

Overall it was a fun game, although the rake bet (Blind) rarely pays, as expected. I played ~35-40 hands and won by 2 cards twice.

One last thing. PH does indeed pay 3:1 for a win margin of 2

Quote: beachbumbabs

7 card natural flush 250:1
7 card wild flush 100:1
6 card natural flush 50:1
6 card wild flush 10:1
5 card natural flush 6:1
5 card wild flush 3:1
4 card natural flush 1:1

That's the correct paytable.

Quote: Ncell

One last thing. PH does indeed pay 3:1 for a win margin of 2

Really glad to hear it. In the demo video, they paid that at 2:1, so I made no assumptions about which paytable they were using. I think I will have to go try it. Pretty frustrated with HCF; maybe this is better.

Quote: beachbumbabs

Really glad to hear it. In the demo video, they paid that at 2:1, so I made no assumptions about which paytable they were using. I think I will have to go try it. Pretty frustrated with HCF; maybe this is better.

First impression, I prefer it to HCF. Ask me again after a few sessions, I suppose. Because it's so new and difficult to read the hands, the game moves a bit slow because the dealers are learning it just like you or I am. It was fun though. Coming from HCF, the wilds mess up your hand reading at first, because you see the dealer with three hearts and think you've won, only to realize they have a deuce of diamonds with it

Quote: Ncell

Here are some things I learned:

Wilds are played the same as Pai Gow Poker, where they take the place of the highest card not already part of your hand. For example, AcTc2d is treated as AKT of clubs.

I ran the numbers for the side bet and came up with a much higher edge for it than listed above, so if someone wants to check my math, they're welcome to shoot me a PM.

I would be curious about optimal strategy too. Intuitively it seems that any hand with a deuce is playable and any 3 card natural would be as well. Not sure beyond that.

Overall it was a fun game, although the rake bet (Blind) rarely pays, as expected. I played ~35-40 hands and won by 2 cards twice.

Is that rule about how the wild card fills in on the table? I could see that leading to confusion.

And good to hear that PH pays 3 to 1 on a two card win, otherwise the house edge probably would be huge.

Not sure if i like the win by setup either. Pushing the blind bet on a 7 card flush would suck.

As for optimal strategy, there are definitely some folds in the game.

How often should we be folding though?

For our weakest hands we want to fold hands that can't win at least this amount (X) of the time:

3X - (1-X)*4 = -2
7X = 2
X = 2/7 ~ 28.57%

Now let's look at the weakest possible starting hands class 2-1-1-1 no deuce

Final flush hand distrubutions for 2-1-1-1 no deuce:

4: (14/47) x (13/46) = 0.0841813136

3: 2 x (14/47) x (33/46) + 3 x (11/47) x (10/46) = 0.5800185

2: (33/47) x (22/46) = 0.335800185

Since the dealer will win nearly all the 2 card hands and some of the 3 card hands, this should almost always be a fold.

But let's see how often a dealer will end up with a 2 card hand to be sure.

Dealer making a two card (ignoring your cards)

C(4,1) x C(12,2)^3 x C(12,1) / C(52,7) = 0.1031494815.

So yeah still a fold here.

What about the dealer probability of making 3 card hand?

Without a deuce it can be:
3-3-1, 3-2-2, 3-1-1-1

3-3-1: C(4,2) x C(2,1) x C(12,3)^2 x C(12,1) = 6,969,600

3-2-2: C(4,2) x C(2,1) x C(12,2)^2 x C(12,3) = 11,499,840

3-1-1-1: C(4,1) x C(12,3) x C(12,1)^3 = 1,451,520

Total non-wild 3 card flushes: 19,920,960
Probability of non-wild 3 card flush: 0.1489032815

With a deuce it can be: 2-2-2 or 2-2-1-1:

2-2-2:

4 deuces x C(4,3) xC(12,2)^3 = 4,599,936

2-2-1-1:

4 deuces x C(4,2) x C(12,2)^2 x C(12,1)^2 = 15,054,336

Total wild 3 card flushes: 19,654,272
Probability of a wild card flush: 0.1469098676

Total probability of a three card flush: 0.2958131491

So this leads to the median hand being a four card flush. If I didn't eff up the math (very possible), the dealer should have a 4 card flush or better 60.1% of the time.

This probably means bigger 2-2-1 scenarios may also be a fold as shown in the video.

4: 2 x (10/47) x (9/46) + 4 x (4/47) x (20/46) + (4/47) x (3/46) = 0.1628122109

3: 4 x (10/47) x (23/46) + 2 x (10/47) x (10/46) + 2 x (4/47) x (23/46) + (11/47) x (10/46) = 0.6540240518

NOTE: 60.3% of the total breakdown would be 3 card flushes from the doubletons, so if you had ace high on both, i might think is a call as half of 60.3% is over 28.3%. Maybe even a bit lower than ace high.

