DIAD Risk of Ruin
September 10th, 2016 at 4:17:07 PM
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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.
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.
I heart Crystal Math.
September 10th, 2016 at 4:23:59 PM
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Great post!!!
No longer hiring, don’t ask because I won’t hire you either
September 10th, 2016 at 4:24:35 PM
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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?
I never understand RoR on these type of things. It seems like $1 3 line is the best option. Am I reading that right?
Expect the worst and you will never be disappointed.
I AM NOT PART OF GWAE RADIO SHOW
September 10th, 2016 at 4:36:51 PM
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Quote: GWAEIs 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.
I heart Crystal Math.
September 10th, 2016 at 5:36:07 PM
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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
September 10th, 2016 at 5:44:56 PM
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Quote: MathExtremistAre 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
I heart Crystal Math.
September 10th, 2016 at 7:12:02 PM
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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
September 10th, 2016 at 10:34:26 PM
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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
September 11th, 2016 at 5:29:50 AM
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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)?
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 :)
September 11th, 2016 at 7:41:42 AM
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Quote: 100xOddsthx!
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.
I heart Crystal Math.
September 11th, 2016 at 8:01:50 AM
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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.
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.
September 11th, 2016 at 8:11:07 AM
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Quote: CrystalMathDo 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 :)
September 11th, 2016 at 8:31:16 AM
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Quote: 100xOddseach 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.
I heart Crystal Math.
September 11th, 2016 at 8:32:16 AM
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Quote: DRichThanks 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.
I heart Crystal Math.
September 11th, 2016 at 10:58:06 AM
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Next project...risk of ruin to get to Super Sucker, err I mean Seven Stars.:-)
DUHHIIIIIIIII HEARD THAT!
September 11th, 2016 at 11:05:03 AM
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Wow, CM, that's quite a gift. Thanks!
If the House lost every hand, they wouldn't deal the game.
September 12th, 2016 at 5:26:52 PM
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5-play 9/5 JOB STP:
EDIT: Added spoiler.
0 0.129506318977621
5 0.104201937737873
10 0.156938040442759
15 0.112087856564135
20 0.077580408135006
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95 7.94643256546628E-05
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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
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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.
September 13th, 2016 at 8:49:17 AM
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Quote: CrystalMathI'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.
September 13th, 2016 at 9:14:47 AM
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Quote: CrystalMathHere'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?
Craps is paradise (Pair of dice).
Lets hear it for the SpeedCount Mathletes :)
September 13th, 2016 at 9:38:41 AM
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Quote: 100xOddsQuote: CrystalMathHere'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.
I heart Crystal Math.
September 13th, 2016 at 9:43:29 AM
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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
September 13th, 2016 at 9:48:10 AM
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Quote: CrystalMathQuote: 100xOddsthx!
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?
Craps is paradise (Pair of dice).
Lets hear it for the SpeedCount Mathletes :)
September 13th, 2016 at 9:54:17 AM
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Quote: GWAEOne 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.
Craps is paradise (Pair of dice).
Lets hear it for the SpeedCount Mathletes :)
September 13th, 2016 at 10:37:09 AM
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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 %...
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
Playing it correctly means you've already won.
September 13th, 2016 at 10:50:24 AM
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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 =).
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 =).
Playing it correctly means you've already won.
September 13th, 2016 at 11:14:13 AM
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Quote: 100xOddsim 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.
I heart Crystal Math.
September 13th, 2016 at 11:15:22 AM
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Quote: RomesFantastic 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.
I heart Crystal Math.
September 13th, 2016 at 11:28:23 AM
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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.
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
September 13th, 2016 at 12:16:07 PM
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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 =).Quote: CrystalMathSure...It's in there now.
Playing it correctly means you've already won.
September 13th, 2016 at 12:53:01 PM
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Quote: RomesSay 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
Craps is paradise (Pair of dice).
Lets hear it for the SpeedCount Mathletes :)
September 13th, 2016 at 1:19:59 PM
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Quote: CrystalMathHere'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: CrystalMathI 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)
Craps is paradise (Pair of dice).
Lets hear it for the SpeedCount Mathletes :)
September 13th, 2016 at 1:30:44 PM
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Quote: RomesTo 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???
Craps is paradise (Pair of dice).
Lets hear it for the SpeedCount Mathletes :)
September 13th, 2016 at 1:46:03 PM
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Quote: 100xOddsQuote: CrystalMathHere'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.
I heart Crystal Math.
September 14th, 2016 at 10:47:31 AM
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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
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
Craps is paradise (Pair of dice).
Lets hear it for the SpeedCount Mathletes :)
September 14th, 2016 at 11:40:05 AM
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Quote: 100xOdds
can you add $2 single line 9/6 JoB?
It's there now.
I heart Crystal Math.
September 14th, 2016 at 2:38:58 PM
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Quote: CrystalMathIt'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?
Craps is paradise (Pair of dice).
Lets hear it for the SpeedCount Mathletes :)
September 14th, 2016 at 5:03:31 PM
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Quote: 100xOddsthx.
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.
I heart Crystal Math.
September 14th, 2016 at 5:34:38 PM
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Quote: CrystalMathstandard 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.
Craps is paradise (Pair of dice).
Lets hear it for the SpeedCount Mathletes :)
September 16th, 2016 at 11:32:08 AM
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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/
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/
Craps is paradise (Pair of dice).
Lets hear it for the SpeedCount Mathletes :)
September 16th, 2016 at 12:47:45 PM
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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.
Playing it correctly means you've already won.
