stabworld
Joined: Mar 10, 2014
• Posts: 297
March 31st, 2016 at 5:12:38 AM permalink
Ok, I did post this question in my other thread - but figured it might deserve its own thread.

Here's my question:

Does playing multi-lines on a \$1 JOB 9/6 - increase the amount I would need in my bankroll to have the same risk of ruin when compared to a single line at the same denomination?

Example: according to the wizard on wizardofodds.com (http://wizardofodds.com/games/video-poker/appendix/1/):
the bankroll needed for a 2.5% risk of ruin on a \$1 JOB 9/6 full pay (\$5 per hand)
with 1% in cashback:
is 7256 units or \$36,280

So if I was playing \$1 JOB 9/6 triple play (\$15 per hand) (1% cashback)- what is the bankroll required here to have the same 2.5% risk of ruin?

1. \$36,280?
2. (\$36,280 X 3) = \$108,840?
3. Or somewhere in between (\$36,280 - \$108,840)?

2 major points here:

1. The \$15 cost to the get dealt the starting hand
2. but, you are "running it" 3 times, to get 3 different results from your starting hand - (thereby decreasing variance).

Any help on this is appreciated.
Romes
Joined: Jul 22, 2014
• Posts: 5459
March 31st, 2016 at 8:25:32 AM permalink

My thoughts are that each has their own RNG and thus you're simply playing 3 separate games at a time, which means you'd get to the long run 3x as fast and thus experience LESS variance.

It was shown though that the hands are slightly correlated because of the starting hand being the starting cards for all 3, so while this does indeed get you to the long run faster, it could make for a slightly bumpier ride (i.e. more variance). There was shown (in that thread) to be slightly more variance when playing multi-line... Though if you have a "proper" bankroll for single line, I would think you're about on track and should be "okay" to play multi-line. Don't take that wrong and think you should go play 100 play all day, but understand that there is slightly more variance due to co-variance with multi-line.
Playing it correctly means you've already won.
stabworld
Joined: Mar 10, 2014
• Posts: 297
March 31st, 2016 at 10:08:19 AM permalink
Quote: Romes

My thoughts are that each has their own RNG and thus you're simply playing 3 separate games at a time, which means you'd get to the long run 3x as fast and thus experience LESS variance.

It was shown though that the hands are slightly correlated because of the starting hand being the starting cards for all 3, so while this does indeed get you to the long run faster, it could make for a slightly bumpier ride (i.e. more variance). There was shown (in that thread) to be slightly more variance when playing multi-line... Though if you have a "proper" bankroll for single line, I would think you're about on track and should be "okay" to play multi-line. Don't take that wrong and think you should go play 100 play all day, but understand that there is slightly more variance due to co-variance with multi-line.

Ah, ok, thanks for the feedback.

Do you happen to know the name of the other thread this topic was discussed?

Thanks.
Romes
Joined: Jul 22, 2014
• Posts: 5459
March 31st, 2016 at 10:54:16 AM permalink
I clicked Gambling. I clicked Video Poker... I saw "How much more variance is triple plan than single line?"

Playing it correctly means you've already won.
stabworld
Joined: Mar 10, 2014
• Posts: 297
March 31st, 2016 at 12:40:21 PM permalink
Quote: Romes

I clicked Gambling. I clicked Video Poker... I saw "How much more variance is triple plan than single line?"

Found it. I read through it. However, although the thread talks about how the triple play and multilines are more variance- it does not talk about bankroll. I understand the higher the variance - the larger your bankroll needs to be - but by how much ? Is what I am trying to figure out.
Romes
Joined: Jul 22, 2014
• Posts: 5459
March 31st, 2016 at 12:49:18 PM permalink
Your variance should go in to your Bankroll calculations. Use the variance you see for the game you want and figure out the long run...

After 1,000,000 hands your EV is X, plus or minus 3SD... EV - 3SD is a good number for bankroll as that should encompass (with 99.9% certainty) every likely outcome. i.e. You know, with 99.9% certainty, the worst you could do is EV - 3SD... So if your bankroll is that amount, you know - with 99.9% certainty - that you won't bust (RoR = 0).

