CrystalMath
CrystalMath
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September 10th, 2016 at 4:17:07 PM permalink
I've been interested in this for a while, and there have been multiple threads discussing this recently, so I wrote a simulator to determine the risk of ruin.

The reason that a simulator is a good option is that VP does not follow a normal distribution with a low number of games played, and it is very likely that the players lowest credit balance is lower than the ending credit balance, so attempting to use the normal distribution leads to erroneous results.

The simulator performs 100,000 Diamond in a Day sessions, where the player earns 5000 tier credits.

So far, I only have it built for Jacks or Better, and the variables I can change are:
denom
number of hands (lines)
dollars per tier credit
paytable

Here's a link to a google doc DIAD ROR which shows the risk of ruin for various settings. Some of these may not be offered, but I included some that I know are available. Maybe in a future revision, I could list where each config is available (according to VPFree2).

It's an eye opener to me, because I assumed the ROR to be much less.

If it is of interest, I think I may add deuces wild next, and I'm open to taking suggestions as to which specific configurations to simulate.
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Wizardofnothing
Wizardofnothing
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September 10th, 2016 at 4:23:59 PM permalink
Great post!!!
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GWAE
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September 10th, 2016 at 4:24:35 PM permalink
Is the 3rd column correct? It shows a .02 with only $4000?

I never understand RoR on these type of things. It seems like $1 3 line is the best option. Am I reading that right?
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CrystalMath
CrystalMath
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September 10th, 2016 at 4:36:51 PM permalink
Quote: GWAE

Is the 3rd column correct? It shows a .02 with only $4000?

I never understand RoR on these type of things. It seems like $1 3 line is the best option. Am I reading that right?



Yes, it shows 0.028 = 2.8% risk of ruin with $4000. $1 3 play does look like the best. 9/5 Jacks is available at Planet Hollywood, and I read another post where someone found 9/6 for $10 per TC, but I'm sure that's not in Vegas.
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MathExtremist
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September 10th, 2016 at 5:36:07 PM permalink
Are columns G or I in Las Vegas? That might be a good distraction during G2E -- and a good place to sit for a few hours and recover from standing on the under-padded floor in the expo hall.
"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
CrystalMath
CrystalMath
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September 10th, 2016 at 5:44:56 PM permalink
Quote: MathExtremist

Are columns G or I in Las Vegas? That might be a good distraction during G2E -- and a good place to sit for a few hours and recover from standing on the under-padded floor in the expo hall.



Column I is at Paris. Spin poker in the high limit room.
Column G is not in Vegas. I saw it in another thread and the location is not specified.

Actually, I didn't do that one right, since the draw cards are correlated.

On second thought, you could play column I at Planet Hollywood, assuming you could play 5 credits on just 9 lines on a 50 or 100 play machine. But, it may be better to play a different number of lines - I'll need to find out.
Last edited by: CrystalMath on Sep 10, 2016
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vegas
vegas
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September 10th, 2016 at 7:12:02 PM permalink
Thanks so much this post. Really puts things in perspective.
50-50-90 Rule: Anytime you have a 50-50 chance of getting something right, there is a 90% probability you'll get it wrong
Deucekies
Deucekies
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September 10th, 2016 at 10:34:26 PM permalink
Fantastic post, Crystal! Thanks!
Casinos are not your friends, they want your money. But so does Disneyland. And there is no chance in hell that you will go to Disneyland and come back with more money than you went with. - AxelWolf and Mickeycrimm
100xOdds
100xOdds
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September 11th, 2016 at 5:29:50 AM permalink
thx!

dstp (9/5 JoB) = 99%
$1 10line/$2 5 line
ev should be -$500 for DiaD.

whats the standard deviation on that (in terms of $, like you have in the spreadsheet)?
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
CrystalMath
CrystalMath
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September 11th, 2016 at 7:41:42 AM permalink
Quote: 100xOdds

thx!

dstp (9/5 JoB) = 99%
$1 10line/$2 5 line
ev should be -$500 for DiaD.

whats the standard deviation on that (in terms of $, like you have in the spreadsheet)?



Do you have an idea about the probability of each multiplier? From there, I can tweak the probabilities to get the right average multiplier. This will be easy to sim after I get that.
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DRich
DRich
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September 11th, 2016 at 8:01:50 AM permalink
Thanks for doing the work on this.

