So I suck at determining whether I should "take the shot" in the active turn. To combat that, awhile ago I put together a bunch of charts that show your % chance of winning a face to face shootout as the active player. It was helpful but I've wanted to distill the information down to one easy to use formula instead of a bunch of charts. Unfortunately, it's a little more cumbersome than I would like, but I wanted to share what I came up with in case people can use or even improve it. Using Excel's Linear Regression capabilities, here is the formula: Target BS = 1.5x-2.0y+0.75z+8.5, where Target BS = The total BS value (after all mods) needed for a 66% chance to win the face to face roll. X = Reactive Unit's Burst Y = Active Unit's Burst Z = Reactive Unit's total BS value On average, this is off by about 0.8 and gets wonky around lower burst values. However, I've found that it's an effective way to ballpark the BS value you should be looking for. It could get more accurate if the formula wasn't linear, but I'm not good enough to do exponentials or the like in my head.
You're such a nerd, Tom. This is pretty cool though. Edit: So what this is saying is that if I want to have a good matchup on a FtF roll against a BS 11 Burst 1 Combi in good range I need to attack with Burst 3 with a modified BS of about 14-15. Does that track though? I guess it does, but it means that if I'm shooting a modified BS 14 dude with B1 in ARO, I need to have B3 and the same or better modified BS to get over a 66% chance of winning the FtF roll. Infinity probability are a little... difficult. I guess the formula is useful if you can do the math in your head. I certainly can't. LOL
I think your math's off. Target BS = (Burst 1 Reactive)(1.5)-(Burst 3 Active)(2.0)+(Reactive BS11)(0.75)+8.5 Target BS = 1.5-6+8.25+8.5 = 12.25 This is roughly in line with the infinity dice calc which gives a ~50-51% chance of a fusilier (BS12 B3 Combi) wounding an Alguaciles (BS11 B1 Combi) with the difference in probability coming from the dice calc factoring in the chance of WOUNDING ON TOP OF the chance to win the F2F roll. It's a really cool and nerdy way to quickly calculate a rough idea of what you need to have an arbitrarily favorable gunfight (66% chance to succeed is pretty good, but not amazing). I feel like I would rely more on my intuition as a player, but as Tom said he's not great at judging these things so this helps :D EDIT: A bit of analysis also gives players a bit of insight regarding the nature of the game's probability. The reactive unit's BS is given roughly half the weight (its coefficient value) as its burst (0.75 for BS and 1.5 for burst). Active burst is also weighted at 2.0, MUCH higher than the reactive unit's BS. Supports the idea that usually, burst is king in this game. EDIT 2 electric boogaloo: It's also *slightly* in line this old rule of thumb I heard of people saying that +1 burst was roughly equal to +3 BS (no, I do not agree with this and realize it requires more context in gameplay) because when I lower the target BS from 12.25 to 9.25 and solve for the burst needed to get the same 66% chance of winning the F2F roll, I get 4.5. Yes it's larger than a +1 burst bonus, but for a back-of-the-envelope formula and calculation, it's close enough.
From looking at Marksmanship LX, +1 Active Burst is roughly equal to +6 Active BS for B1 weapons (there are situations where it's worth slightly more and other where it's worth slightly less). The value of 1 extra burst depends on how much burst you already had. It seems the +3 estimate is for when the base burst is 3 (though it seems in many situations going from 3 to 4 burst is worth slightly less than if you could get +3 BS instead). For a HMG, getting Marksmanship L2 is a significantly higher boost than being a part of a Haris.
Yea, the point of this is to really be back of the envelope. Realistically trying to compress about 1280 individual data points into one linear formula is never going to give the entirety of the picture. 66% is just chosen since it's when you are twice as likely to succeed as your opponent.
I think that makes sense, assuming you can do the math without any hassle. 66% of winning a FtF is definitely an 'I'll take that matchup' situation. And my math isn't off, I don't think. The Reactive BS is 14, not 11. I had a reactive BS 11 Combi in good range. So a total modified BS of 14. A lot of combi engagements are going to happen within 16 inches. So you have: (1.5)(1) = 1.5 (2.0)(3) = 6 1.5 - 6 = -4.5 (0.75)(14) = 10.5 -4.5 + 10.5 + 8.5 = 14.5 I think that's how the formula is supposed to work, yea? (((1.5)(Reactive Burst)) - ((2.0)(Active Burst))) + ((0.75)(RBS)) + 8.5 The Infinity Dice Calculator (and god bless ghostlords) is a snake pit of conditional probabilities. Tom is only looking at winning a FtF roll. The dice calculator is great for assessing outcome, which is very good from a risk management and efficiency perspective. But in Infinity you really want to be winning FtF rolls. If you can wrap your head around the probabilities of winning a FtF roll you should be in pretty good shape, assuming you can play in a way that keeps your units in that 66%+ 'sweet spot'. The nice thing about having a good feel for the probabilities is that you can avoid 'overstacking'. That is, if I've got Cammo and good range I can afford to break cover because all I need is a 6 point swing in order to have a 66%+ chance of winning the FtF roll. Tom, do you find that negative opponent mods, e.g. cammo, cover, ODD, Surprise, are mathematically similar to positive mods, e.g. range? I imagine that it should be, excepting situations in which you neg an opponent down to an auto fail. If we take our example with the reactive BS 11 vs BS 14, your formula gives a 14.5 desired Active BS if the Reactive BS is 14, and 12.25 is the reactive BS is 11. That's only a difference of 2.25, but this also puts a 3.0 difference within your 0.8 margin of error.
