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gordonm888
gordonm888
Joined: Feb 18, 2015
  • Threads: 46
  • Posts: 2859
July 16th, 2020 at 8:05:19 AM permalink
Quote: DRich

What is the payback of the base game and the payback of the bonus bet?



This is what I am currently calculating for RTP when you don't get a Red Ball, and for when you do get a Red Ball. When I combine them I don't get agreement with RealizeGaming's numbers, but I have not yet been able to find my error(s).


Numbers Picked
No Red Ball RTP
Red Ball RTP
Total RTP
Quoted RTP
1
0.5
1.004997
0.82754086
0.9621
2
0.5
1.004997
0.82754086
0.9621
3
0.451315
1.005534
0.810781329
0.9455
4
0.448823
1.021180
0.820053571
0.957
5
0.297566
1.137409
0.842288243
0.9938
6
0.319266
1.104856
0.828799412
0.9765
7
0.322280
1.125509
0.843254405
0.9942
8
0.233721
1.138249
0.820397969
0.9727
9
0.240579
1.049738
0.76539929
0.9068
10
0.246148
1.148563
0.831454504
0.986
11
0.211856
1.120330
0.801092311
0.9507
12
0.273963
1.126439
0.826878906
0.9776
13
0.278526
1.153831
0.846248695
1.0004
14
0.312576
1.147463
0.854083658
1.0072
15
0.267476
1.158171
0.845180913
1.0009


The Total RTP column is based on a red ball appearing with a frequency of 0.6486.

When a red ball is present, the multipliers account for increasing the RTP, on average, by a factor of 1.6164. The rest of the increase in RTP when a Red Ball appears is attributable to the additional draws, ranging from +1 to +10.

My calculations are all done using combination math, not simulations.
Last edited by: gordonm888 on Jul 16, 2020
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
RealizeGaming
RealizeGaming
Joined: Aug 1, 2013
  • Threads: 57
  • Posts: 582
July 17th, 2020 at 6:06:02 AM permalink
Quote: gordonm888

This is what I am currently calculating for RTP when you don't get a Red Ball, and for when you do get a Red Ball. When I combine them I don't get agreement with RealizeGaming's numbers, but I have not yet been able to find my error(s).


Numbers Picked
No Red Ball RTP
Red Ball RTP
Total RTP
Quoted RTP
1
0.5
1.004997
0.82754086
0.9621
2
0.5
1.004997
0.82754086
0.9621
3
0.451315
1.005534
0.810781329
0.9455
4
0.448823
1.021180
0.820053571
0.957
5
0.297566
1.137409
0.842288243
0.9938
6
0.319266
1.104856
0.828799412
0.9765
7
0.322280
1.125509
0.843254405
0.9942
8
0.233721
1.138249
0.820397969
0.9727
9
0.240579
1.049738
0.76539929
0.9068
10
0.246148
1.148563
0.831454504
0.986
11
0.211856
1.120330
0.801092311
0.9507
12
0.273963
1.126439
0.826878906
0.9776
13
0.278526
1.153831
0.846248695
1.0004
14
0.312576
1.147463
0.854083658
1.0072
15
0.267476
1.158171
0.845180913
1.0009


The Total RTP column is based on a red ball appearing with a frequency of 0.6486.

When a red ball is present, the multipliers account for increasing the RTP, on average, by a factor of 1.6164. The rest of the increase in RTP when a Red Ball appears is attributable to the additional draws, ranging from +1 to +10.

My calculations are all done using combination math, not simulations.



gordonm888,

Hard to argue with your math you provided. I think the appearance of the multipliers is what attributes to the difference in RTP between yours and ours. Your numbers seem to be the RTP expected in most keno games.
gordonm888
gordonm888
Joined: Feb 18, 2015
  • Threads: 46
  • Posts: 2859
Thanks for this post from:
RealizeGamingMrCasinoGames
July 17th, 2020 at 9:32:39 AM permalink
I did a check on my calculations for frequency of hits and compared it to the results you have posted on your information page of the demo. Here is an example.