When you decide to expand it I would like to see Bonus Deuces at $0.05 and $0.10 in a 50 play configuration that is available at a Total Rewards property.
At my age, a "Life In Prison" sentence is not much of a deterrent.
100xOdds
100xOdds
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September 11th, 2016 at 8:11:07 AM permalink
Quote: CrystalMath

Do you have an idea about the probability of each multiplier? From there, I can tweak the probabilities to get the right average multiplier. This will be easy to sim after I get that.



each multiplier?
no I don't. :(

from wiz's page (https://wizardofodds.com/games/video-poker/tables/double-super-times-pay/), the avg multiplier is 4.01.
2 chances in getting a multiplier: once on deal and once on the draw.
1 in 15 chance of getting a multiplier on either.

so in theory you should see a multiplier every 7.5 hands?
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
CrystalMath
CrystalMath
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September 11th, 2016 at 8:31:16 AM permalink
Quote: 100xOdds

each multiplier?
no I don't. :(

from wiz's page (https://wizardofodds.com/games/video-poker/tables/double-super-times-pay/), the avg multiplier is 4.01.
2 chances in getting a multiplier: once on deal and once on the draw.
1 in 15 chance of getting a multiplier on either.

so in theory you should see a multiplier every 7.5 hands?



Ok. I'll play on VideoPoker.com to try to get an estimate.
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CrystalMath
CrystalMath
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September 11th, 2016 at 8:32:16 AM permalink
Quote: DRich

Thanks for doing the work on this.

When you decide to expand it I would like to see Bonus Deuces at $0.05 and $0.10 in a 50 play configuration that is available at a Total Rewards property.



You're welcome. I'll put this in line right behind dstp.
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Ibeatyouraces
Ibeatyouraces
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September 11th, 2016 at 10:58:06 AM permalink
Next project...risk of ruin to get to Super Sucker, err I mean Seven Stars.:-)
DUHHIIIIIIIII HEARD THAT!
beachbumbabs
beachbumbabs
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September 11th, 2016 at 11:05:03 AM permalink
Wow, CM, that's quite a gift. Thanks!
If the House lost every hand, they wouldn't deal the game.
CrystalMath
CrystalMath
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September 11th, 2016 at 2:32:55 PM permalink
Here's an updated file. I corrected the standard deviation, added several JOB bet configurations, and added Double Super Times Pay JOB.

DIAD ROR
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CrystalMath
CrystalMath
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September 12th, 2016 at 5:20:18 PM permalink
I've made another update with Bonus Deuces.

DIAD ROR

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RS
RS
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September 12th, 2016 at 5:26:52 PM permalink
5-play 9/5 JOB STP:


