s2dbaker
s2dbaker
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February 20th, 2011 at 10:07:51 AM permalink
I was in Las Vegas for Super Bowl weekend and staying at the Flamingo. Luckily, I only came home with a mild flu and no bedbug bites or norovirus. While I was there, I saw a new table game named Wild52' rel='nofollow' target='_blank'>http://lasvegasblog.harrahs.com/las-vegas-casinos/flamingo/its-time-to-get-wild-52-at-flamingo-las-vegas/"]Wild52 (link here). The game is a seven card stud game of you + five of your closest friends vs. the dealer. The deck contains one fully wild card that substitutes for any card in the deck that's not already in your hand (sorry, no flushes with two aces allowed) except when it makes a five of a kind. Each person including the dealer is dealt five cards and two community cards are dealt face down. To play, you must ante (table minimum was $10 when I was there), once you receive your cards, you can choose to bet by placing double your ante in the bet circle or fold and lose your ante bet. One of the community cards is then turned over and you now get to either raise by placing double your ante in the raise circle or stand (no bet). The dealer the turns the second community card over and evaluates his own hand. If he doesn't have a pair of fives or better (a little less than a quarter of the time) then he returns your "Bet" and "Raise" but the "Ante" still plays. The dealer must have a pair of fives or better to qualify your bet and raise.

There are two bonus bets, one is for the joker appearing in either your hand or the two community cards and has about a 11.6% casino advantage and the other bonus bet is a pay table based on your final hand that is about 10.5% to the casino's advantage.

I'm just beginning to put together an engine to calculate a betting strategy for this game. My initial goal was to try to figure out which hands to fold and which hands to automatically bet and raise. So far, a pair of Queens or better is an automatic bet and raise. There is no easy formula for figuring out when to fold .. yet.

Here's a spreadsheet of my' rel='nofollow' target='_blank'>http://www.dottygale.com/p1x/wild52_bet_anaysis.xlsx"]my initial Monte Carlo simulation. It shows the starting five card hand, the ranks of that cards within it (in code), How many wins, losses, push, How many times the players hand won but the dealer didn't qualify, same for losses, the Ante (as a negative number), wins/losses based on a single bet, wins/losses based on a bet and a raise and then some calculated columns to decide whether to fold, bet and/or raise.

So far, the casino advantage is 12.5%. When I add logic for betting four card flushes it may improve a little bit but in my initial opinion, this game stinks!
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
MathExtremist
MathExtremist
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February 20th, 2011 at 11:05:27 AM permalink
Does that mean they took out Pokerjack?

Edit: I just found this link:
http://www.totalrewards.com/casino-gambling/table-finder/table-finder-home.shtml
Pretty informative, if it's up to date. (And no, Pokerjack isn't on there).
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
JB
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JB
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February 20th, 2011 at 1:17:15 PM permalink
I actually kicked off an exhaustive analysis of the Ante bet (including the Play and Option bets) last night, but it probably won't be done for a couple of weeks. There are 150,891 * 48 * 47 * 1,370,754 = 466,618,500,732,384 unique scenarios to analyze, so obviously it is going to take a while to finish.

What didn't take long was an analysis of the two sucker side bets. The house edge on the Joker bet is 11.3208% and the house edge on the Bonus bet is 10.4271%. I won't know the house edge (or element of risk) of the Ante bet until the exhaustive analysis is finished.

I also made an assumption that I hope is correct. Consider the following scenario:

Community cards: Ac Ad
Dealer has: Joker, Kc, Kd, 2s, 3h
Player has: Ah, Ks, Kh, 2h, 3s

Both the dealer and the player have Aces full of Kings as their best 5-card hand. I made the assumption that, for the ante bet, only the rank matters, and that it does not matter whether it is natural or wild. Hopefully that is correct. The Bonus paytable makes a distinction between Natural and Wild hands (preferring Naturals), but I assumed that for showdown purposes, only the poker rank matters, and that in the above scenario the player and dealer tie, and therefore the player's Ante, Play, and Option bets would push.
s2dbaker
s2dbaker
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February 20th, 2011 at 4:41:55 PM permalink
It took my humble PC three days to go through all 154,143,080 hands in a 53 card deck just to see if my joker evaluation engine was working correctly. Thanks to the Flying Spaghetti Monster, it worked on the first try. I like the Monte Carlo method because I can get a good feeling for trends without having to evaluate trillions of scenarios. As you can see, I came pretty close to your numbers on the sucker bonus bets.