Player Picks 5 Numbers

Hits
Payout
Freq, % (RG Simul)
Freq,% (Gordon calcs)
Return (w/o mult)
0
0
17.659190
17.66139845
0
1
0
37.260590
37.25610053
0
2
0
30.460460
30.45880463
0
3
2
12.100430
12.1036472
0.242072944
4
30
2.342790
2.34313486
0.702940458
5
100
0.176550
0.176914335
0.176914335
Total
1
1
1.121927737


So the agreement in frequency is excellent. My calcs should be theoretically precise.

The Return (without multipliers) is 1.122 units, and given the initial wager of 2 units, the RTP (w/o multipliers) when player picks 5 numbers is 56.1%. I'll address multipliers in my next post.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
gordonm888
gordonm888
Joined: Feb 18, 2015
  • Threads: 46
  • Posts: 2859
Thanks for this post from:
ksdjdjRealizeGamingMrCasinoGames
July 17th, 2020 at 9:51:14 AM permalink
I have found an error in the way I interpreted the frequency of multipliers. Although, to be fair, your information page described the Frequency of Multipliers table in two different ways:

- Frequency of multipliers in all rounds played (which appears to be correct definition)
- Frequency of multipliers in all rounds with extra balls

I previously used the latter definition, but when I use the first definition I get good agreement with your team's simulation results:
Numbers Picked
No Red Ball RTP
Red Ball RTP
Combined RTP
Quoted RTP
1
0.5
1.212633
0.96221375
0.9621
2
0.5
1.212633
0.96221375
0.9621
3
0.451315
1.213281
0.945526231
0.9455
4
0.448823
1.232159
0.956895017
0.957
5
0.297566
1.372402
0.99470481
0.9938
6
0.319266
1.333123
0.976853713
0.9765
7
0.322280
1.358044
0.994076379
0.9942
8
0.233721
1.373416
0.972927162
0.9727
9
0.240579
1.266618
0.906067626
0.9068
10
0.246148
1.385861
0.985365774
0.986
11
0.211856
1.351795
0.951220276
0.9507
12
0.273963
1.359166
0.977825451
0.9776
13
0.278526
1.392217
1.000865863
1.0004
14
0.312576
1.384533
1.007847516
1.0072
15
0.267476
1.397454
1.000379723
1.0009



Again, my RTP numbers should be precise because they are based on combinatorial number theory.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
RealizeGaming
RealizeGaming
Joined: Aug 1, 2013
  • Threads: 57
  • Posts: 582
Thanks for this post from:
MrCasinoGamesgordonm888
July 19th, 2020 at 8:25:23 AM permalink
Quote: gordonm888

I have found an error in the way I interpreted the frequency of multipliers. Although, to be fair, your information page described the Frequency of Multipliers table in two different ways:

- Frequency of multipliers in all rounds played (which appears to be correct definition)
- Frequency of multipliers in all rounds with extra balls

I previously used the latter definition, but when I use the first definition I get good agreement with your team's simulation results:

Numbers Picked
No Red Ball RTP
Red Ball RTP
Combined RTP
Quoted RTP
1
0.5
1.212633
0.96221375
0.9621
2
0.5
1.212633
0.96221375
0.9621
3
0.451315
1.213281
0.945526231
0.9455
4
0.448823
1.232159
0.956895017
0.957
5
0.297566
1.372402
0.99470481
0.9938
6
0.319266
1.333123
0.976853713
0.9765
7
0.322280
1.358044
0.994076379
0.9942
8
0.233721
1.373416
0.972927162
0.9727
9
0.240579
1.266618
0.906067626
0.9068
10
0.246148
1.385861
0.985365774
0.986
11
0.211856
1.351795
0.951220276
0.9507
12
0.273963
1.359166
0.977825451
0.9776
13
0.278526
1.392217
1.000865863
1.0004
14
0.312576
1.384533
1.007847516
1.0072
15
0.267476
1.397454
1.000379723
1.0009



Again, my RTP numbers should be precise because they are based on combinatorial number theory.



gordonm888 your skills are incredible! Thank you so much for confirming the math for this game. I can't even begin to think about how long it took you to do it.
RealizeGaming
RealizeGaming
Joined: Aug 1, 2013
  • Threads: 57
  • Posts: 582
July 24th, 2020 at 6:32:34 AM permalink
Game has been updated with the math to show the RTP and a few other nice little features requested on here.

Demo:
https://realizegamingllc.com/demo/multidrawKeno/

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