Wizard
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Wizard
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May 3rd, 2014 at 2:48:26 PM permalink
Double Draw Poker is a ShuffleMaster game that I just saw at the Cromwell. For those who haven't heard of the Cromwell, it is the new Caesars property where the Barbary Coast used to be.

Photo from G2E:



Rack Card:



Bonus Bet pay table.

Hand Pays
Five of a Kind 500
Natural Royal Flush 100
Wild Royal Flush 50
Straight Flush 50
Four of a Kind 20
Full House 5
Flush 3
Straight 2
Three of a kind 1
Two pair Push
Pair Loss
Trash Loss


I have just started my analysis. To give you a preview, here is my count of poker hands on the deal. Remember that the two jokers are treated the same was as in pai gow poker.

Hand Count
Five of a Kind 6
Natural Royal Flush 4
Wild Royal Flush 80
Straight Flush 540
Four of a Kind 1,320
Full House 5,328
Flush 11,388
Straight 34,704
Three of a kind 75,048
Two pair 156,816
Pair 1,341,888
Trash 1,535,388
Total 3,162,510
It's not whether you win or lose; it's whether or not you had a good bet.
tringlomane
tringlomane
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May 3rd, 2014 at 2:56:32 PM permalink
So the bonus bet at the Cromwell pays even money for three of a kind? Unfortunately reports say casinos in Detroit treat three of a kind as a push for the bonus bet, which definitely makes the game terrible.
Ibeatyouraces
Ibeatyouraces
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May 3rd, 2014 at 3:23:00 PM permalink
deleted
DUHHIIIIIIIII HEARD THAT!
Wizard
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Wizard
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May 3rd, 2014 at 4:38:12 PM permalink
Quote: tringlomane

So the bonus bet at the Cromwell pays even money for three of a kind? Unfortunately reports say casinos in Detroit treat three of a kind as a push for the bonus bet, which definitely makes the game terrible.



Yup. ShuffleMaster, I mean Ballys, was kind enough to give me the math report by GLI on the game. The report indicates the two pay tables mentioned. They report a house edge of 1.7479% for the Cromwell pay table and 3.8503% for the Detroit pay table.

The number of combinations in this game is 28,587,727,358,190. To put that in perspective there are 3,986,646,103,440 in video poker. So, this game as 7.17 times as many. Without any short cuts, this game would take months, perhaps years, of computer time to cycle through. With enough short cuts, I could get it down to days, but it is time consuming for me to put in short cuts.

I hate to do this, but I think I'm going to trust the GLI number until the game gets enough placements for me to warrant the time to analyze.
It's not whether you win or lose; it's whether or not you had a good bet.
MathExtremist
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May 3rd, 2014 at 6:17:04 PM permalink
Quote: Wizard

Yup. ShuffleMaster, I mean Ballys, was kind enough to give me the math report by GLI on the game. The report indicates the two pay tables mentioned. They report a house edge of 1.7479% for the Cromwell pay table and 3.8503% for the Detroit pay table.

The number of combinations in this game is 28,587,727,358,190. To put that in perspective there are 3,986,646,103,440 in video poker. So, this game as 7.17 times as many. Without any short cuts, this game would take months, perhaps years, of computer time to cycle through. With enough short cuts, I could get it down to days, but it is time consuming for me to put in short cuts.

I hate to do this, but I think I'm going to trust the GLI number until the game gets enough placements for me to warrant the time to analyze.


Didn't you already do an analysis of generic double draw VP? Isn't this just a modified version with two bugs and restricted drawing rules?
"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
Ibeatyouraces
Ibeatyouraces
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May 3rd, 2014 at 8:44:22 PM permalink
deleted
DUHHIIIIIIIII HEARD THAT!
tringlomane
tringlomane
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May 3rd, 2014 at 9:26:00 PM permalink
Quote: MathExtremist

Didn't you already do an analysis of generic double draw VP? Isn't this just a modified version with two bugs and restricted drawing rules?



He did do double draw VP, but double draw VP didn't allow you to have a double draw for every hand either...

http://wizardofodds.com/games/video-poker/tables/double-draw/

Quote: Ibeatyouraces

I would change five of a kind to five aces. Some people might get confused as to how the jokers work even though it's mentioned on the rack sheet.



I agree with this.
jopke
jopke
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May 3rd, 2014 at 11:48:36 PM permalink
Quote: Wizard

Yup. ShuffleMaster, I mean Ballys, was kind enough to give me the math report by GLI on the game. The report indicates the two pay tables mentioned. They report a house edge of 1.7479% for the Cromwell pay table and 3.8503% for the Detroit pay table.