2: (23/47) x (22/46) - (11/47)*(10/46) = 0.1831637373

Pretty sure deuce with a rainbow would be okay here.

The dealer making a four flush a lot concerns me about playing a poor 3 suit like 568 suited if you have 2 singletons with it.

3-1-1 no wild:

5: (13/47) x (12/46) = 0.0721554117 (reasonable chance of 3 to 1 blind pay)

4: 2 x (13/47) x (34/46) = 0.408880666

3: (34/47) x (33/46) = 0.5189639223

I think the blind payout saves us here.

Let's say dealer has 2 card 10%, 3 card 30%, 4 card 30%, and 5+ 10% and we'll lose 80% of 4/5 card battles that are even with the dealer since our 3 suited cards are weak. Let's say we lose all 3 card battles.



(8 units)*(0.0721554117)*(0.1) + (6 units)*(0.0721554117)*(0.3) + (3 units)*(0.0721554117)*(0.3) +(3 units)*(0.0721554117)*(0.1)*(0.2) - (4 units)*(0.0721554117)*(0.1)*(0.8)

Plus

(6 units)*(0.408880666)*(0.1) + (3 units)*(0.408880666)*(0.3) + (3 units)*(0.408880666)*(0.3)*(0.2) - (4 units)*(0.408880666)*(0.3)*(0.8)

Plus
(3 units)*(0.5189639223)*(0.1) - (4 units)*(0.5189639223)*(0.9)

0.2359481963 + 0.2943940795 - 1.7125809436 = -1.1822386678

Still better than folding.

Tired of doing math. Wiz or someone else can take over. Unfortunately i think 2-2-1 or deuce with a rainbow. may be dependent on hand strength.

tringlomane -This is a great start. I agree that the 2-1-1-1 is a clear fold without a deuce, even ace high. You have no backup plan.

With a lone deuce, even with a rainbow, you're guaranteed an ace high three card. Not super strong, but not horrible either.

With a rainbow plus a deuce, you'll get two suited community cards (11/47) * (10/46) = 0.0509 = 5.1% of the time, ignoring additional deuces. The deuce substituting for an ace is the saving grace on any deuce only hand.

You seem to have a solid understanding of this. Could I interest you in checking my math on the side bet? I'm convinced I made an error, but I've gone over it many times and don't see anything out of place.

Quote: Ncell

Could I interest you in checking my math on the side bet? I'm convinced I made an error, but I've gone over it many times and don't see anything out of place.

Here is my pay table. I assumed a hand of 2,4,6,7,J,K,A all clubs would count as a Natural 7 card, not a Wild 7 card.

Hand	Pays	Ways	Probability	Return
7 card natural	250	6864	0.000051306	0.012826592
7 card wild	100	38896	0.000290736	0.029073609
6 card natural	50	247104	0.001847029	0.092351464
6 card wild	10	906048	0.006772441	0.067724407
5 card natural	6	3243240	0.024242259	0.145453556
5 card wild	3	7636248	0.057078694	0.171236083
4 card natural	1	20420400	0.152636448	0.152636448
4 card wild	-1	24271680	0.181423626	-0.181423626
3 card natural	-1	54537120	0.407648835	-0.407648835
3 card Wild	-1	8677152	0.064859144	-0.064859144
2 card natural	-1	13799808	0.103149482	-0.103149482
Total		133784560		-0.085778927

miplet never ceases to amaze me.

I'd say based on the rules from the first page, that hand isn't a 7 card natural because the 2 becomes the Qc.

Quote: BTLWI

I'd say based on the rules from the first page, that hand isn't a 7 card natural because the 2 becomes the Qc.

Maybe, but having the rules that way leads to mad customers, imo.

Also miplet's numbers for the house edge match the Washington state tribal gaming report for the 3 significant figures that they report the house edge (8.58%). Forcing a 7 card natural not to have a two in it would change the house edge by more than 0.01%.

Quote: Ncell

tringlomane -This is a great start. I agree that the 2-1-1-1 is a clear fold without a deuce, even ace high. You have no backup plan.

With a lone deuce, even with a rainbow, you're guaranteed an ace high three card. Not super strong, but not horrible either.

With a rainbow plus a deuce, you'll get two suited community cards (11/47) * (10/46) = 0.0509 = 5.1% of the time, ignoring additional deuces. The deuce substituting for an ace is the saving grace on any deuce only hand.

You seem to have a solid understanding of this. Could I interest you in checking my math on the side bet? I'm convinced I made an error, but I've gone over it many times and don't see anything out of place.