I've added extra granularity to my spreadsheet for each 5 card dealt hand, whether it has a wild, four card flush or an outside straight. I'm going to expand my definition of an outside straight to include a situation like 3,5,6,7,9 where it takes one of two card ranks to complete the straight. Previously, I was only capturing the four cards in a row. Once I get a few million hands generated, I'll add a new link in this thread.
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
JB
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JB
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February 20th, 2011 at 5:09:55 PM permalink
Quote: s2dbaker

It took my humble PC three days to go through all 154,143,080 hands in a 53 card deck just to see if my joker evaluation engine was working correctly. Thanks to the Flying Spaghetti Monster, it worked on the first try. I like the Monte Carlo method because I can get a good feeling for trends without having to evaluate trillions of scenarios. As you can see, I came pretty close to your numbers on the sucker bonus bets.

I've added extra granularity to my spreadsheet for each 5 card dealt hand, whether it has a wild, four card flush or an outside straight. I'm going to expand my definition of an outside straight to include a situation like 3,5,6,7,9 where it takes one of two card ranks to complete the straight. Previously, I was only capturing the four cards in a row. Once I get a few million hands generated, I'll add a new link in this thread.


I'm curious about your simulator. What strategy are you using the for Play and Option bets?

For example, some hands should be folded before seeing the first community card. Some hands you should make the Play bet but not the Option bet. Other hands you should make both the Play and Option bets. This is one of those games where you need to analyze what you would do later on in order to determine what you should do earlier on.

Are you determining optimal strategy on the fly as the cards are dealt?
s2dbaker
s2dbaker
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February 20th, 2011 at 5:49:24 PM permalink
Quote: JB

...Are you determining optimal strategy on the fly as the cards are dealt?

With me, these thing evolve. First, I got MS-SQL to randomize a deck of cards ( later cut to the first 40 cards to speed it up ), previously I had programmed a series of functions that could evaluate a 5,6 or 7 card hand for "Texas Hold'em Bonus" and so I converted those over to Wild52 to consider the possibility of a wild card. Then I wrote a script to deal out two 5-card hands and 2 community cards to see if I was doing that right. I expanded the script to store all of the pertinent information into a table and expanded it to six player hands and one dealer hand per deck. I set it to run in a loop for awhile. I occasionally pluck the info out of the table and store it in a spreadsheet to see if I can make a determination about strategy.

That's where I am now.

Here's the SQL statement that generates the data I put in' rel='nofollow' target='_blank'>http://www.dottygale.com/p1x/wild52_bet_analysis2.xlsx"]in this spreadsheet (link fixed):

select		c_index,
wild_5 is_wild,
Four_Card_Flush,
Outside_Straight,
SUM(win) Win,
SUM(loss) Loss,
SUM(push+dnq_push) Push,
SUM(dnq_win) DNQ_Win,
SUM(dnq_loss) DNQ_Loss,
sum(win+loss+push+dnq_win+dnq_loss+dnq_push)*-1 Ante
From wild52.dbo.wild52_test
Group By c_index,
wild_5,
Four_Card_Flush,
Outside_Straight
Order By 1,2,3,4


After a little analysis, I'll create another table that stores wins and losses for bets made per the instructions I give it. For example, I'll tell it to bet on any hand that has a pair of Queens or better, Has a joker in it, four of a suit or an outside straight. Then I'll include the first community card into the evaluation and see where I am. I'll probably tell the engine to raise if the 6 card hand evaluates to a pair of Queens or better. If I see the percentages for the player improve, I know I'm guessing better on strategy. My goal is to get a strategy that's easy to remember that minimizes the casino's vig.
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
s2dbaker
s2dbaker
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February 20th, 2011 at 7:44:24 PM permalink
Quote: JB