Just throwing some numbers into the formula, it seems that it is boiling down to some pretty easy rules of thumb: If your target has B1: B1 - Just don't B2 - I need 1 Step better mods B3 - I need equal mods and an equal BS attribute B4 - My BS attribute can be 1-2 points lower with equal mods B5 - I can take 1 Step worse mods If your target has B2: B1 - Really don't B2 - I need 1 Step better mods and a higher BS attribute, or 2 Steps better mods B3 - I need 1 Step better mods B4 - I need equal mods and an equal BS attribute B5 - My BS attribute can be 1-2 points lower with equal mods If your target has B3: B1 - What, are you stupid? B2 - I need 2 Steps better mods B3 - I need 1 Step better mods and a higher BS attribute, or 2 Steps better mods B4 - I need 1 Step better mods B5 - I need equal mods and an equal BS attribute So it seems to work out to a little sliding scale.
I think the BS you plug in is supposed to be AFTER all modifiers including cover, so the reactive BS should be 11. That's, at least, what I did.
This kind of reasoning is fine but breaks as values get more extreme. If I'm a TO unit shooting from cover at a TR bot, I won't care if my burst is lower because my B3 at 11+ is always better than it's B4 at 2. The same goes for MA -- once your value is high enough above 20, it doesn't really matter if you have B1 -- statistically speaking MA3 is usually favored over MA4. The general rule is that B1 is equal to 3.6 BS or so, but only around really average BS values. Once you get to the 1s and 20s, stuff gets weird.
If you're B1 to my B4, and you don't null my attack with modifiers, you are still not doing very well in that matchup. I'm going to have about an 18% chance to crit thanks to volume of dice, compared to your 5% chance to crit. And if you have negative mods, say from Cover, your straight BS isn't going to be good for more than a 50-60% chance or so to beat my successes. If you want to comfortably win that matchup, you've got to do more than throw a B1 shot my way.
B1 at 20 is better than B4 at 10. There's a 50% chance I roll higher than 10 and outright beat you unless your crit, and on average I think I win even if I roll below 10 about 1/3 of the time. I'd eyeball this at maybe a 60% chance I win the f2f? This is the thing people don't get about MMLX that they also don't seem to get about why smoke dodging can be really broken.
That's not what I was talking about, was it? Where are you getting a modified BS of 20? How common is that? More often in BS attacks you're trading negative MODs. CC, sure. But the math gets even weirder when you take auto successes into account. And CC is very often a B1-2 situation. You CC me with three dudes with CC 19+ and MA, yea, I'm gonna die. We don't need to discuss whether that is a good matchup or not. But when you talk about your sniper or your ML putting B1 into a TR bot... Even at good range, that's not a great idea unless you want to shove orders at it with high ARM and hope you don't eat a crit. And again, 4 dice, 5 dice... You've got a good chance of rolling a crit. Edit: I think Tom's formula is a handy way of seeing how Burst is a really big deal. If you can get Burst 2 in ARO, you are in phenomenally better shape. This is one reason the Feuerbach Tsyklon is such a good ARO piece. With Enhanced Reaction or Overclock you'v got B2 in ARO with +0 to +3 on most of the table and the EXP trait. If you put B4 into that with good mods, yea, you can get a pretty good chance of winning the FtF roll. But you've also got a healthy chance to roll bad dice and lose, and then you're dealing with a lot of high damage ARM rolls. So you can risk it, but the downside is pretty damn crappy.
I dislike relying on this argument because yes, everyone always has a chance to crit in pretty much any roll. Where did I ever talk about this? That said, look at a BS12 sniper against a TR bot from outside of 32 inches, the odds are still pretty okay. Sniper B2 at 12 is probably going to beat a TR bot at 5s
Yes, that is how you are supposed to do it. That's fair but you also have an 18% chance to crit once you roll 4 dice and 22% at 5. It's a pretty substantial difference, although I think where it starts swinging results way harder is once you start adding ARM saves into the equation. For the record, this formula is based off a bunch of brute force rolls that obviously had crits so that aspect of it is also accounted for here.
Sounds like a Pheasant Sniper using Marksmanship LX when they are not in cover against a TR HMG that is in cover. B1 BS20 (and ARM 2) vs B4 BS8 (and ARM 3) Active Player 48.58% Imperial Agent, Pheasant Rank (MSV 1) inflicts 1 or more wounds on Hùsòng Yáokòng (Unconscious) 21.52% Imperial Agent, Pheasant Rank (MSV 1) inflicts 2 or more wounds on Hùsòng Yáokòng (Unconscious 2) Failures 19.00% Neither player succeeds Reactive Player 32.42% Hùsòng Yáokòng inflicts 1 or more wounds on Imperial Agent, Pheasant Rank (MSV 1) (Unconscious) 7.93% Hùsòng Yáokòng inflicts 2 or more wounds on Imperial Agent, Pheasant Rank (MSV 1) (Dead)