I put a quick 100,000 hand sim here. Just put in your 5 card hand. The link hand is AS, 9S, 3C, 3D, 3H. This is a really close hand. Sometimes it shows -2 or worse for a fold, sometimes better than -2 for a play.

Quote: miplet

I put a quick 100,000 hand sim here. Just put in your 5 card hand. The link hand is AS, 9S, 3C, 3D, 3H. This is a really close hand. Sometimes it shows -2 or worse for a fold, sometimes better than -2 for a play.

Playing around with it a bit. It unfortunately shows that high cards for "blockers" make quite a bit of difference. :(

KKKKx is playable for example.

I think the average player might fold a bit too often in this game.

A quick look at your calculator (i.e. I didn't double check, so please forgive any typos)
Play
(i) Any wild card (i.e. "2").
(ii) Any three+ carded flush.
(iii) (2-2-1 hands) Any Ax, Kx+K, Kx+Jx, Qx+Qx+T, Qx+Tx+A, Jx+Jx+A.
(iv) (2-1-1-1 hands) A9, A4+A, KQ+A, Kx+A+A, Kx+K+K+K, Qx+A+A+K.
There are obviously in-between hands e.g. [A9] A7+9+9+3 [A4+A], so you'd be unlucky not to want to play A7.

Quote: miplet

Here is my pay table. I assumed a hand of 2,4,6,7,J,K,A all clubs would count as a Natural 7 card, not a Wild 7 card.

Hand	Pays	Ways	Probability	Return
7 card natural	250	6864	0.000051306	0.012826592
7 card wild	100	38896	0.000290736	0.029073609
6 card natural	50	247104	0.001847029	0.092351464
6 card wild	10	906048	0.006772441	0.067724407
5 card natural	6	3243240	0.024242259	0.145453556
5 card wild	3	7636248	0.057078694	0.171236083
4 card natural	1	20420400	0.152636448	0.152636448
4 card wild	-1	24271680	0.181423626	-0.181423626
3 card natural	-1	54537120	0.407648835	-0.407648835
3 card Wild	-1	8677152	0.064859144	-0.064859144
2 card natural	-1	13799808	0.103149482	-0.103149482
Total		133784560		-0.085778927

All my numbers line up except the 5 card wild, which is skewing my final house edge. I'm getting 7764120 ways, with a probability of 0.058034500. Your numbers agree with ShuffleMaster, so I can only assume I made an error.

I'll walk through my steps.

First, the are three basic ways (Cases) for getting a 5 card wild:
4 natural + 1 wild + 2 others
3 natural + 2 wild + 2 others
2 natural + 3 wild + 2 others
The deuce of the matching suit counts towards the natural cards, so three wilds is the max.

For the groups of cards, you have 13 natural cards, 3 deuces, and 36 remaining cards.

For each case:
Case Choose naturals * choose wilds * choose others
1 combin(13,4) * combin(3,1) * combin(36,2)
2 combin(13,3) * combin(3,2) * combin(36,2)
3 combin(13,2) * combin(3,3) * combin(36,2)

Add the cases, then multiply by 4 suits

((combin(13,4) * combin(3,1) * combin(36,2)) + (combin(13,3) * combin(3,2) * combin(36,2)) + (combin(13,2) * combin(3,3) * combin(36,2)))*4 = 7,764,120 ways

Divide to get the probability:
7,764,120 / combin(52,7)= 7,764,120 / 133,784,560 = 0.058034500

I used this same process for the 6 card wild, only with different natural quantities, which got the correct results.

The game owner asked that I create a page for Flushes Gone Wild and kindly provided me the math report by Elliot Frome. While you wait for me to write up a page on the game, here is a close to optimal basic strategy Elliot came up with.


• Play all 5-card hands that are at least a 3-card Flush or contain a Deuce/Wild Card
• If the hand consists of TWO 2-Card Flushes, then:
o Play if at least one of the 2-Card Flushes is at least K-8 High
o Play if at least one of the 2-Card Flushes is King High and the 5th card (not part of either Flush) is at least a Queen
o Play if Both 2-Card Flushes are at least Queen High
o Play if one Flush is King High and the other is 10-High (or better)
o Play if one Flush is Queen High and the other is Jack-High and 5th card is a King or Ace
o Play if all 4 cards in the 2-Card Flushes are 10's or Higher
• If the hand consists of only ONE 2-Card Flush, then:
o Play if the 2-Card Flush is at least a K-8 High

Here are the results of his simulation of this strategy:

Total Hands Played	100,000,000
Total Play	75,215,051
Total Fold	24,784,949
Fold Frequency	24.78%
Total Units Wagered	350,430,102
Total Units Returned	342,969,379
Overall Payback	97.87%
Player Wins by 0	15,464,602
Player Wins by 1	20,894,042
Player Wins by 2	7,082,683
Player Wins by 3	1,107,757
Player Wins by 4	84,317
Player Wins by 5	2,527
Player Loses	30,299,692
Player Ties	279,431

His payback of 97.87% would imply an Element of Risk of 2.13%.

