help with the math

[alpax]

It is hard to gauge the rate you were playing from the amount you lost from a high variance game like DDB. You have said you got a low quad witch a kicker which will pay out 200 dollars, thus that money will go much longer ways.

I would say the next time you play, to measure your rate of play.

1. Put your total rewards card in the machine and write down your current tier score.
2. Set a stop watch on your phone for 1 hour
3. start playing, do not purposely try to play fast. Be accurate since you are playing a negative expectation game
4. Once the hour passes take the club card out and put it back in
5. Write down your updated tier score
6. Use a calculator if necessary. Take the score from #5 and subtract it from #1. E.g. 2300 - 2225 = 75
7. Now multiply that number by 8 to get the hands per hour

Reason for this is $10 coin in per point. 8 hands of $1.25 bet is $10 for 1 tier point.

Some slots go through longer up and downs through the course, but those are at $5 per tier score. Just be glad you barely got over 1000 points since the bonus gave you more.

[Vman96]

Ok I ran some results for 7200 hands. I picked 7200 hands because the way notes described the slot play, I didn't think he earned much more than 100 Tier on them.

First an 8/5 DDB game:

                                                                       Results
Sims                                                               10000.000000
BuyIn                                                                  1.000000
ROI %                                                                -3.224143
SD                                                                     6.479954
Sim. Loss of $1k or greater                                           14.310000
Sim. Loss of $1k or greater w/o Royal                                 17.053986
Sim. Loss of $1k or greater w/no Royal and 1 or less 800+ cred win    49.356223

$`Return Results Cont.`
                                                                                Results
Sim. Loss of $1k or greater no royal, <2 800+ credit quad and <4 400 cred wins 60.05416
% of Royalless Sims                                                            83.91000
% Sims with no Royals and 1 or less 800+ cred win                             20.97000
% Sims 1 or less 800+ quad and 3 or less 400 quad                             14.77000

$`Win/Loss Summary`
   Min. 1st Qu. Median    Mean 3rd Qu.    Max.
-2128.0 -793.8 -398.8 -303.1   100.0 4255.0

$`Summary of Hands`
   Min. 1st Qu. Median    Mean 3rd Qu.    Max.
   7200    7200    7200    7200    7200    7200

$`Summary of Royals`
   Min. 1st Qu. Median    Mean 3rd Qu.    Max.
0.0000 0.0000 0.0000 0.1759 0.0000 4.0000

$`Summary of Aces/2-4s with kicker`
   Min. 1st Qu. Median    Mean 3rd Qu.    Max.
    0.0     1.0     3.0     2.7     4.0    10.0

$`Summary of 2s-4s`
   Min. 1st Qu. Median    Mean 3rd Qu.    Max.
0.000   2.000   3.000   2.751   4.000 10.000

$`BR w/o RF`
   Min. 1st Qu. Median    Mean 3rd Qu.    Max.    NA's
-2128.0 -864.4 -522.5 -476.1 -135.0 1915.0 1609.0

$`BR w/no RF and 1 or less 800+ quad`
   Min. 1st Qu. Median    Mean 3rd Qu.    Max.    NA's
-2128.0 -1211.0 -990.0 -972.5 -753.8   435.0 7903.0

$`BR w/no RF and 1 or less 800+ quad and 3 or less 400 quads`
   Min. 1st Qu. Median    Mean 3rd Qu.    Max.    NA's
-2128.0 -1269.0 -1084.0 -1057.0 -847.5   435.0 8523.0


Now 9/6 DDB:

                                                                       Results
Sims                                                               10000.000000
BuyIn                                                                  1.000000
ROI %                                                                -1.019065
SD                                                                     6.479584
Sim. Loss of $1k or greater                                           6.420000
Sim. Loss of $1k or greater w/o Royal                                  7.650143
Sim. Loss of $1k or greater w/no Royal and 1 or less 800+ cred win    25.299473

$`Return Results Cont.`
                                                                                                       Results
Sim. Loss of $1k or greater w/no royal w/only 1 or less 800+ credit win and w/3 or less 400 cred wins 32.93954
% of Royalless Sims                                                                                   83.92000
% Sims with no Royals and 1 or less 800+ cred win                                                     20.87000
% Sims 1 or less 800+ quad and 3 or less 400 quad                                                     14.39000

$`Win/Loss Summary`
   Min. 1st Qu. Median    Mean 3rd Qu.    Max.
-1998.0 -590.3 -194.4 -101.1   307.5 4515.0

$`Summary of Hands`
   Min. 1st Qu. Median    Mean 3rd Qu.    Max.
   7200    7200    7200    7200    7200    7200

$`Summary of Royals`
   Min. 1st Qu. Median    Mean 3rd Qu.    Max.
0.0000 0.0000 0.0000 0.1751 0.0000 4.0000

$`Summary of Aces/2-4s with kicker`
   Min. 1st Qu. Median    Mean 3rd Qu.    Max.
0.000   2.000   3.000   2.705   4.000 10.000

$`Summary of 2s-4s`
   Min. 1st Qu. Median    Mean 3rd Qu.    Max.
0.000   2.000   3.000   2.749   4.000 10.000

$`BR w/o RF`
   Min. 1st Qu. Median    Mean 3rd Qu.    Max.    NA's
-1998.0 -661.2 -322.5 -274.6    67.5 2019.0 1608.0