I also made an assumption that I hope is correct. Consider the following scenario:

Community cards: Ac Ad
Dealer has: Joker, Kc, Kd, 2s, 3h
Player has: Ah, Ks, Kh, 2h, 3s

Both the dealer and the player have Aces full of Kings as their best 5-card hand. I made the assumption that, for the ante bet, only the rank matters, and that it does not matter whether it is natural or wild. Hopefully that is correct. The Bonus paytable makes a distinction between Natural and Wild hands (preferring Naturals), but I assumed that for showdown purposes, only the poker rank matters, and that in the above scenario the player and dealer tie, and therefore the player's Ante, Play, and Option bets would push.



Funny you should voice that concern. I had an email exchange with "Ken" from the Wild52 web site and I gave him a similar scenario only in Flush vs. Flush with joker. He said that the two hands would push. I'm sure he wouldn't mind me posting the redacted email trail:

Quote: Kevin

Hi Ken,

Last weekend, when I was at the Flamingo, I didnít get the opportunity to ask the dealer about certain situations that may arise with the use of the wild card. Iím hoping that you can clear something up for me. My understanding is that the wild card will substitute for any card in the deck. So according to the rules of Wild52, which hand would be superior:

Joker, Ace Diamonds, 9 Diamonds, 7 Diamonds, 3 Diamonds for a Flush Or
Ace Clubs, King Clubs, 9 Clubs, 7 Clubs 3 Clubs for a Flush?

Since the Joker substitutes for any card in the deck, if you have four Aces and a Joker, for what card is the Joker substituting to make 5 of a kind?

Iím a computer programmer and want to get my simulation of your new game as correct as possible.

Thanks You,

Kevin


His reply:
Quote: Ken

Hi Kevin,

Thanks for the e-mail. To answer your questions, both flushes are equal. The joker would be a king of diamonds. Between the dealer and player, the hand would be a "push". If the player held the joker and placed a joker bet, he or she would be paid 4 to1 or 10 to 1, if joker was one of the community cards.

Regarding the other question, the joker would be recognized as a fifth ace and make the highest hand in the game of Wild 52!

Thanks again,

Ken N.

Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
Wizard
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Wizard
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February 20th, 2011 at 8:04:07 PM permalink
I will definitely have a look my next visit to the Strip.
It's not whether you win or lose; it's whether or not you had a good bet.
s2dbaker
s2dbaker
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February 21st, 2011 at 5:45:39 PM permalink
I'm going back to Las Vegas from April 29 through May 2. Maybe I'll have all the bugs worked out of my Wild52 simulator by then. Meanwhile, here's 14+ million more random hands.

edit:

It looks like I found a strategy (Hand 2) that lets me be up after 2600 hands. That's probably more than I'll ever play in a lifetime. It's pretty easy to follow too. I'll crunch the numbers some more. I'm sure that Hand 2 will come back to reality sooner or later.

Hand win win_played loss loss_played push_count fold_count win_count loss_count vig
1 3077 991 3181 1665 2 1096 1372 1283 -0.01661872802
2 3361 1049 3178 1606 2 1007 1384 1269 0.02798593057
3 3252 1080 3518 1574 3 805 1335 1318 -0.03929098966
4 3459 1187 3717 1469 1 526 1344 1310 -0.03595317725
5 3816 1290 3933 1363 4 280 1362 1291 -0.01509872241
6 3707 1305 4324 1344 8 0 1305 1344 -0.07682729423
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
s2dbaker
s2dbaker
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February 21st, 2011 at 9:08:16 PM permalink
I seem to have stumbled on to a strategy that yields a mere 2.9% to the house. I'll have a better read on it in the morning.

Bet with:
a Wild Card in your Hand Or
A,J,10,x,x or better Or
Four cards to a Flush Or
and Outside Straight

Otherwise fold.

Raise with:
a Wild Card in your Hand Or
J,J,Q,x,x or better if the exposed community card is not a Wild Card Or
J,J,J,x,x or better Or
( Four cards to a Flush AND An Outside Straight ) <- Include the community card
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez

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