I had a few minutes to kill and I was getting seriously annoyed by all the talks about hot or cold dice, both on forums and video battle reports. Seeing people swapping out "cold" dice is mind-boggling to me, but I was still curious to answer simple questions like "evade or focus?" and "focus or target lock?"

I whipped up a small simulator in Excel to see what one should generally expect. You tell it the number of red and green dice to run, it creates (at this point) 10,000 grouped rolls and you get a table showing you the expected number of hits. On any given roll, you can get some very extreme results, but over a large enough number, you get a better idea of what is generally a better idea.

With 10k rolls, the result distribution generally deviates by less than 1% from the expected results, so it's not a perfect model, but, to me, it's close enough.

I figured others may appreciate the musings this lead to, although I would not suggest taking it as gospel. This is just to feed into other people's thought process, not to replace it.

To explain the format:

Each sub-table has a header telling you how many red and green dice were part of that sample, I stopped at 4 of each, though planned the model to go up to 6 easily, it just doesn't happen that often, at least with the ships I have.

The actual number is the expected number of hits, a negative number means none, but I didn't round up to zero to give an idea as to which defense is more likely to yield an actual "no hits" in play situation. I rounded to one decimal as I'd rather people not take this as gospel and it's easier when the results look similar, but may actually be slightly different.

To save space, I went with short form title, they are:

• D: just the defence dice
• F D: Defense dice, using a focus
• E D: Defense dice, adding an evade
• F-E D: Defence dice, using a focus and adding an evade
• A: just the attack dice
• F A: attack dice, using a focus
• TL A: attack dice, using a target lock
• TLF A: attack dice, using a target lock, but also rerolling the focus
• F-TL A: attack dice, using a focus and then a target lock on remaining blanks (I just wanted to test this)
• TL-F A: attack dice, using a target lock to reroll blanks, then a focus
• TLF-F A: attack dice, using a target lock to reroll blanks and focus, then using the focus.

It mostly confirms very obvious (to me) hypothesis. Like:

• for purely defensive reasons, unless you have a massive amount of green dice, go for the evade, not the focus
• focus only is generally better than target lock only, though marginally so.
• You should not reroll focus dice with target lock, and should keep the focus until after you've rerolled with a target lock.
• And, the very obvious, raw attack dice always have an edge on raw defense dice.

Basically, nothing new is learned, but it supports a lot of the thoughts I had watching countless battle reports and seeing people make strange decisions.

I'd be happy to discuss (or debate). I could also make the file available for people to play with, though I'd have to extract it from my collection manager, no one needs to know how many of each cards and ships I have (though some may like to use such a tracker to plan purchases, I know I am).

One thing I've learnt through this game is, that much like no battle plan surviving contact with the enemy, statistics & probability go out the window when rolling dice. I've rolled 5 evade dice and come up all blank, and last night I rolled a five dice unmodified attack and came up three crits and two hits naturally (goodbye Howlrunner).

Personally, I steer well clear of Mathwing and any related topic. I fly what I like; seek to fly as well as I can, and let the dice fall how they will.

Yeah, as noted above, any single dice roll will not represent the generally expected outcome, variability is a very important thing to consider. It was mostly a thought exercise into, as noted, evade or focus?, target lock or focus?

It gives an idea as to which is likely to yield better results, but there are no guarantees. Except that on a ship with 0 agility, the evade is much, much better for defense than the focus

Probability evaluations like this are good in evaluating an event as a good idea or a bad idea knowing full well that an individual dice roll is a high variance event. You should be trying to make as many favorable choices (from a probability standpoint) as possible while minimizing the unfavorable. In the long run, making more "good" decisions will lead to more success.

Just because you pushed some damage through using a 2 Attack ship with no Actions against a 4 Agility ship at Range 3 and through an obstacle with a Focus token, does not mean that it was a good idea. That being said, if it is the only shot you have, you take it anyway.

One thing I find interesting is that if you have a focus token and a TL, it doesn't hurt your average result very much if you decide to reroll the eyes as well, and then decide to use the focus token. This means that you can make the following decision. Say you have both, and expect an enemy to shoot back at you later in the round. So consequently, you want to save your focus for defense. But there is a possibility that you are going to destroy the opposing ship, in which case he won't fire back at all. Then you can decide to reroll the eyes: if the reroll gives enough eye results to (probably) destroy the other ship, then you spend the focus, otherwise you keep it for defense.

Normally, if I have a focus and a TL, I will only reroll the blanks. This is the most advantageous, but it looks like the difference is quite small.

There are also cases where you want to keep only one eye and reroll the others. Poe Dameron or Ten Numb w. Calculation, for example.

• focus only is generally better than target lock only, though marginally so

This is your margin of error in 10k simulation rolls. Mathematically speaking, focus and TL yield exactly the same result, 75% chance. I've enumerated out the results before and calculated the probabilities.