$`BR w/no RF and 1 or less 800+ quad`
   Min. 1st Qu. Median    Mean 3rd Qu.    Max.    NA's
-1998.0 -1002.0 -791.2 -770.3 -541.9   580.0 7913.0

$`BR w/no RF and 1 or less 800+ quad and 3 or less 400 quads`
   Min. 1st Qu. Median    Mean 3rd Qu.    Max.    NA's
-1998.0 -1074.0 -880.0 -858.8 -645.6   580.0 8561.0

_________________________________________________________________________________


So the data to glean from this the most:

Percentage of sessions with a 4 digit loss:
8/5 DDB: 14.31%
9/6 DDB: 6.42%

Median Loss: (will lose more than this 50% of the time)
8/5 DDB: $398.80
9/6 DDB: $194.40

Mean Loss: Average Loss overall
8/5 DDB: $303.10
9/6 DDB: $101.10

Probability of the royal and premium quad scenario that you personally seen (or worse):
~14.5%

And Finally the chances you lose $1000 given the royal/quad scenario that you experienced (or worse):
8/5 DDB: 49.4%
9/6 DDB: 25.3%

DDB reminds you variance is a cruel *****.

[notes1]

Vman, first and foremost, i am so grateful for all the effort you put into this. i had no idea you needed to spend so much time to do the calculations. i am trying to better understand how small changes can really affect overall expectations and results. second, i must admit i do not understand a lot of the results you posted.  a couple of questions, please scale your answers to a 2nd grade level, so i can understand. in your first post, which was very easy for me to compute, in a 8/5 game, at quarter level, at 5000 hands over 12 hours, you stated the expected loss was about $63/hour. in this post, at 7200 hands, your calculations, the median expected loss is $303. why the difference? under the 9/6 level, you stated an expected loss at about $20/hr. this seems spot on to what my average loss was years ago. the $63/hr loss under 8/5 also seems pretty accurate for the results i am seeing now. again, that median expected loss in this post seems low. i think many of the posters here would gladly accept that amount of loss for a 10-12 session. can you explain? it could be i am misunderstanding the term 'median', i know it is not average, just a point at which 50% lose more or less.  thanks again! 

[alpax]

I think it means that if you get to play 7200 hands (or past 5000 hands) you will average a lesser loss since you will reach a odds cycle to hit quad aces "and/or" quad 2s,3s,4s with any Ace,2,3,4, since the odds for those are greater than 1 in 5000 odds. Then again, if you reach a cycle, you're chance of hitting it is 1/e which is about 64%.

Also to add, 1 out of every 4164 5-card draws on average, you will be dealt a quad.

[Vman96]

I think it means that if you get to play 7200 hands (or past 5000 hands) you will average a lesser loss since you will reach a odds cycle to hit quad aces "and/or" quad 2s,3s,4s with any Ace,2,3,4, since the odds for those are greater than 1 in 5000 odds. Then again, if you reach a cycle, you're chance of hitting it is 1/e which is about 64%.

Nah, he has the expected loss numbers in his head messed up I think.

I think you were confused by this. alpax gave expected losses for quarters and dollars for 400 hands/hr. -$64/hr is for dollars.

400 hands an hour (relative speed for those using touchscreen all the time) at $1.25 per bet (5 credit quarters) is $500 coin in an hour.

The average loss on a 9/6 DDB is $5.10 in quarters ($20.40 in dollars)
The average loss on a 8/5 DDB is $16.05 in quarters ($64.20 in dollars)



The simulations I ran were for 600 hands/hr of quarter play over 12 hours (i.e. 7200 hands). For 8/5 DDB, this becomes -$25.26/hr on average which is a little over 50% higher than alpax's quarter estimate. This makes sense because I'm assuming you played 50% more hands per hour than he did. My sim ran a little cold. It returned 96.65% overall (return over the eternal run should be 96.79%). For 9/6 DDB, the expected loss from the simulation on an hourly basis of 600 hands/hr was $8.43/hr.

Like mentioned previously, the median represents where half your other results are either worse or better than that number. In VP, medians are always lower than the "average" or "mean" result. This is because what causes you to get big wins are rarer events (i.e. Royals, AWAK, Aces, etc.) that pay very well, so when you are lucky enough to hit these things, you balance shoots up much more in the positive direction which influences the "average" or "mean" closer to zero. But when you're losing hands, you're only losing $1.25 at a time, so losses from bad sessions are bunched closer together than wins.

You can see this from looking at the Bankroll Histogram Graphs for these 2 sims.

Here is 8/5 DDB:



And here is 9/6 DDB:


You can see the losses on the left are more bunched together than the wins on the right. But those wins go further right as well. Also you can see that the graph on the 8/5 game is more shifted to the left than the 9/6 game thanks to the lower full house/flush payouts.

[Eduardo]

It all makes sense now.

[chattycattty]

Now that's funny Eduardo. Unfortunately for me my results are probably closer to Daburglar's than they are to Ted's.

[Vman96]

Now that's funny Eduardo.



Post of the year Eduardo!

[Galeygoo]

[QUOTE=chattycattty] Now that's funny Eduardo.



Post of the year Eduardo! [/QUOTE]

YOU ARE HYSTERICAL, EDUARDO...

[Tedlark]

  I tip my sombrero to you Eduardo...Ole'