DDB 9-5 vs 9-6 (Very confused by the outcome)

[player_25085]

Hi Any maths whizzes out there ? I'm sure there are. Most years when I go to Vegas, I go for 8-9 days (from the UK) and play mostly DDB. Over that length trip, I play around 50,000 hands. As most of my play is on the strip, I only get to play 9-5 and maybe a few 9-6 machines. I decided today to work out how much less it would cost me (on average) to play 9-6 DDB for 50,000 hands vs 9-5 for the same stretch. I'm rather surprised at what I'm seeing. I pulled out the game analysis from my WinPoker for both paytables. Dropped in the "Occurs Every" figure into a spreadsheet then looked at the results for both paytables. The first thing that surprised me was that according to WinPoker, you end up with a differing hit frequency between the machines on just about all hands. For example on 9-5 it says you will get a Royal 1 in every 40065 hands. But for 9-6, it's 1 in every 40799 hands. Even stranger to me is the high pair frequency. With 9-5 you hit a high pair 1 in 4.71 hands, but on 9-6, it's 1 in 4.73 hands. I took all these figures and divided each one by 50,000 (my usual trip total of hands). So, I would expect to hit 1.24 royals on 9-5, and 1.22 royals on 9-6. The total expected loss at 25c max coin on 9-5 over 50,000 hands came out at $1312. But for 9-6 it came out at $1328. How can this be ? Any help would be much appreciated.Thanks Steve 

[shadowman]

The return of all games requires you to look at all paytable elements. In the case of 9/6 vs. 9/5 DDB it should be reasonable that one would go for fewer flushes since they pay less (it's the only difference in the paytable). And, since you'd go for fewer flushes you get fewer flushes. That might also lead to slight increases in other items.
 
What you've done is look at the items where there were slight increases in frequencies and ignored the flush that drops from 91.11 to 88.04 when you move up to 9/6 DDB. Also, the SF drops from 9389 to 9123.
 
The easiest way to compute your cost is to look at the overall return. 97.87 vs 98.98. The difference is 1.11 %. If you are playing quarters you would take 50K hands times $1.25 per hand for the total coin-in. This is $62.5K. Now multiply that by the difference in return (1.11%).
 
62,500*.0111 = $693.75

[Eduardo]

I still don't understand the "expected loss" numbers posted since 9/5 is a smaller loss than 9/6. User error, programming error, or error in my understanding?

In any case, you can't expect to lose any particular amount (or what is the point in playing?) There is a wide range of amounts you can end up at. I would look at my odds of coming out ahead personally.

[player_25085]

Thanks, yes I see that I need to look at all the paybacks, which was exactly what I did. I took the frequency of all the different hands individually and divided them into 50,000.So, on a 9-5 machine, the expected payback for 50,000 hands came out like this (in coins) - 




RF

4991.83


SF

1331.37


4 A W/K

6162.12


4 2,3,4 W/K
5728.07


4 ACES

6942.80


4 2,3,4

7688.52


4 5-K

20403.50


FH

24453.86


FL

13721.19


ST

12943.32


3K

56518.46


2P

30788.18


JoB

53078.56


Nothing

0.00







Total return
244751.78


 A loss of 5248 coins. Doing the same thing for the 9-6 hand frequencies gave a return of 244685 coins . A loss of 5314 coins. In the past I have always used the method you mentioned. i.e. the 9-6 payback gives a 1.11% advantage over the 9-5 payback and easily came to the same figure you gave. Just today though I decided to look at it from a different angle and still can't figure out why when viewed in this way, the 9-6 payback is less than the 9-5 payback. Surely it must mean that there could be a strategy flaw in perfect play ? (or i have made some basic error in my spreadsheet !)

[Eduardo]

That is weird. Since you are multiplying by 50,000 or dividing into it, there could also be a pretty big margin of error from rounding. How many digits did you have to start with?

