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There are 36 total outcomes.

For the person with the +1 there are 21 outcomes that mean they win, 5 where they draw and 10 where they lose.

It would be 58.3% of winning if not for draws causing re-rolls, with re-rolls it comes closer to 66.5% for the player with the +1 and 33.5% for the opponant.

 Amishprn86 wrote:
Wait.. this just made me think of something.

All re-rolls happens before modifiers, does that means ties are always re-rolled because the +1 is a modifier?

No, the re-roll for tied rolls for deployment isn't the same as re-roll auras in game. Please don't give people on this website another thing to argue about (good job this isn't in YMDC).

 Amishprn86 wrote:

orkswubwub wrote:
Well we always have our mods to rely on to move this to YMDC :-)

Just made one, he was asking about math so lets leave it about math.
https://www.dakkadakka.com/dakkaforum/posts/list/747640.page

God dammit.

 Amishprn86 wrote:
Dont join in then lol, i mean IDK why it bothers you if your not there

It's cause YMDC always leaks into other boards, and it's especially bad when someone stubborn takes a side in something as ambiguous as this and starts throwing around their opinion like it's fact, derailing threads. But that's dakka for you.

Zustiur wrote:

Then seize comes into it.
Also I got different numbers somehow.

I generally work with fractions so...
36 combinations. 5 we can rule out due to rerolls.
21/31 win. 67.8%
10/31 lose. 32.2%

Unfortunately, that's not how fractional chance works, you can't disregard the 5.

The calculation is:
21/36 + (5/36 * 21/36) + (5/36 * 5/36 * 21/36)... To win - the calculation is infinite in this case due to the chance of infinitely rolling a draw.

Then you do the same thing for lose but replace 21 with 10.

 Cybtroll wrote:
The appropriate math (correct me if I'm wrong, symbols are nasty with a single line of text) should be:

lim n→∞ [Σ(5/6^n*21/36)

TBH right now I don't know (if) how this limit can be solved, but there are tool online to crunch it if you want to have the real value.

lim n→∞ [Σ(5/36^(n-1)*21/36)]

Mandragola wrote:
So having +1 on the roll makes you about twice as likely to go first.

What makes you think that?

TwinPoleTheory wrote:Since you're already on top of the math, how does rolling to seize for the loser affect the percentages?

Kaptin Blacksquigg already pumped out the math for that:

kaptin_Blacksquigg wrote:Which gives us ((5/6)*(21/31)) + ((1/6)*(10/31)) after seize the initiative: 0.5645 + 0.0538 = 0.61827, or about 62% chance of going first.