socks
socks
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May 5th, 2014 at 7:29:23 PM permalink
Quote: jopke

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
...



Do you have any 24 buckets? I think there should be.

Take a look at the pairs section on http://wizardofodds.com/games/video-poker/methodology/

I might be missing something, but there are no 6's, and the majority are 24's. Similarly, the 2 pairs section is half 12's and half 24's.
MathExtremist
MathExtremist
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May 5th, 2014 at 7:35:19 PM permalink
Quote: jopke

Standard deck reduces to 204087
2s6hTdQhQd 486266 01212 12
2s6dThQhQd 486266 01221 12


There should be 134459 buckets. The two lines I copied should be in the same bucket.
"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
FleaStiff
FleaStiff
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May 5th, 2014 at 7:37:07 PM permalink
I'm lost on the math but 1.74 percent house edge ain't so bad.
I forget the paytable at the Hard Rock (Hollywood, FL) but I did enjoy playing the game despite the initial confusion when I heard the dealer mention something about five aces and thought it was a joke.
jopke
jopke
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May 5th, 2014 at 11:52:46 PM permalink
Quote: MathExtremist

There should be 134459 buckets. The two lines I copied should be in the same bucket.



Good point, that would cut down on the number of hands needed to be calculated, but won't affect the overall outcome.

The reduced set I have is pretty quick when spread over EC2 instances, but reducing further would cut the costs a bit, so I'll likely look into it. Thanks for pointing it out.
tringlomane
tringlomane
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May 6th, 2014 at 12:37:14 AM permalink
Quote: jopke

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.



What also concerns me is that the house edge number submitted to the Washington gaming commission doesn't match either of these numbers...

http://www.wsgc.wa.gov/activities/game-rules/double-draw-poker.pdf

Obviously the math is very difficult for this game.
jopke
jopke
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May 6th, 2014 at 1:09:19 AM permalink
Quote: tringlomane

What also concerns me is that the house edge number submitted to the Washington gaming commission doesn't match either of these numbers...

http://www.wsgc.wa.gov/activities/game-rules/double-draw-poker.pdf

Obviously the math is very difficult for this game.



Very strange, those numbers are very different. Maybe there is some "House Edge" vs "Element of Risk" confusion in the Bally literature...

If anyone wants to compare notes with individual hands, I'd be happy to. I played around with a basic strategy but didn't get very far. It is complicated for sure and I doubt any reasonable strategy will be close to the theoretical house edge. I haven't looked at it for a while, I might dig back into it with a clear head.
socks
socks
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May 6th, 2014 at 1:44:14 AM permalink
Quote: tringlomane

...Obviously the math is very difficult for this game.


This makes me laugh a little. I've put an embarrassing # of hours into trying to get any correct result for various games and I've come up pretty empty. As far as I can tell all games are absurdly hard to analyze. With Video poker, my result was so close, the error disappeared if I forced it into a float, but there had been no division to that point, so it couldn't be a rounding error. The smallest additional error I could purposefully introduce was 4x as large.
jopke
jopke
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May 6th, 2014 at 2:47:35 AM permalink
Quote: MathExtremist

There should be 134459 buckets. The two lines I copied should be in the same bucket.



I tweaked my code, it isn't pretty, but it is now reduced to 134459 hands. With 2 jokers the total is 152646.

Thanks guys for the input. Now if we could figure out why the DoubleDraw HE numbers are so inconsistent...
jopke
jopke
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May 6th, 2014 at 2:52:35 AM permalink
Quote: socks

This makes me laugh a little. I've put an embarrassing # of hours into trying to get any correct result for various games and I've come up pretty empty. As far as I can tell all games are absurdly hard to analyze. With Video poker, my result was so close, the error disappeared if I forced it into a float, but there had been no division to that point, so it couldn't be a rounding error. The smallest additional error I could purposefully introduce was 4x as large.



IMO, probably the easiest poker based table game to analyze is Mississippi Stud. There are no draws, it is just a straight 5 card hand. I started with that one and it is quick enough no reductions are needed.
socks
socks
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May 6th, 2014 at 1:16:22 PM permalink
Quote: jopke

IMO, probably the easiest poker based table game to analyze is Mississippi Stud. There are no draws, it is just a straight 5 card hand. I started with that one and it is quick enough no reductions are needed.


A good suggestion. Maybe I'll take a second look. I actually noticed MS a couple of months back when I was working on video poker. Like you say, it's small enough that a straightforward approach can work. At the time, I didn't want to get too far off track of what I was doing, but I took a couple of days to look at it anyway. The initial results were pretty close, but a run with my naive approach went overnight, and I went back to VP before figuring out exactly what went wrong.

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