0	0.129506318977621
5 0.104201937737873
10 0.156938040442759
15 0.112087856564135
20 0.077580408135006
25 0.0944362545162095
30 0.0637944629094563
35 0.0472677152567407
40 0.0365055568256933
45 0.0235204895028114
50 0.0454844359313312
55 0.00803561351701343
60 0.00803738375320404
65 0.00319179429272829
70 0.00373479736433423
75 0.0189741986148372
80 0.00332921385517499
85 0.0139095563664693
90 0.0019549741146444
95 7.94643256546628E-05
100 0.00717006487871052
105 0.00511272050074394
110 0.000143712716053784
115 5.0759789660765E-05
120 0.00446164091481837
125 0.00439899909753825
130 0.000152899305389557
135 0.00195940852974756
140 0.00123600086016238
145 0.000746536916876677
150 0.00328778656805832
155 0.000832518706699833
160 0.00101837370355463
165 0.000404142523525345
170 0.000279263611182407
175 0.000828975359747684
180 0.000386595478271364
185 0.00276078256502137
190 3.65132236700169E-05
195 0.00010379939003566
200 0.00171274043966041
205 3.82134721124702E-06
210 0.000124421908222642
215 0.000739519044649249
220 9.2397530991688E-05
225 0.00205618116749097
230 1.22472900055188E-06
235 2.55091882259011E-07
240 0.000364652705897207
245 7.54466636247486E-05
250 0.00115170274276842
255 0.000369427631493459
260 6.7817794406215E-05
265 1.76753954228235E-05
270 6.79763970534208E-05
275 0.000218125383832348
280 0.000261881924333298
285 6.68761204780921E-06
290 1.63140677635787E-05
295 0.000278143992742154
300 0.000535336498399238
305 2.79726476654862E-06
310 1.11891167891338E-05
315 9.69847377844207E-05
320 0.000167319388824311
325 0.00011045550075084
330 3.89677441805909E-06
335 1.37843778980377E-07
340 0.000160610784581006
345 1.54070199721691E-06
350 0.00018963717693587
355 3.58058395115834E-06
360 0.000152308735259673
365 3.55200273246396E-12
370 3.35237893772705E-05
375 0.000321902257225812
380 1.34560575716635E-06
385 1.10618151500673E-07
390 3.05399936482059E-06
395 7.06868342337936E-09
400 0.000341397094903092
405 4.67643223490824E-05
410 4.64658229144175E-08
415 2.17608142983752E-11
420 6.12114070672803E-05
425 0.00023844994021737
430 8.98015135833228E-06
435 1.92603469350329E-05
440 3.49656505919565E-05
445 8.64000105758883E-13
450 0.000100648745707305
455 5.00450368095875E-14
460 5.87499129352727E-07
465 1.96803056478894E-05
470 3.09757068020868E-09
475 1.36224558720081E-06
480 5.39291843831343E-05
485 5.61561793670913E-16
490 9.1613805874598E-07
495 5.06153136063434E-06
500 0.000223407113050643
505 6.11552034714328E-07
510 3.24944889041116E-06
515 3.13580408317807E-07
520 1.71780612372428E-05
525 7.22241664072551E-05
530 5.2690057315526E-07
535 3.1678363464158E-08
540 1.85444151820623E-05
545 8.6869912035876E-07
550 2.54809062167224E-05
555 6.5114074881469E-05
560 2.12610195713544E-05
565 6.57695003330628E-08
570 9.93548594566057E-07
575 9.26146631232563E-07
580 8.61987378416519E-06
585 6.73299922454092E-07
590 3.37746278425387E-06
595 5.5368784995388E-15
600 0.000128521343939119
605 3.19092015501642E-16
610 3.39667866380717E-08
615 9.0074612990173E-08
620 9.52761331807214E-06
625 0.000272276065169047
630 6.53098681479778E-08
635 2.19282807372758E-13
640 9.51383245859086E-06
645 1.74315203830379E-05
650 1.17529599687549E-05
655 9.53930457348214E-15
660 2.45656643105475E-06
665 7.51012936190109E-16
670 1.67382048730554E-09
675 5.68523451123285E-05
680 6.08773580625906E-05
685 7.46888973702375E-17
690 1.8519746654406E-08
695 3.44971750743705E-17
700 2.05164577500624E-05
705 6.01288008181955E-09
710 4.34785194069226E-08
715 2.42101542004504E-18
720 1.83013074916463E-06
725 1.27977757178859E-05
730 4.3131461751348E-14
735 1.77838564258336E-06
740 3.15518007563094E-05
750 6.006258221325E-05
755 1.65999678953129E-08
760 7.48518061548045E-07
765 9.79636245464765E-07
770 6.37723788671735E-08
775 1.43661307409834E-05
780 1.03708675446582E-06
785 2.80089167210811E-12
790 5.51778287127733E-09
795 4.31010825055975E-07
800 2.59551843713593E-05
805 6.04937689452221E-17
810 1.15603594064573E-06
815 1.60878756572547E-17
820 4.36733136721942E-08
825 5.5755967921208E-06
830 2.64238459337413E-13
840 1.75105086241045E-05
850 4.16335120255569E-05
855 1.1348521733207E-07
860 8.45164959110605E-06
870 1.91067228058923E-07
875 3.20085765228833E-07
880 1.9775129145995E-07
885 6.55625125750037E-06
890 1.04940992726668E-14
895 1.78940621369012E-18
900 1.75044317078048E-05
910 6.07689732687848E-16
915 6.59355266400747E-08
920 2.2449464305603E-07
925 4.7327701114652E-05
930 2.61441230410909E-08
940 2.91533611776427E-09
945 6.44238511820724E-08
950 8.36440354193803E-07
960 1.07410116225063E-05
970 6.81896463743252E-18
975 1.80352116337009E-06
980 8.6224758428825E-07
990 4.7565781955526E-09
1000 2.50280821236736E-05
1005 3.46870971666375E-09
1010 7.42601980876371E-09
1015 1.02720612005037E-14
1020 4.84777430503474E-07
1025 6.66972376418877E-08
1030 3.80776210100194E-09
1035 8.11378639328987E-09
1040 8.53742528562215E-07
1045 5.17484005169269E-20
1050 1.14912141536616E-05
1060 2.05796378487319E-07
1065 8.43994788487322E-08
1070 3.84665842064776E-10
1075 1.26774693368443E-05
1080 6.77456374722362E-06
1090 1.05484893186421E-08
1095 8.37257786937933E-14
1100 1.05955722508954E-06
1110 4.67353803514051E-10
1120 2.99140972616203E-06
1125 2.30716883730983E-05
1130 7.98629646901476E-10
1140 5.63393034117358E-08