Since the minimum bet is two units, the house edge (ratio of expected loss to initial wager) would be (350,430,102-342,969,379)/2*100,000,000 = 3.73%.

Elliot's report confirms Miplet's 8.58% house edge on the side bet.

Quote: Ncell

All my numbers line up except the 5 card wild, which is skewing my final house edge. I'm getting 7764120 ways, with a probability of 0.058034500. Your numbers agree with ShuffleMaster, so I can only assume I made an error.

I'll walk through my steps.

First, the are three basic ways (Cases) for getting a 5 card wild:
4 natural + 1 wild + 2 others
3 natural + 2 wild + 2 others
2 natural + 3 wild + 2 others
The deuce of the matching suit counts towards the natural cards, so three wilds is the max.

For the groups of cards, you have 13 natural cards, 3 deuces, and 36 remaining cards.

For each case:
Case Choose naturals * choose wilds * choose others
1 combin(13,4) * combin(3,1) * combin(36,2)
2 combin(13,3) * combin(3,2) * combin(36,2)
3 combin(13,2) * combin(3,3) * combin(36,2)

Add the cases, then multiply by 4 suits

((combin(13,4) * combin(3,1) * combin(36,2)) + (combin(13,3) * combin(3,2) * combin(36,2)) + (combin(13,2) * combin(3,3) * combin(36,2)))*4 = 7,764,120 ways

Divide to get the probability:
7,764,120 / combin(52,7)= 7,764,120 / 133,784,560 = 0.058034500

I used this same process for the 6 card wild, only with different natural quantities, which got the correct results.

Your case 3 is double counting some hands. Here is how I did it:
1 wild:
4 of one suit; 2 of one suit; wild cant be of the 4-suit: 4*COMBIN(12,4)*3*COMBIN(12,2)*3
4 of one suit; 1 of two suits; wild cant be of the 4-suit: 4*COMBIN(12,4)*COMBIN(3,2)*12*12*3
2 wilds:
3 of one suit; 2 of one suit; 2 wilds: 4*COMBIN(12,3)*3*COMBIN(12,2)*COMBIN(4,2)
3 of one suit;1 of two suits; 2 wilds: 4*COMBIN(12,3)*COMBIN(3,2)*12*12*COMBIN(4,2)
3 wilds:
2 of two suits; 3 wilds: COMBIN(4,2)*COMBIN(12,2)*COMBIN(12,2)*4
2 of one suit; 1 of two suits; 3 wilds: 4*COMBIN(12,2)*COMBIN(3,2)*12*12*4
4 wilds:
1 of three suits; 4 wilds: 4*12*12*12

Just wrote up a new page on Flushes Gone Wild. Please click the link and let me know what you think. As always, I welcome all comments, questions, and especially corrections.

Looks good. Having both an advanced ("geek") strategy, as well as a simple rack-card type strategy is a good convention.

Played this game for the first time a couple of days ago. Pretty fun, although the lack of decisions make it seem like it might get old fast. Beginners luck worked out, as I lost the first hand or two (along with everyone else) and the person to my immediate right quit, but stuck around the table. The very next hand, I got dealt 5 clubs and was holding off putting my 2x out there waiting for them to leave. They didn't, and the dealer flipped a club for one of the community cards.

Similar to my experience with HCF, I should probably never play again, dying as a lifetime winner in a carnival game :-)

Quote: miplet

Your case 3 is double counting some hands. Here is how I did it:
1 wild:
4 of one suit; 2 of one suit; wild cant be of the 4-suit: 4*COMBIN(12,4)*3*COMBIN(12,2)*3
4 of one suit; 1 of two suits; wild cant be of the 4-suit: 4*COMBIN(12,4)*COMBIN(3,2)*12*12*3
2 wilds:
3 of one suit; 2 of one suit; 2 wilds: 4*COMBIN(12,3)*3*COMBIN(12,2)*COMBIN(4,2)
3 of one suit;1 of two suits; 2 wilds: 4*COMBIN(12,3)*COMBIN(3,2)*12*12*COMBIN(4,2)
3 wilds:
2 of two suits; 3 wilds: COMBIN(4,2)*COMBIN(12,2)*COMBIN(12,2)*4
2 of one suit; 1 of two suits; 3 wilds: 4*COMBIN(12,2)*COMBIN(3,2)*12*12*4
4 wilds:
1 of three suits; 4 wilds: 4*12*12*12

Just realized I never responded to this. Thanks for the info. I did indeed mix up that case and correcting it made everything agree