"Advanced math question" Topic

Okay I'm trying to figures out some odds here. This is beyond my skill.

Two soldiers – Red and Blue – fight. Each rolls a D6. High die wins. In case of a tie, compare Skill levels. Higher skill level wins. If Skill Levels are also tied, toss up: 50% red wins, 50% blue wins.

If Red has a higher skill level what are his chances of winning one combat?

If both fighters have an equal skill level what is their chance of winning one combat?

Thanks in advance.

41.6% if both sides equal, 16.666 a draw. 58.333 if one side has advantage – not advanced – this is in the dna of tabletop gamers.

2D6 means there are 36 total combos.
1vs1, 1vs2…
There are a total of 6 ties 1vs1, 2vs2, 3vs3…
If one side wins ties then 15+6 wins vs 15 wins
The higher skill win 58.333% of the time (21/36)*100=%
if equal skill either side win 15+3 or 18/36 = 50%

you can draw a grid with 1 to 6 across and 1 to 6 down and figure out each possible result.

They will tie one time in six, so of 36 possible outcomes, blue wins 15 and higher-skilled red wins 21. If skill levels are equal, it's 50-50: each wins 18 of those 36 outcomes.

Oh. You wanted a percentage? You divide the chance of one outcome by the total number of possible outcomes. 21 divided by 36 is 58% (approx.) Red vs 42% (approx.) blue.

Unless, one side mentions the word "one", while the other side is about to roll, or you take an inordinately long time to roll, or you are rolling and you really need to win this combat….then the result is jinxed…probability and advance math does not come into the equation.

Similarly if Red gets a plus 1 on the roll,
Then Red wins 21 outright, with 5 ties.
If Red has higher skill as well he wins the 5 ties 26/36=72.222% wins. If Red has the plus 1 but lower skill then only 21/36=58.333%, if equal skill, 58.333% + 1/2*(5/36)100=65.3%

Me, playing a 10 year odl: Well sonny, with my bonus you need a 7 on a D6 to beat me. Muahahahaha!!!!

*kid rolls a 7*

Me:

Now if Red gets +2, there are just 4 tie outcomes.
Red wins 15+6+5 outright that is 25/36 combos or 69.44%
If Red is higher skill then 4/36 combos more or 11.11% more so 80.55% are wins for Red.
If equal skill only 1/2 or those extra wins or 5.555% more so then just about 75% Red wins.

Here is an image of how you can work this:
i.stack.imgur.com/WCOYx.png

From this page:
link

I have not read through this page, but I suspect it will help.
If not, just ask more questions.

Dang it didn't show as I had hoped, How about another try:

That looks better, that is from here:
link

Sadistics!!!!!! I hated that class in college.

'Advanced math' is a bit of an overstatement here ;-)

Because this type of questions pops up regularly, I did write a couple of articles about the statistics of popular dice mechanics and submitted them to one of the glossies. They have not been published yet, hopefully in the near future.

'Advanced math' is a bit of an overstatement here ;-)

It's not statistics either. It's really some very basic discrete probability theory. But if you've never taken a course explaining this, it can seem kind of arcane and mysterious ;-)

Because this type of questions pops up regularly, I did write a couple of articles about the statistics of popular dice mechanics and submitted them to one of the glossies. They have not been published yet, hopefully in the near future.

More than + – / * is advanced….

Just create a 6X6 graph and populate it. All will become clear.

We play a lot of Bloody Big Battles which uses 2D6 for most calculations. It becomes second-hand.

And DBA uses opposed die rolls, so that is closer to what you're doing.

Don't tell me the odds.

DyeHard and robert piepenbrink are correct. sillypoint is wrong.

EQUAL SKILL LEVELS: 50%. Red will win half of the unequal rolls, and half of the coin tosses when the dice are equal.

HIGHER SKILL LEVEL: Red wins half of the unequal rolls, or 1/2 * 5/6 = 5/12. Red also wins all of the ties, or 1/6. 5/12 + 1/6 = 5/12 + 2/12 = 7/12 = 58.3% of the time.

No need for tables.