1150 1.56136743866826E-07
1155 2.60742785680158E-09
1160 3.28228937688999E-06
1170 3.927597272846E-10
1175 4.37300369586876E-09
1180 3.17878848866684E-06
1185 1.66618966408228E-10
1190 6.72335246372569E-17
1200 1.08071858218207E-05
1210 3.87468875966279E-18
1215 2.87824511011922E-07
1220 3.19687401913994E-08
1225 1.29337137642426E-06
1230 1.50267183318941E-12
1240 3.58027972659839E-06
1245 5.12933479890272E-13
1250 2.61359993028401E-05
1260 3.12560221725134E-08
1270 2.66271980381206E-15
1275 7.12458352926178E-07
1280 1.34050977845807E-06
1290 6.53559938591516E-12
1300 1.47663639559514E-06
1305 3.92088397550085E-08
1310 1.15834412677997E-16
1320 9.22584685095755E-07
1325 3.03006778676974E-07
1330 9.11944279659418E-18
1335 2.03657167786022E-14
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1350 4.92123173518698E-06
1360 4.76457298322708E-07
1365 1.17963301051171E-15
1370 9.06936610924312E-19
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1380 3.93395745012747E-09
1390 4.18894268760213E-19
1395 1.33533129406709E-09
1400 2.22090468174348E-06
1410 6.22182824420917E-16
1420 4.09209594418095E-08
1425 8.25347036214701E-08
1430 2.93980443862612E-20
1440 1.79148563603453E-07
1450 2.25723079044896E-06
1455 1.32368137079572E-17
1460 4.05943169424452E-14
1470 1.0500168025774E-17
1475 4.76818273272264E-06
1480 1.18319252910941E-05
1500 2.79557070054389E-06
1510 2.01571038728799E-10
1515 1.44151551039806E-08
1520 1.52435633264892E-07
1525 4.79531102836907E-08
1530 3.3806340413254E-09
1540 2.02227579840312E-09
1545 7.3915381960626E-09
1550 2.39828455540934E-06
1560 1.65814779529041E-07
1570 3.40108274470271E-14
1575 1.23164486344696E-07
1580 1.4674433240344E-10
1590 7.53524002637616E-09
1600 9.81990896383287E-07
1605 7.46704281655153E-10
1610 7.3456719433484E-19
1620 1.46309074424227E-07
1625 9.5552617990649E-07
1630 1.95352775838093E-19
1635 2.04764792655993E-08
1640 1.63779309013231E-08
1650 6.34777954746881E-07
1660 2.48695020552859E-13
1665 9.07166436531456E-10
1675 2.36303621109218E-09
1680 6.24360384245956E-09
1695 1.55028107927934E-09
1700 3.20541064326559E-07
1710 2.29025433985605E-09
1720 3.16937050272232E-06
1725 7.2204360442759E-09
1740 1.90103469703693E-08
1750 5.63328636945366E-08
1755 1.58068349464826E-16
1760 7.33740387495596E-12
1770 3.59357636740762E-16
1775 6.13814391627143E-08
1780 9.87431933730823E-15
1785 1.30512136060557E-16
1790 2.17285040233801E-20
1800 5.88715329688429E-06
1815 7.52145465111012E-18
1820 5.71943277823857E-16
1825 6.08914754136678E-14
1830 4.41078210306302E-18
1840 2.60725788228977E-09
1845 3.62142324515978E-18
1850 7.88795020442205E-06
1860 6.47433354699194E-10
1875 5.28276312642798E-06
1880 1.09325122563159E-09
1890 1.35550242459285E-14
1900 1.01665726844339E-07
1905 5.16880903092929E-15
1920 5.19398966317631E-10
1925 1.89631116858297E-09
1935 1.0578164166071E-15
1940 6.41784907052472E-18
1950 8.18977551409046E-08
1960 3.23342844111156E-07
1965 2.24855036374936E-16
1975 1.21177430115075E-10
1980 4.74206382485515E-17
1995 1.7702447781624E-17
2000 6.97002199030885E-07
2010 2.66585599700503E-12
2020 6.9891664852128E-09
2025 2.09326917126248E-07
2030 1.24732171720402E-16
2040 1.79762090281524E-07
2050 1.09336586553097E-08
2055 1.76052400944131E-18
2060 3.58377609506065E-09
2070 9.95227886141027E-19
2075 3.73042530829289E-13
2080 1.49297576270522E-07
2085 8.1314769818159E-19
2090 6.28373434848398E-22
2100 4.09073461151195E-08
2120 7.93205034874424E-08
2125 6.90011086985948E-12
2140 3.62038439590377E-10
2145 5.70667920439187E-20
2150 2.11291630890758E-06
2160 1.86506090538739E-07
2175 2.85155198218244E-08
2180 9.92798994695725E-09
2200 3.53086518605204E-07
2220 4.39838272257676E-10
2225 1.4811430384438E-14
2240 6.5330621373887E-08
2250 3.84982678305107E-06
2260 7.5165143237786E-10
2265 3.91284957532375E-10
2275 8.57914916735786E-16
2280 2.1782291423202E-08
2295 4.49170386904089E-13
2300 2.37792989852209E-09
2310 1.47154444932221E-09
2320 3.10670429051686E-08
2325 3.19585642345857E-09
2340 1.03105316503718E-10
2350 7.2883440180806E-10
2355 6.60210179854055E-14
2360 1.19204568335485E-06
2370 1.2803879451658E-10
2375 7.79906052814884E-17
2380 6.32786114233006E-17
2385 3.38874745985357E-10
2400 9.28797673119051E-08
2415 1.42592455370881E-18
2420 3.64676589144733E-18
2425 9.62677360578708E-18
2430 5.64064234186532E-19
2440 1.19882775730612E-08
2445 3.79214211921005E-19
2450 2.15561896078347E-07
2460 2.04753522435077E-18
2480 4.62840456394964E-09
2500 3.20709418284908E-06
2520 1.17134340598006E-08
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122600 5.06296312389254E-18
122650 1.68779473097498E-18
122700 9.66412320707793E-14
122750 1.12748293576968E-13
122950 5.74070203224546E-23
123750 6.37983383027051E-24
125000 8.2319890031561E-15
128000 7.93314729958323E-13
128040 2.95180169912274E-13
128080 3.90815162307161E-18
128120 1.30277685783059E-18
128160 1.10327796762403E-13
128200 2.39848215620601E-13
128360 2.43993157503472E-23
129000 2.71136997003934E-24
130000 6.17396297458216E-15
160000 6.15684383509643E-09
160050 1.96786779941516E-13
160100 2.60543441538107E-18
160150 8.68517905220393E-19
160200 7.35518645082689E-14
160250 1.59898810413734E-13
160450 1.62662105002314E-23
161250 1.80757998002623E-24
162500 4.11597531638811E-15
200000 4.10420997240652E-09