The number of combinations in this game is 28,587,727,358,190. To put that in perspective there are 3,986,646,103,440 in video poker. So, this game as 7.17 times as many. Without any short cuts, this game would take months, perhaps years, of computer time to cycle through. With enough short cuts, I could get it down to days, but it is time consuming for me to put in short cuts.

I hate to do this, but I think I'm going to trust the GLI number until the game gets enough placements for me to warrant the time to analyze.



I analyzed this game a while back and my numbers differ from these published results. I get a HE of 3.915% for the Cromwell paytable. I did it pretty quickly, so there might have been an error, but double checking my code nothing stands out. It is a big enough difference, though, that something must be wrong.

The way I did it was to reduce the number of starting hands from 3,162,510 to 226,408. I did this by building a map of hand rank and suit patterns. The nice thing is this map reduction is useful for other games, it isn't specific to Double Draw. It works like this:

Each card rank has a prime number value. Multiply them together to get a unique total for any given hand. This is the technique used by Cactus Kev's hand evaluator.

I then also make a suit pattern, which is a 5 char string that works something like this:

if the hand is AsKd3s4c5h the suit map would be: "01023". This shows that the first and third card are the same suit, the others are different suits. This works because from an EV perspective, AsKd3s4c5h and AdKs3d4c5h are equivalent.

I then calculate the frequency for each rank and suit pattern. For instance:

Example Hand: JsQhKhAsAd
Rank Value: 55915103
Suit Pattern: 01102
# of occurrences: 12

I took the 206,408 hands and split them in to 100 hand files. I wrote code to read the file, loop over each hand and evaluate the EV. I spun up a bunch of Amazon EC2 instances to churn through the files.

A few hours later I used another program to consolidate the results and multiply each hand EV by the number of occurrences for that hand. Then I found the average EV.

Anybody see an issue with this approach?
socks
socks
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May 4th, 2014 at 8:29:33 PM permalink
Quote: jopke

Anybody see an issue with this approach?



Huh, can it be that easy? I recently tried to write a similar bucketing algorithm for the standard 52c deck (and thus avoid manually copying the suit patterns by hand from the wizard's vp programming tip page).

Are you sorting beforehand? By value and suit? 2s3s3c6d7h == 2d3c3d6s7h, but my algorithm misses a couple of cases like this, where the suits in pairs are reversed, and I end up with approx 136k buckets instead of 134k.

How many buckets do you get for the standard 52c deck, w/o jokers (~2.6M hands)?
jopke
jopke
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May 5th, 2014 at 6:41:54 PM permalink
Quote: socks

Huh, can it be that easy? I recently tried to write a similar bucketing algorithm for the standard 52c deck (and thus avoid manually copying the suit patterns by hand from the wizard's vp programming tip page).

Are you sorting beforehand? By value and suit? 2s3s3c6d7h == 2d3c3d6s7h, but my algorithm misses a couple of cases like this, where the suits in pairs are reversed, and I end up with approx 136k buckets instead of 134k.

How many buckets do you get for the standard 52c deck, w/o jokers (~2.6M hands)?



Standard deck reduces to 204087

The code grabs all 5 card combinations, sorted by value from low to high. It gets the rank product and the suit pattern and stores them in a map, keeping track of how many of each exists. Here is a sample from the file generated.

It is example hand | rank product | suit | frequency

2h6sThQsQh 486266 01010 6
2s6hTsQhQd 486266 01012 12
2h6dThQsQh 486266 01020 12
2s6dTsQhQd 486266 01021 12
2s6hTsQdQc 486266 01023 12
2s6hThQsQh 486266 01101 6
2s6hThQsQd 486266 01102 12
2h6sTsQsQh 486266 01110 6
2s6hThQhQd 486266 01112 12
2h6dTdQsQh 486266 01120 12
2s6dTdQhQd 486266 01121 12
2s6hThQdQc 486266 01123 12
2s6hTdQsQh 486266 01201 12
2s6hTdQsQd 486266 01202 12
2s6hTdQsQc 486266 01203 12
2h6sTdQsQh 486266 01210 12
2s6hTdQhQd 486266 01212 12
2s6hTdQhQc 486266 01213 12
2h6dTsQsQh 486266 01220 12
2s6dThQhQd 486266 01221 12
2s6hTdQdQc 486266 01223 12
2h6dTcQsQh 486266 01230 12
2s6dTcQhQd 486266 01231 12
2s6hTcQdQc 486266 01232 12
3s7s7hQsQh 487227 00101 6
3s7s7hQsQd 487227 00102 8
3s7s7hQhQd 487227 00112 4
3h7h7dQsQh 487227 00120 4
3s7s7dQhQd 487227 00121 8

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