# maths/variance question

• Bronze
Joined: 13.02.2011
Hello everyone

I'm trying to sort one of my mindset problems out by running a variance simulation.
I know there are some kind of variance simulators but i decided that the best proof would be actually physically running it myself step by step.

In order to do it i created an empty EV graph which i will be filling with results of throwing dice.

I decided to start with using three dice. Each containing the digits from 1 to 6
That means the results can vary from minimum #3 to maximum #15 = 13 combinations.

I decided that 7 chosen numbers will give me a +EV result, while the other 6 chosen numbers will give me a -EV result

I would like to know if my assumptions below are correct:

if 13 numbers = 100%
is 7 numbers = 65% ?
and is 6 numbers = 35% ?

is EV EDGE = +15% ?
• 9 replies
• Super Moderator
Super Moderator
Joined: 02.09.2010
First off, I think that the maximum would be 18.

Then only looking at the totals, there would be 16 combinations 3 to 18.
Some totals can be made far more ways than others.

3 for example has only 1 combination, as does 18

For each combination where the numbers on the 3 dice are all different there are 6 different ways to roll that combo.

For each combination where two dice are the same, there are 3 ways to roll that combination

12 for example could be:
6,5,1 - 6 combinations
6,4,2 - 6 combinations
6,3,3 - 3 combinations
5,5,2 - 3 combinations
5,4,3 - 6 combinations
So 12 has 24 combinations

So just picking 7 numbers "at random" to be your +EV totals isn't the whole story.

There are 6^3 or 216 ways to roll 3 dice.
Make a table for each of the numbers and their combinations like so:
3: 1 combo
4: 3 combos
5: 3 Combos
6: 9 combos
etc

When you have your table built, you will be able to select sets of numbers that give you different percentages. I'm guessing that 12 will have the most combos.

Interesting exercise. I'd be interested in seeing the table.

I think perhaps writing a simple script -- perhaps in Excel or similar -- would give a faster result.

All the best,
--VS
• Bronze
Joined: 13.02.2011
that's right it's 18 so 16 combos thanks

i see yes, good point, hm i will try to work it out somehow, thanks

ps. script would probably be good, but i really really want to do it manually to see with my own eyes the process of lets say a downswing of 20 rolls when the chances were like 65% vs 35%
• Bronze
Joined: 13.02.2011
i found some help but it's hard for me to wrap my head around it

• Bronze
Joined: 27.07.2011
Hey,

from your diagram of dice combos and odds.... you can take a score of 5-9 inclusive to be your ~65% edge. (this is actually 66.67% but close enough).

Then you could say hitting between 5-9 would give you +1 and anything else would be -1.

I've drafted up an simple excel sheet that can run these simulations + graph + max drawdown etc. However this doesn't need to be done with the dice.... simple numbers would work just as well.

PM your Skype and i can send it over .
• Bronze
Joined: 13.02.2011
So i managed to come up with a way to run an EV simulation on paper to witness the variance with my own eyes
I was using Backgammon percentages to either hit a certain number or avoid getting hit by a certain number - using two dice and Backgammon rules (doubles)

* 6 different rolls with different chances (positive and negative but +EV altogether) - randomized every time

* for 6 different "big blinds" amounts - also randomized every time as well

the general EV of my chances was +EV 54.63% if not I'm not mistaken

depending on the outcome of the randomness, I was playing for either:
50bbs, 100bbs, 150bbs or 200bbs

So after exactly 74 rolls i hit a -1700 (900bbs below EV) downswing and ran out of space on my chart that is almost A2 size lol

Will have to expand the chart and will carryon to see when i will finally be above my 0EV line lol

Or maybe i should increase my edge a bit ehehe.

It's a pretty cool exercise i must admit It makes it a lot easier to realise that the soft is not rigged and that is actually quite possible to get your AAxx fucked in 400bbs pots in PLO like 5 times in a row

It's also eazier to believe it's possible and accept it, when you actually physically do it yourself instead of having to believe that EV simulations software is right

• Bronze
Joined: 14.08.2010
AAxx is a strong hand preflop but will get you in trouble in big pots
• Bronze
Joined: 13.02.2011
erm, that is correct yes
• Bronze
Joined: 05.07.2011
No offense, but it almost makes me laugh you use omaha as a comparison to 3 1-6 dices.

I know you wanna do something that seems possible to wrap the head around.
I know nothing about PLO though, i do know that "naked aces" is useless in multiway pots. Even if you are more than 200bb deep they start to become very useless, unless you play hu. Even in hu they actually also lose value if they are naked, and you start to become deep (200bb+).

If you play 6m i would almost go as far as saying you are toying with thin value spots if you open, somone flats, bb pots it. Already here you deffinately either need double suited, or atleast 1 suited with connectors (not connectors like A A 7 8 - but like A A K Q
Unless ofc if you play Hi/lo
Does the lowest low exceed 8 to 9, or it that low too high? Is the lowest low 8?

Just because im curious, and dont understand SHIT about plo, do you openfold UTG 6m A A A K - if not, do you openfold A A A 6

This is what happens when you compare backgammon to PLO/FLO/8-game:
• Bronze
Joined: 13.02.2011
haha yeah, Gus Hansen, what a degen

no offence taken bro

I was not trying to compare dice rolls to playing PLO, I was just using dice equities to simulate PLO stackoffs in different spots

You sometimes stackoff with ~70%, sometimes with ~60% , sometimes with ~55% sometimes with ~50%, sometimes with ~45% , sometimes with ~40% (i was not taking any pot odds into consideration , just pure equities)
Sometimes for effective ~50bbs , sometimes for ~100bbs , sometimes ~150bbs, sometimes ~200bbs.

So dice rolls just helped randomise those and simulate different spots

Obviously there is no way to simulate the whole actual game of PLO when there are thousands of other things involved