EDIT: Added spoiler.
DRich
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September 13th, 2016 at 8:49:17 AM permalink
Quote: CrystalMath

I've made another update with Bonus Deuces.

DIAD ROR



Thank you again.

Earlier I told a friend he should be good only taking $3,000 to play the 10 cent 50 play. I am surprised it is a 16% chance to go broke on that. I guess I should have told him $4,000.
At my age, a "Life In Prison" sentence is not much of a deterrent.
100xOdds
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September 13th, 2016 at 9:14:47 AM permalink
Quote: CrystalMath

Here's an updated file. I corrected the standard deviation, added several JOB bet configurations, and added Double Super Times Pay JOB.

DIAD ROR


thx!

and what do you mean by standard deviation?
ie: $7,434.53 for $1 10play dstp

2 sigma?
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CrystalMath
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September 13th, 2016 at 9:38:41 AM permalink
Quote: 100xOdds

Quote: CrystalMath

Here's an updated file. I corrected the standard deviation, added several JOB bet configurations, and added Double Super Times Pay JOB.

DIAD ROR


thx!

and what do you mean by standard deviation?
ie: $7,434.53 for $1 10play dstp

2 sigma?



It is 1 sigma on the final balance. But, the results are also not a normal distribution. I put it in there to see later if there is a correlation between SD and ROR.
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GWAE
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September 13th, 2016 at 9:43:29 AM permalink
One thing I don't like about RoR is that you might fall in the non ruined but only have $9 left.
Expect the worst and you will never be disappointed. I AM NOT PART OF GWAE RADIO SHOW
100xOdds
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September 13th, 2016 at 9:48:10 AM permalink
Quote: CrystalMath

Quote: 100xOdds

thx!

and what do you mean by standard deviation?
ie: $7,434.53 for $1 10play dstp

2 sigma?



