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![[Post New]](/s/i/i.gif) 2013/07/12 05:30:29
Subject: Math and 40k
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Guardsman with Flashlight
Idaho
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So does anyone know some math formulas for figuring out the odds of successful wounds. One can usually get a good intuitive feel for the likelyhood of success, but what about actually breaking down the numbers.
For example say you have 10 attacks hitting on a 3+ and then wounding on a 4+
im sure that is really easy to figure out, but what about re rolling
10 attacks hitting on a 3+ with re roll for failed hits, then wound on 4+
what do you do to your formula to figure out the percentage of wounds for that?
Or just to make things complicated how about re rolling failed hits of dice results of 1 only
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![[Post New]](/s/i/i.gif) 2013/07/12 05:37:02
Subject: Re:Math and 40k
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Douglas Bader
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It's all just basic probability.
The chance of passing a roll with a re-roll is equal to 1 minus the chance of failing two rolls. For example, a 4+ re-rollable is a 75% chance, p = (1 - (0.5 * 0.5)). A 3+ re-rollable is about 89%, p = (1 - (0.333 * 0.333)). Etc.
Re-rolling 1s would be the chance of passing the first roll + (1/6) * (chance of passing the first roll). You take the starting number of successes and then 1/6 of the time you roll again and add those results to the total.
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There is no such thing as a hobby without politics. "Leave politics at the door" is itself a political statement, an endorsement of the status quo and an attempt to silence dissenting voices. |
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![[Post New]](/s/i/i.gif) 2013/07/12 05:39:15
Subject: Math and 40k
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Norn Queen
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You don't need a formula, it's basic math.
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![[Post New]](/s/i/i.gif) 2013/07/12 06:11:44
Subject: Math and 40k
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Big Mek in Kustom Dragster with Soopa-Gun
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a formula? i guess if you wanted to get the ideal, perfect situation math you might need it, otherwise its just basic math.
I dont even do the math because physical dice have this way of going FU to logic and probability for me. When im curious what something might pull, i grab dice and start throwing to see what would happen and i usually give the worse-case-scenario (4+ ruins cover, going to ground, etc) so i know if i do atleast average with worst case scenario, it'll work in the average joe battlefield.
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An ork with an idea tends to end with a bang.
14000pts Big 'n Bad Orkz
6000pts Admech/Knights
7500pts Necron Goldboys |
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![[Post New]](/s/i/i.gif) 2013/07/12 08:29:13
Subject: Math and 40k
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World-Weary Pathfinder
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It goes like this:
2+ = 5/6 = 83.3% chance
3+ = 2/3 = 66.6% chance
4+ = 1/2 = 50% chance
5+ = 1/3 = 33% chance
6+ = 1/6 = 16.6% chance
So its is 10 rolls @ 3+ for example is between 6 and 7 successful rolls, on average.
To work out casualties with, for example, marines shooting marines, you can ballpark it as:
10 shots x 0.66 = 6 hits x 0.5 = 3 wounds x 0.33 = 1 death, approximately, on average. Marines are hard to kill!
Once you work it out for a few different things, you get a good handle on the common numbers and you can get in your head a good number for how many kills you can reasonably expect a unit to make.
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Ulthwé Eldar 2.5k points and growing! |
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![[Post New]](/s/i/i.gif) 2013/07/12 08:44:41
Subject: Math and 40k
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Douglas Bader
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Vineheart01 wrote:I dont even do the math because physical dice have this way of going FU to logic and probability for me.
No they don't. You roll average dice just like everyone else does, and the math is indisputably correct.
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This message was edited 1 time. Last update was at 2013/07/12 08:44:52
There is no such thing as a hobby without politics. "Leave politics at the door" is itself a political statement, an endorsement of the status quo and an attempt to silence dissenting voices. |
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![[Post New]](/s/i/i.gif) 2013/07/12 09:33:30
Subject: Math and 40k
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Executing Exarch
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Now you may need to calculate the probabilities to a 95% confidence interval for that result or worse. (that would require some relatively basic tables and a tiny bit of formula)
The basic probabilities is just the likelihood of a failure subtracted from the total. For a reroll it is the likelihood of the failure multiplied by the likelihood of a second failure and then subtracted from one to determine success. Check out wikipedia, it has a decent article on probabilities.
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![[Post New]](/s/i/i.gif) 2013/07/12 13:56:23
Subject: Math and 40k
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Major
Fortress of Solitude
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Peregrine wrote: Vineheart01 wrote:I dont even do the math because physical dice have this way of going FU to logic and probability for me.
No they don't. You roll average dice just like everyone else does, and the math is indisputably correct.
