Probability of Winning 1st Turn

[Diagramdude]

So far in my 8th edition games the player who wins first turn has most often won the game. I wanted to figure out how important the +1 to go first is, because if it is massively significant then it will impact list building (minimizing drops)

 

I'm a bit stuck though because of the rerolling of ties, although I can tell the +1 in a D6 vs D6 comparison is huge.

 

  1 2 3 4 5 6

1 L T W W W W 

2 L L T W W W

3 L L L T W W

4 L L L L T W

5 L L L L L T

6 L L L L L L

 

I wrote out all the outcomes. If your opponent has +1, you will win 10/36 outcomes, tie 5/36, and lose 21/36. In other words, you have a 27.8% chance to win, a 58.33% chance to lose, and 13.9% you will tie and reroll.

 

And then the loser has a flat 1/6 chance or 16.7% chance to seize and win outright.

 

Anyone know how to figure an final probability of winning first turn with +1?

Edited February 13, 2018 by Diagramdude

[Kallas]

Each individual result has a 2.77* chance of occuring.

 

So base you're looking at a 27.7*% chance of winning the roll; 13.8*% chance of a tie; and a 58.3*% chance of losing.

A tie gives you a 27.7* chance of winning the reroll, so 27.7*% of 13.8*% = 3.8579*% chance of a tie then win, for a 31.6357*% chance of success.

 

It can go a lot deeper, with further rolls resulting in ties, and I'm sure my math is pretty rough here, but it looks like finishing deploying second gives you a roughly 31.6% chance of grabbing first turn. If you add on Seizing the Initiative (16.6*% of 68.3642*% = 11.394%) you have an approximately 43% chance of getting first turn, if you lost the initial (re)roll.

 

If someone has better math than I do, please correct me (and please help me understand how to do bellcurve percentages better! :D )

[Halandaar]

Working on the basis that you'd only need to re-roll once due to a tie, I reckon the probability of getting the first turn if you have the +1 to your rolls is somewhere around 60%, which seems to tally reasonably well with what Kallas has said.

 

That includes the odds of you winning outright, the odds of you winning a re-roll where the first roll was a tie, the odds of you seizing if you lost either of the previous rolls, and the chance that even if you won, your opponent seizes back from you.

[Bonzi]

You're never going to put a solid number to the value of the +1. Too many intangibles and variables between armies a builds. +1 is valuable because it's increases your odds of being in the driver's seat, but it's not foregone that you want to go first.

 

I've had opponents who I wanted to go before me because their long range was negligible and their first turn would put me in rapid fire. In my Astra Militarum lists I build with the assumption that I'm not going to get to choose. My win loss ratio there doesn't mimic your observations. My win loss over all my armies doesn't mimic your assumptions.

Edited February 13, 2018 by Bonzi

[Diagramdude]

Right, the value of +1 is situational and subject to opinion, but the actual probability of winning first turn based on a D6 to D6+1 comparison should be able to be calculated.

 

My thought process is if it was well known that getting the +1 to go first gives you a 65% chance to go first, that may influence list building priorities. If it only gives you a 55% chance to go first, it may influence list building priorities. For all the math-hammering we do on this forum, is there any roll more important than the one that determines first turn?

Edited February 13, 2018 by Diagramdude

[Bonzi]

Right, the value of +1 is situational and subject to opinion, but the actual probability of winning first turn based on a D6 to D6+1 comparison should be able to be calculated.

 

My thought process is if it was well known that getting the +1 to go first gives you a 65% chance to go first, that may influence list building priorities. If it only gives you a 55% chance to go first, it may influence list building priorities. For all the math-hammering we do on this forum, is there any roll more important than the one that determines first turn?

Ah, I get it. I thought you wanted to link the odds of getting the +1 to the odds of winning.

 

I'm bad at this type of statistics. My gut says in any given roll it gives you a 16% better chance but that might not be right. Any tie goes to the +1, and any loss by -1 results in a tie and another roll off. A roll of 6 by the +1 is unbeatable, so there a three outcomes in the D6 roll that the +1 comes to your aid. Thus, in any given roll off, a +1 will help or trump in 50% of the possible roll values.

 

Gut check says +1 is quite valuable.

[The Unseen]

Kallas math checks out to me, and also fits with how it feels.

Just under 60% to go first, after factoring in seizing, if you have the +1 on the roll.

So it's a pretty significant increase in your odds, but not worth crippling your list for.

 

I would argue, a 7% increase in going first isn't in general worth running larger squads to reduce drops, MSU as marines is too valuable with raw math, with morale and the extra specials/attacks more sergeants give you.

Especially since marines are usually running min sized squads to try and get some extra CP as well.

[Diagramdude]

It's also worth mentioning that if you have many drops and your opponent has few, then you know his entire deployment before you deploy your key units, and you still have a reasonable chance to go first.

[Pendent]

It's also worth mentioning that if you have many drops and your opponent has few, then you know his entire deployment before you deploy your key units, and you still have a reasonable chance to go first.

A very valid point. I generally deploy all my deepstriking stuff first for this very reason

[Kallas]

It's also worth mentioning that if you have many drops and your opponent has few, then you know his entire deployment before you deploy your key units, and you still have a reasonable chance to go first.

For the tournament I am attending I'm taking a Brigade with 20 drops, including 7 Deep Strike units (Captain, Librarian, Lieutenant, Vanguard, Company Vets, 2x Inceptors) - one of the reasons I'm not too worried about the first turn roll is exactly what you're saying.

 

Against low drop lists, I'll get to see a lot of their deployment (even assuming they have Deep Strikers themselves) and get to drop my more disposable units (ie, Tarantulas) if I need to drag it out further; and against lists with more drops than me (looking at you Guard!) then I'll likely get the +1 (and my Deep Strike will help to at least get them to deploy some stuff).

[Ceril]

ITC is rules the second player is favoured more at tournament skill level.

First player gets the alpha, but many lists can take it and deal a good beta. The second player gets a big tactical edge with the way scoring works.

Are you screening properly? Do you have enough terrain? Is your list well made? What scenarios are you playing?

A lot factors in on first vs second.

[Are Verlo]

I can’t quite remember the source or the details behind the numbers (sample size and so on). But in the ITC, the player who goes second won the most often.

 

But since I don’t have the details I have no idea how this breaks down in each mission and how this differs from fraction to fraction.

[Panzer]

Yeah around 54% of the player who went second won with the ITC rules iirc

[Dont-Be-Haten]

Going second allows you the final turn, so the final push to claim/contest objectives.

 

Geoff O'Neal always preached that in previous editions. Tournament type settings going 2nd is more advantageous where as BRB missions, going first is usually better.