I believe Bob Dancer and others have software that can calculate your bankroll for you given inputs.
Playing it correctly means you've already won.
odiousgambit
Joined: Nov 9, 2009
• Posts: 8218
March 31st, 2016 at 1:07:03 PM permalink
getting to the long run does not reduce variance. I think there is this confusion again about the long run making results closer to expected value ... this happens by viewing it as a percentage, but does not happen in dollars. In fact, as Mathextremist recently pointed out, in dollars it gets less and less likely to be exactly the same as the EV [while closer as a percentage]

common sense would also seem to say you need a bigger bankroll
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
Romes
Joined: Jul 22, 2014
• Posts: 5459
March 31st, 2016 at 1:44:30 PM permalink
Getting to the long run reduces your standard deviations within respect of your EV. It's quite possible for many hours/hands or trials of any game to have your SD be greater than your EV for some time. The point is when you hit "the long run" of the game you're playing it is mathematically impossible for your SD to be greater than your EV at that point... (at least in the games we're discussing, such as VP). Thus, if you're playing with an advantage your advantage is realized because you're guaranteed to be positive.

I disagree with the last part though... If you want to play 1,000,000 hands of VP. You can calculate your 3SD for 1 hand, 100 hands, 10,000 hands, 100,000 hands and 1,000,000 hands. Your 3SD will be the largest at the largest number of trials. Largest as in physically the largest amount. Thus, what you're saying at 1,000,000 hands is I expect EV, plus or minus 3SD, where 3SD is (with 99.9% certainty) the mathematically WORST you can do.

If you encompass the worst case scenario in your bankroll, where all other points in the timeline must be smaller 3SD's, then you should reduce your RoR to zero.

Let's assume you found a pay table in JoB which gave you a 1% advantage, thus the payback was 101%.

Variance = 19.514676, SD = 4.417542 (from the wiz)

AvgBet = \$5 (\$1 single line, 5 coins)
OriginalSD = SD * AvgBet = 4.4 * 5 = 22

SD(x hands) = SQRT(x) * OriginalSD... Thus:

Num Hands Expected Value 3 SD
1
\$0.05
+-\$66.00
1,000
\$50.00
+-\$2,087.10
10,000
\$500.00
+-\$6,600
100,000
\$5,000
+-\$20,871.03
1,000,000
\$50,000
+-\$66,000
5,00,000
\$250,000
+-\$147,580.49

Thus, we can see that "the long run", or N0, or "break even"... whatever you want to call it... is between 1,000,000 and 5,000,000 hands as with 3SD of confidence at 5,000,000 hands we will GUARANTEED mathematically have profits.

This tells us that if you have a bankroll of ~\$150,000... your RoR (with 99% confidence) is 0. Actually, it'll be less than that. You need to find the exact break even point and take 3SD at that number of trials. I'll leave that as an exercise for the OP.
Last edited by: Romes on Mar 31, 2016
Playing it correctly means you've already won.
mustangsally
Joined: Mar 29, 2011
• Posts: 2463
March 31st, 2016 at 2:00:17 PM permalink
Quote: Romes

<snip>where 3SD is (with 99.9% certainty) the mathematically WORST you can do.

100% FALSE.
nice try
Oh,
yuk try, imo

to be outside of 3 sd is easy at a 1 in 371 chance
happens all the time
and more times when one says it can't happen

real money is lost and won gambling
only thing that matters

hajhahahaj
"the mathematically WORST you can do"
take that to the bank!
<<<>>>
for the OP
there are software that calculates bankrolls and risk of ruin for VP game sessions
one still has to understand what 1 in 20 can mean for example

most have no clue or think it means something totally from what it does mean.
have fun and have luck
I Heart Vi Hart
Romes
Joined: Jul 22, 2014
• Posts: 5459
March 31st, 2016 at 2:03:26 PM permalink
Quote: mustangsally

100% FALSE.
nice try
Oh,
yuk try, imo...

Wikipedia disagrees with you.

...3σ = .1, thus comes with 99.9% confidence.
Playing it correctly means you've already won.