It is 1 sigma on the final balance. But, the results are also not a normal distribution. I put it in there to see later if there is a correlation between SD and ROR.


im surprised theres no correlation.

if I did 10 DiaD days for 7Stars, then multiply RoR by 10?
ie: for $1 10play dstp(9/5 JoB), a bankroll of $7000 = 4.2% RoR.
so if I did 10 of those, then RoR = 42%?

also, for dstp (9/5 JoB), can you add $2 denom 3play?
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100xOdds
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September 13th, 2016 at 9:54:17 AM permalink
Quote: GWAE

One thing I don't like about RoR is that you might fall in the non ruined but only have $9 left.


but the goal is DiaD (15k tc).
if u reached 15k tc no matter how little $ left, you've succeeded and will now enjoy the Diamond perks.
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Romes
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September 13th, 2016 at 10:37:09 AM permalink
Fantastic post/contribution CrystalMath.

Interestingly enough this definitely also is confirmed by the "reverse engineering" aspect of calculating EV +/- SD's to approximate the RoR. Clearly your simulation is MUCH MORE exact =P.

i.e. Say you're playing $5 denom 9-6 JoB... Okay, so AvgBet = $25, HouseEdge = 0.46% (0.0046)... At 25/pull and $10 per tier credit we're earning 2.5 tier credits per hand... 5000/2.5 = 2000 = NumHands.

Variance of JoB = 19.5147
Std JoB = Sqrt(19.5147) = 4.4176

OriginalSD = Std * AvgBet = 4.4176 * 25 = 110.44
SD(x hands) = Sqrt(x) * OriginalSD

EV(2000 hands) = (25*2000)*(-.0046) = -230
SD(2000 hands) = Sqrt(2000) * 110.44 = 4939.03...

So with 68% confidence, one would expect to lose $230 +/- $5k...
With 99% confidence, one would expect to lose $230 +/- $15k... So a $15k bankroll should get your RoR down to under 1%.

Could I trouble you to run $5 SINGLE LINE on your simulation and give the same bankroll/RoR approximations? I'm wondering if I can draw a direct correlation from the SD % confidence to bankroll RoR %...
Last edited by: Romes on Sep 13, 2016
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Romes
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September 13th, 2016 at 10:50:24 AM permalink
To also do some more on my end, I'll do the same as above but for $25 demon ($125/pull) single line... which is 12.5 tier credits per pull.

AvgBet = $125
NumHands = 5000/12.5 = 400

OriginalSD = 4.4176 * 125 = 552.2

EV(400 hands) = (125*400)*(-0.0046) = -230
SD(400 hands) = Sqrt(400) * 552.2 = 11,044

So with 68% confidence, one would expect to lose $230 +/- $11,044...
With 99% confidence, one would expect to lose $230 +/- $33,132...

Hypothesis: There is a correlation between the % of confidence and the % of RoR... being such that 100 - % of confidence well approximates your RoR.

INTERESTINGLY enough, according to your chart with an ~10k bankroll you're looking at an RoR of about 36%, and we're 68% confident here with $11k. Dropping the bankroll to $10k would slightly lessen your confidence (from 68% to 64%, I can't tell exactly but this is interesting and appears correlated).

INTERESTINGLY enough (again), according to your chart with an ~$30k bankroll you should have 0% RoR, and this would certainly have the RoR < 1%. I can see here that it is still quite accurate, but starting to pull away from your more exact numbers (you have 0% RoR at $20k). So it's still going to cover you, just with overkill =).
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CrystalMath
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September 13th, 2016 at 11:14:13 AM permalink
Quote: 100xOdds

im surprised theres no correlation.

if I did 10 DiaD days for 7Stars, then multiply RoR by 10?
ie: for $1 10play dstp(9/5 JoB), a bankroll of $7000 = 4.2% RoR.
so if I did 10 of those, then RoR = 42%?

also, for dstp (9/5 JoB), can you add $2 denom 3play?



I added a column with this simulation. I suspected it would be worse than just 10*DIAD ROR because you are likely to be down a little more for each of the 10 sessions.
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CrystalMath
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September 13th, 2016 at 11:15:22 AM permalink
Quote: Romes

Fantastic post/contribution CrystalMath.

Could I trouble you to run $5 SINGLE LINE on your simulation and give the same bankroll/RoR approximations? I'm wondering if I can draw a direct correlation from the SD % confidence to bankroll RoR %...



Sure...It's in there now.
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Deucekies
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September 13th, 2016 at 11:28:23 AM permalink
Quote: Romes


So with 68% confidence, one would expect to lose $230 +/- $11,044...
With 99% confidence, one would expect to lose $230 +/- $33,132...



Loving that plus sign! :D

Seriously though. Good God.
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Romes
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September 13th, 2016 at 12:16:07 PM permalink
Quote: CrystalMath

Sure...It's in there now.