That is untrue. Statistically you have to repeat an experiment hundreds of thousands of times before the standard deviation is reached. It is perfectly possible that he has rolled better or worse than other people. If everyone kept rolling constantly for a hundred years, we would all come out nearly the same, but until then, the most remarkable thing about statistics is how un-statistical it is.
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Celesticon 2013 Warhammer 40k Tournament- Best General
Sydney August 2014 Warhammer 40k Tournament-Best General |
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![[Post New]](/s/i/i.gif) 2013/07/12 17:40:20
Subject: Re:Math and 40k
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The Conquerer
Waiting for my shill money from Spiral Arm Studios
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Take the number of attacks you get and multiply them by the fraction representing the D6 roll needed.
Needing a 5+ is 1/3
So 10 shots at BS2(5+ to hit) would be 10(1/3)
10 shots at BS4 would be 10(2/3)
The same for to wound rolls.
So 10 bolter shots at a squad of orks would be the following.
10(2/3)(1/2)=3.333 wounds.
Saves can then be added too. Now you would be trying to figure out the probability of getting past the same, so you would do the chance of failure. A 5+ save would have a 2/3 chance of failure.
So 10 bolter shots at orks with a 5+ cover save would be,
10(2/3)(1/2)(2/3)=2.2222 unsaved wounds.
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Self-proclaimed evil Cat-person. Dues Ex Felines
Cato Sicarius, after force feeding Captain Ventris a copy of the Codex Astartes for having the audacity to play Deathwatch, chokes to death on his own D-baggery after finding Calgar assembling his new Eldar army.
MURICA!!! IN SPESS!!! |
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![[Post New]](/s/i/i.gif) 2013/07/12 21:17:54
Subject: Math and 40k
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Douglas Bader
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ImotekhTheStormlord wrote:That is untrue. Statistically you have to repeat an experiment hundreds of thousands of times before the standard deviation is reached. It is perfectly possible that he has rolled better or worse than other people. If everyone kept rolling constantly for a hundred years, we would all come out nearly the same, but until then, the most remarkable thing about statistics is how un-statistical it is.
The point is the dice are the same no matter who is rolling them. The idea that one person inherently has better or worse luck with dice is complete nonsense.
And you don't need hundreds of thousands of rolls to converge on the expected outcome. If you roll a 4+ 100 times the chances of getting more than 55 successes is only 13%, and the chance of getting more than 60 is less than 2%. Increase that to 1000 rolls and you have less than a 0.1% chance of rolling more than 5% above average. So it's safe to say that if anyone thinks they consistently roll significantly better or worse than average it's nothing more than confirmation bias.
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There is no such thing as a hobby without politics. "Leave politics at the door" is itself a political statement, an endorsement of the status quo and an attempt to silence dissenting voices. |
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![[Post New]](/s/i/i.gif) 2013/07/12 21:26:34
Subject: Math and 40k
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Fighter Pilot
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Peregrine wrote: ImotekhTheStormlord wrote:That is untrue. Statistically you have to repeat an experiment hundreds of thousands of times before the standard deviation is reached. It is perfectly possible that he has rolled better or worse than other people. If everyone kept rolling constantly for a hundred years, we would all come out nearly the same, but until then, the most remarkable thing about statistics is how un-statistical it is.
The point is the dice are the same no matter who is rolling them. The idea that one person inherently has better or worse luck with dice is complete nonsense.
And you don't need hundreds of thousands of rolls to converge on the expected outcome. If you roll a 4+ 100 times the chances of getting more than 55 successes is only 13%, and the chance of getting more than 60 is less than 2%. Increase that to 1000 rolls and you have less than a 0.1% chance of rolling more than 5% above average. So it's safe to say that if anyone thinks they consistently roll significantly better or worse than average it's nothing more than confirmation bias.
^ This is true. Just look at the "luck" of rolls over one game. One turn, you roll 15 and wound on a 3+, but you only get 3 wounds! Oh, such terrible luck!
Another turn, your opponent needs to make 3 2+ saves, and they roll 3 1's. This all happened last night.
Also, looking at it strictly as 3+ only looks at it from one perspective. Whether your opponent or you are rolling, you both want the opposite results.
"Luck" comes and goes in a game with dice rolling. It evens out.
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Here's to me in my sober mood,
When I ramble, sit, and think.
Here's to me in my drunken mood,
When I gamble, sin, and drink.
And when my days are over,
And from this world I pass,
I hope they bury me upside down,
So the world can kiss my ass!
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![[Post New]](/s/i/i.gif) 2013/07/12 21:48:10
Subject: Math and 40k
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Kid_Kyoto
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Peregrine wrote: ImotekhTheStormlord wrote:That is untrue. Statistically you have to repeat an experiment hundreds of thousands of times before the standard deviation is reached. It is perfectly possible that he has rolled better or worse than other people. If everyone kept rolling constantly for a hundred years, we would all come out nearly the same, but until then, the most remarkable thing about statistics is how un-statistical it is.
