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Simple question for those of us not mathematically inclined:
How much more likely is the +1 to first turn (post-Chapter approved). Is it simply 1/6 more likely? As some numbers can no longer tie (double 6's) and others are now rerolled where previously would have lost (1 + 1 vs 2)

And so if it is 1/6 then assuming each player has a 50% chance of going first -
50 * 1/6 + 50 = 58ish%
vs
42ish for opponent?

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.

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?

 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).

 mrhappyface wrote:

 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).

I mean there are other things than aura, powers, abilities like No Escape etc... its not like i want arguing or anything, i thought about it and GW has been very consistent in this part of the rules at least.

Tho since it isnt YMDC i wont discuss it farther here.

noooooooooooooooo......

I want another 9 page diatribe festival that DakkaDakka practices!!!!!!!

How dare you shut down this possible enterprise of joy!!!

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

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

 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.

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

 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.

Honestly I really only care about how this will be standardized at ITC - such as LVO

Re-roll of ties must come after modifiers as any other approach allows ties to happen as the final result.

Breng77 wrote:
Re-roll of ties must come after modifiers as any other approach allows ties to happen as the final result.

You keep your dirty logic out of this. Nothing but unvarnished opinion and shady rhetoric will carry the day here.

That said, I agree, and I don;t need YMDC to tell me what's what.

 mrhappyface wrote:
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.

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%

That's before seizing

21/31 * 1/6 is the chance of your opponent seizing.
21/31-21/186 is your chance of winning. 56.5%. I think. Which means it's pretty close to even.

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.

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.

 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)]

 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.

I think the probability of wining (with +1) it should be {lim n→∞ [Σ(5/36^n*21/36)]} + 21/36 ,

But logically it should tend towards 21/31, as any reroll will produce an identical chance of winning, losing and rerolling as the original roll. (assuming rerolls after modifiers and that the modifier is kept for all rerolls).

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.

So ~12%? I'm happy someone is doing this, it's actually a pretty important decision for some players when it comes to list-building and deployment.

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

It looks to me like having a small-ish number of units is still very helpfil in the CA scenarios. Good to know.

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

What makes you think that?

 mrhappyface wrote:
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.

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

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.

 mrhappyface wrote:

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.

This is what I get for lazily skimming the post, thanks!

For anyone interested in the comparison with the old method. The chance of going first when the opponent could reroll seize, but the first to finish deploying went first was 69.4%, so a little better, but not as much as you may have thought.

 mrhappyface wrote:

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

What makes you think that?

If you've got +1 there are 21 results out of 36 where you go first. The other guy has 10 results where he goes first. The person with +1 is therefore going to go first more than two times out of three.

Once you add in the chance of the loser or the first roll seizing the initiative, the chances converge slightly. It ends up with the person who finished deploying first getting first turn 62% of the time, vs 38% for the other guy. So more like 3/5 than 2/3.

anyway the point is that you're a lot more likely to go first if you finish deploying first. The +1 bonus might not feel all that huge but it actually is a big deal.

Opponent can still reroll seize right?

No. That was changed in CA

You can entirely ignore re-rolls from drawn results. They have no impact on the final result. Nothing about what might have happened previous has any impact on rolling now, nor does anything in the future. Everything resets to a base state.

There aren't 36 possible results when two people each roll a d6 if they have to re-roll ties. Without a +1, there are 30 results. With it, there are 31.

It's like predicting a coin flip based on previous coin flips.

21/31 chance to win the initial roll. 5/6 chance of surviving a seize.

So the real answer is 56.45% chance to go first if you have the +1.