Thanks! Interesting to see that the higher up the bankroll the more profound the difference between the SD and RoR, but in the good direction =P. Good to know on the things I didn't program a SIM I've always overestimated =).
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100xOdds
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September 13th, 2016 at 12:53:01 PM permalink
Quote: Romes

Say you're playing $5 denom 9-6 JoB... Okay, so AvgBet = $25, HouseEdge = 0.46% (0.0046)... At 25/pull and $10 per tier credit we're earning 2.5 tier credits per hand... 5000/2.5 = 2000 = NumHands.

Variance of JoB = 19.5147
Std JoB = Sqrt(19.5147) = 4.4176

OriginalSD = Std * AvgBet = 4.4176 * 25 = 110.44
SD(x hands) = Sqrt(x) * OriginalSD

EV(2000 hands) = (25*2000)*(-.0046) = -230
SD(2000 hands) = Sqrt(2000) * 110.44 = 4939.03...

So with 68% confidence, one would expect to lose $230 +/- $5k...
With 99% confidence, one would expect to lose $230 +/- $15k... So a $15k bankroll should get your RoR down to under 1%.


lets see if I can calc my DiaD at $2 single line 9/6 JoB.
bet = $10, # hands = 5k

OrigSD = 4.4176 x $10 = 44.176
SD(5k hands) = sqrt(5k) x 44.176 = $3.1k

1 sigma (68%)= -230 +/- $3.1k
2 sigma (95%)= -230 +/- $6.2k
3 sigma (99%)= -230 +/- $9.3k

if it was 6/5 JoB:
EV = 95% = $50k x 5% = $2500
1 sigma (68%)= -$2500 +/- $3.1k


Now lets do it if I played $1 10play dstp (9/5 JoB).
EV = 99% = $50k x 1% = -$500
Var dstp= 2.5 x JoB= 50
sd = sqrt (50)= 7
bet = $70, # hands= 714

OrigSD = 7 x 70 = 490
sd(714 hands) = sqrt (714) x 490 = $13.1k

1 sigma (68%)= -500 +/- $13.1k
2 sigma (95%)= -500 +/- $26.2k
3 sigma (99%)= -500 +/- $39.3k

If it was dstp (6/5JoB):
EV = 95.5% = $50k x 4.5% = -$2250
1 sigma (68%)= -$2250 +/- $13.1k

Interestingly, assuming my math is right, Return of game only has a small effect on high variance games. -$2250 is relatively small compared to +/- $13.1k, as opposed to -$2500 compared to +/- 3.1k.

If so, then There's not much difference in bankroll requirements between the best paytable of
10play dstp (double double bonus) and the worse paytable?
Last edited by: 100xOdds on Sep 13, 2016
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100xOdds
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September 13th, 2016 at 1:19:59 PM permalink
Quote: CrystalMath

Here's an updated file. I corrected the standard deviation, added several JOB bet configurations, and added Double Super Times Pay JOB.

DIAD ROR


why is there a difference in SD between:
$1 10play dstp (9/5 JoB) and $2 5play? ($7,434.53 vs $8,355.54)

Both have $70 coin-in, and 714 hands needed for DiaD.


Quote: CrystalMath

I added a column with this simulation. I suspected it would be worse than just 10*DIAD ROR because you are likely to be down a little more for each of the 10 sessions.


thx.
and it's 7Stars, not Platinum like you titled that column.
(For Caesars, platinum is BELOW Diamond)
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100xOdds
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September 13th, 2016 at 1:30:44 PM permalink
Quote: Romes

To also do some more on my end, I'll do the same as above but for $25 demon ($125/pull) single line... which is 12.5 tier credits per pull.

AvgBet = $125
NumHands = 5000/12.5 = 400

OriginalSD = 4.4176 * 125 = 552.2

EV(400 hands) = (125*400)*(-0.0046) = -230
SD(400 hands) = Sqrt(400) * 552.2 = 11,044

So with 68% confidence, one would expect to lose $230 +/- $11,044...
With 99% confidence, one would expect to lose $230 +/- $33,132...

Hypothesis: There is a correlation between the % of confidence and the % of RoR... being such that 100 - % of confidence well approximates your RoR.

INTERESTINGLY enough, according to your chart with an ~10k bankroll you're looking at an RoR of about 36%, and we're 68% confident here with $11k. Dropping the bankroll to $10k would slightly lessen your confidence (from 68% to 64%, I can't tell exactly but this is interesting and appears correlated).