There is a big difference between .011 and .014 when you multiply it by 50,000. (550 and 700)

[player_25085]

EDIT - Please ignore all of this. I had an error in the spreadsheet whereby I hadn't changed the flush payback for 9/6....d'oh ! Case closed.....Probably best if I copy in the whole spreadsheet. Originally I only used 2 decimal places, but have expanded that by including all decimal places shown in winpoker. Consequently the figures are slightly different from my original post, but still the problem remains.If anyone else has a more up to date copy of WinPoker (mine is about 10 or 11 years old I think), would you kindly check the hand frequencies for me please. 











 
9/5 DDB
9/6 DDB
50000
No of hits in
50k hands 9/5
Coins paid
No of hits in
50k hands 9/6
Coins paid



RF
40065.450000
40799.320000
 
1.247958029
4991.832
1.225510621
4902.0425



SF
9388.770000
9123.103000
 
5.325511222
1331.378
5.480591417
1370.1479



4 A w/k
16228.170000
16236.350000
 
3.081062128
6162.124
3.079509865
6159.0197



4 2,3,4 w/k
6983.155000
6983.408000
 
7.160087382
5728.07
7.159827981
5727.8624



4 ACES
5761.366000
5761.031000
 
8.678497426
6942.798
8.679002074
6943.2017



4 2,3,4
2601.281000
2601.419000
 
19.22129904
7688.52
19.22027939
7688.1118



4 5-K
612.647300
613.432400
 
81.61302596
20403.26
81.50857372
20377.143



FH
92.010920
92.080990
 
543.41376
24453.62
543.0002436
24435.011



FL
91.108690
88.039540
 
548.795071
13719.88
567.9266384
14198.166



ST
77.266510
78.331500
 
647.1108893
12942.22
638.3128116
12766.256



3K
13.273100
13.286370
 
3767.017502
56505.26
3763.255125
56448.827



2P
8.120286
8.125880
 
6157.418593
30787.09
6153.179717
30765.899



JoB
4.714643
4.732104
 
10605.25686
53026.28
10566.1245
52830.622



Nothing
1.811288
1.808852
 
27604.66585
0
27641.84134
0



 
 
 
 
 
 
 
 



 
 
 
 
Total coins paid
244682.3
 
244612.31



 
 
 
 
Total coins outlay
250000
 
250000



 
 
 
 
Total coins lost
5317.668
 
5387.6896



 
 
 
 
Total $ lost (for 25c
play)
1329.417
 
1346.9224

[optimumplay]

It's because you are trying to calculate the affect over 50K hands on each individual line. See the Royal Flush total of 4991 playing 9/5? A fair question is why would I win more playing 9/5 than 9/6 (4902)? It's because of the slight increase in potential hits over 50K handscaused by the 'additional' flushes you are hitting in 9/6 which are actually free to become any other hand on 9/5, even a Royal Flush. However in reality you wont see this potential extra win because you cant get .2479 of a Royal Flush!!
 
Just as shadowman said - you need to look at the difference in overall payback percentage to work out your winnings. This eliminates this kind of anomoly that really isn't reflective of VP play.
 
Hope that helps

[optimumplay]

a quick update - I've just plugged your figures into my own spreadsheet and your calculation for the 9/6 flush is incorrect - you've multiplied the figure by 5 instead of 6!! Correct that and your figures should actually make more sense!!
 
Good luck

[player_25085]

Thanks for the response, but I wasn't really looking at it in a reality way, just a mathematical way.  Anyway, I found the problem. Basic error. I hadn't changed the calculation to pay 30 coins for the flush in the 9/6 column The end result is now correct. A difference of $692 between the 2 machine paytables over 50,000 hands. I know I could have arrived at the same/similar figure by just using the 1.11% difference figure, but this was more at seeing how the individual hand paybacks changed.

[player_25085]

a quick update - I've just plugged your figures into my own spreadsheet and your calculation for the 9/6 flush is incorrect - you've multiplied the figure by 5 instead of 6!! Correct that and your figures should actually make more sense!!
 
Good luck
 Yes, I found it just 10 mins ago. But thanks for looking. Stupid mistake !