Rather than see this as average hits minus average evades, I think it makes more sense to look at it as two numbers:

- Percent chance to hit (do at least one damage)

- Average damage of the subset of rolls that are hits

Any attack made actually has a positive expected value of damage applied, since rolling extra evades doesn't heal your ship, and it's always possible that green blanks get rerolled into blanks.

Also, you can replace 10k random rolls with the exactly 4096 unique combinations of 8 faces on 4 dice. That would make the slight difference between focus and TL go away.

Thanks for crunching numbers!

That said , the OP's graphs are useful to give you an idea of the relative strengths of attacks vs defense. For example, an X-Wing shooting a Phantom with no dice modifiers causes on average as much damage as a TIE fighter /w a focus token shooting at a tokenless phantom. Some Phantom players might dismiss the threat of the TIE fighter in that situation, when they really shouldn't.

To me, that was the point of the exercise. Models don't meet reality. As for faking 10k rolls instead of mathematically getting the results, it's just more fun to do it this way, for me. I like that some variance remains, pressing F9 with the same input changes the results, going with a lower number of rolls, even more so, which drives home that the only sure shot is modifying the results (say, with an evade) rather than hoping the roll comes out average or better.

But then again, "switching out cold dice" only makes sense in your head since, given balanced dice, any dice could yield any result at any time.

I'm happy to see many skeptics, it would be disappointing to have people buy into any kind of model as a representation of reality, it's in part why I never actually finished my masters', selling a model as certainty doesn't work for me.

This is ridiculous! everyone knows the Dice are controlled by sentient beings who wish for our destruction!

This is ridiculous! everyone knows the Dice are controlled by sentient beings who wish for our destruction!

Everyone thinks the reds are superior but the greens will themselves to turn up blank.

I always get a kick out of things when people try to tell me "expected" results based on X number of test rolls. While you may get the number down why not just use the ACTUAL probability of results instead of what test rolls will get you.

If you roll 2 dice in X-Wing there are EXACTLY 64 possible combinations where each should have an equal chance of appearing. I'll grant that many of those final results will look alike but you still get get 8x8 ways the dice could land. Rolling 3 dice leads to 512 possible results and 4 dice leads to 4096 possible results. You sure don't need to collect data from 10,000 computer generated "rolls" to learn what the expected results should be. Spending a Focus doesn't change how much data you'd need although it does change the data. Adding rerolls will add another dimension as those are mostly up to chance and depend on what criteria is used to determine a reroll.

Perhaps this is "mathwing" but its results are certain and really just about as easy to get as brute force methods especially once you've completed the analysis.

With expected results. 1.5 = 1 in the first volley and also 1 in the second volley. Just kill off any decimal as there is no such thing as a 0.4 hit or such.

My math suggests TL is slightly better than focus vrs un-shielded foes as the chance of rolling a crit on either the primary or secondary roll has the potential to do double damage or secondary effects. Me I'd go with focus on my low PS pilots and TL on pilots which are > enemy PS, or un-shielded foes. But hey I'm a Reb or Scum player, what do I know :-)

Just because you pushed some damage through using a 2 Attack ship with no Actions against a 4 Agility ship at Range 3 and through an obstacle with a Focus token, does not mean that it was a good idea. That being said, if it is the only shot you have, you take it anyway.

Was it omega leader with juke? Because he does that all day long!

Most of the issue here is psychological. I think that most people understand the basic dice probabilities, even though a few people are confused about how probabilities work with multiple dice (I had someone tell me once that 4 red dice were guaranteed to roll 1 blank, because 25%+25%+25%+25%=100% ).

The issue is that our brains pay more attention to less likely or unexpected results, especially when they are bad for us. I don't remember all of the times that I rolled 1 or 2 evades against 1 or 2 hits. I can only vaguely remember times that I've rolled 3 or 4 evades against a single hit. I remember distinctly, and with horrible clarity, every time I've rolled 4 blanks against 3 hits, or rolled 5 blanks on 5 red dice.

The net effect is that we come away with the feeling that the dice hate us, even though we know that they are pretty good random result generators. We are also susceptible to things like the gambler's fallacy, where we expect dice to produce good results in the future to "average out" bad results in the past, even when we know that that's not how dice work.

Just because you pushed some damage through using a 2 Attack ship with no Actions against a 4 Agility ship at Range 3 and through an obstacle with a Focus token, does not mean that it was a good idea. That being said, if it is the only shot you have, you take it anyway.

Was it omega leader with juke? Because he does that all day long!

Nope, it was just a hypothetical situation. However, I have flown enough TIEs to have seen this happen.

For me my dice rolling usually goes one of two ways. Either my red dice or green dice completely abandon me with the other picking up the slack. So when my red dice are rolling hot, I can't roll an evade to save my life and vice versa.

In regards to taking the shot you have, even if it is unlikely to hit, I refer to the great philosopher Hermes Conrad: "When push comes to shove, you've got to do what you love. Even if it's not a good idea."