In Crystal Math's spreadsheet, $10k bankroll = ~3.6% RoR, not 36%?
so 96.4% confident of making DiaD and not 64% like in your calc???
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CrystalMath
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September 13th, 2016 at 1:46:03 PM permalink
Quote: 100xOdds

Quote: CrystalMath

Here's an updated file. I corrected the standard deviation, added several JOB bet configurations, and added Double Super Times Pay JOB.

DIAD ROR


why is there a difference in SD between:
$1 10play dstp (9/5 JoB) and $2 5play? ($7,434.53 vs $8,355.54)

Both have $70 coin-in, and 714 hands needed for DiaD.


It is because of the covariance between the hands. The Wizard has a page here: Multi Hand Poker Variance
I didn't use theoretical calculations for this, though. I calculated the standard deviation of the sample ending balance.

Quote:


and it's 7Stars, not Platinum like you titled that column.
(For Caesars, platinum is BELOW Diamond)


Fixed, thanks.
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100xOdds
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September 14th, 2016 at 10:47:31 AM permalink
CrystalMath,

can you add $2 single line 9/6 JoB?

I want to compare what you have with my calc of my DiaD a few posts above using Rome's method.

thx
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CrystalMath
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September 14th, 2016 at 11:40:05 AM permalink
Quote: 100xOdds


can you add $2 single line 9/6 JoB?


It's there now.
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100xOdds
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September 14th, 2016 at 2:38:58 PM permalink
Quote: CrystalMath

It's there now.


thx.

just noticed this discrepancy between your 1sigma standard deviation of dstp (9/5 JoB) and mine for $1 10play.
your spreadsheet says ~$7500.
my math says $13.1k. (https://wizardofvegas.com/forum/gambling/video-poker/26887-diad-risk-of-ruin/4/#post553007)

where did I go wrong?
did I use the incorrect value for variance?
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CrystalMath
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September 14th, 2016 at 5:03:31 PM permalink
Quote: 100xOdds

thx.

just noticed this discrepancy between your 1sigma standard deviation of dstp (9/5 JoB) and mine for $1 10play.
your spreadsheet says ~$7500.
my math says $13.1k. (https://wizardofvegas.com/forum/gambling/video-poker/26887-diad-risk-of-ruin/4/#post553007)

where did I go wrong?
did I use the incorrect value for variance?



standard deviation = sd(single game)*sqrt(total hands)*bet per hand
In this case, total hands = 7140, bet per hand = 7.
I see that you estimated the variance to be about 2.5 times jacks or better. I calculate it to be about 4 times.

So, standard deviation = sqrt(36*4)*sqrt(7140)*7 = 7098. The 36 is from the variance of 10 play 9/6 jacks. Also, the standard deviation is even higher due to the dealt royal with a multiplier, which I didn't take into account.
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100xOdds
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September 14th, 2016 at 5:34:38 PM permalink
Quote: CrystalMath

standard deviation = sd(single game)*sqrt(total hands)*bet per hand
In this case, total hands = 7140, bet per hand = 7.
I see that you estimated the variance to be about 2.5 times jacks or better. I calculate it to be about 4 times.

So, standard deviation = sqrt(36*4)*sqrt(7140)*7 = 7098. The 36 is from the variance of 10 play 9/6 jacks. Also, the standard deviation is even higher due to the dealt royal with a multiplier, which I didn't take into account.


ahh.. you used total hands = 7140 and bet = $7.
I used total hands = 714 and bet = $70.
both equates to coin-in = $50k for DiaD.

but there's HUGE difference between 'sqrt (7140) x $7' and 'sqrt (714) x $70.'
591 vs 1870

so basically my calculations in my post is completely wrong. :(

Why did you use 7140 hands and $7 instead of 714 hands and $70?
for 10play, each spin is $70 and there's 714 spins to make DiaD.
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100xOdds
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September 16th, 2016 at 11:32:08 AM permalink
Request:
Can you do one for $1 single line multi-strike (9/6 JoB) for 5,10, and 20 coin-in?
99.8%

https://wizardofodds.com/games/video-poker/tables/multi-strike/
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Romes
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September 16th, 2016 at 12:47:45 PM permalink
The thread is quite demanding of you CrystalMath... I just want to thank you again for putting all of this together. It's a fun math exercise looking at your simulation results and finding a correlating link to RoR in my opinion. I guarantee a formula exists, but I feel I can give a pretty accurate educated guess (plus the bankroll requirement from 3SD's is always >= the requirements from the SIM, so I know I'm covered =p.
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