The point is the dice are the same no matter who is rolling them. The idea that one person inherently has better or worse luck with dice is complete nonsense.
...With the same dice. Assuming everyone uses different dice, then it's down to the original manufacturing precision of the dice.
We've had a decent study done here on dakka and there are numerous dice vs precision dice commentaries out there. They are interesting.
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![[Post New]](/s/i/i.gif) 2013/07/12 21:51:40
Subject: Math and 40k
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Douglas Bader
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daedalus wrote:...With the same dice. Assuming everyone uses different dice, then it's down to the original manufacturing precision of the dice.
And the manufacturing differences should not add up to all that much, especially since that same variation would exist between all of the dice in a cube. Unless you always use the same poorly-balanced die for every shot "I always miss with my lascannons so I don't take them anymore" is nothing more than confirmation bias.
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There is no such thing as a hobby without politics. "Leave politics at the door" is itself a political statement, an endorsement of the status quo and an attempt to silence dissenting voices. |
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![[Post New]](/s/i/i.gif) 2013/07/12 21:53:41
Subject: Re:Math and 40k
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Kid_Kyoto
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That's an entirely valid point.
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![[Post New]](/s/i/i.gif) 2013/07/12 22:04:01
Subject: Math and 40k
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Been Around the Block
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The problem with statistical dice is while the may be mathematically equal they dont account for luck, which is essentially timing.
Which is why the hardest roll n BB is a 2+ ;-) .
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Gaming in Kent
hydragamingclub.freeforums.org
twitter - bobmanRN - wargames rambling |
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![[Post New]](/s/i/i.gif) 2013/07/12 22:28:55
Subject: Math and 40k
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Executing Exarch
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Actually dice are not truly random. There are sometimes (rarely) individual bias for rollers and dice. Particularly, it has been shown that long term gamblers sometimes develop certain biases in their rolling and the dice themselves are not perfectly weighed and even surfaced.
These are outliers though and an almost negligible number of cases. It is more likely that selective memory (you tend to remember bad events better than normal or good events) and small data sets are what have created most cases of "bad" or "good" luck.
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![[Post New]](/s/i/i.gif) 2013/07/12 23:03:29
Subject: Math and 40k
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Fireknife Shas'el
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This actually happened the other day during a game. I put about 5 S10 railgun shots, 6 melta gun hits, and 6 MC smash attacks into a single Land raider over the coarse of 3-4 turns. Bad averages on my part with never passing more than a single penetration roll until the last smash attack.
Later on I happened to make a couple saves and it's suddenly "You're rolling so well!"
Take a note book and just make a few quick notes for several of the high volume rolls and you'll see that there is only a small variation from the average through the game. There will always be the extremes when you roll 8 1's in a row or manage to tank 30 3+ saves. Over the coarse of the game or even a few games it evens out. But it really helps to show your subconscious bias.
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I'm expecting an Imperial Knights supplement dedicated to GW's loyalist apologetics. Codex: White Knights "In the grim dark future, everything is fine."
"The argument is that we have to do this or we will, bit by bit,
lose everything that we hold dear, everything that keeps the business going. Our crops will wither, our children will die piteous
deaths and the sun will be swept from the sky."
-Tom Kirby |
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![[Post New]](/s/i/i.gif) 2013/07/13 03:30:37
Subject: Math and 40k
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Regular Dakkanaut
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It's notable that certain sorts of very important rolls in 40k are also such that they exhibit high variance, and this can make it very easy to think that you're getting very lucky or very unlucky.
For example, if I Fortune an Archon with a Shadowfield, he has a rerollable 2++. He'll successfully save 35 out of every 36 wounds, on average. But in 25% of games he'll lose the field to one of the first 10 wounds he takes. In these 25% of games, most failures will occur in the first 5 wounds. A player who sees this sort of result is going to feel very unlucky, but it's actually just not very unlikely to happen.
The flip side of this is that in another 25% of games the same Archon will shrug off at least 49 wounds before taking one, and won't fail until (at least) his 74th save in half of that 25%. A player going up against this is going to feel like the dice hate him, but, again, this result just isn't very uncommon.
The number of rolls it actually takes to see some result will commonly vary by almost as much as the number of rolls you /expect/ to take to achieve that result. This gets smaller as the number of expected rolls goes down. I already talked about a 1 in 36 chance. If you expect to see a result in 10 rolls, 50% of the time it will actually occur in the first three rolls or after the 13th roll. If you expect to see a result in 4 rolls, 50% of the time it will occur on the first roll or on the fifth or later roll. 4+ saves are going to be a lot more consistent than 2+ saves, and will produce results which are closer to the expectation value with fewer saves taken. On top of this, models with 4+ saves tend to be cheaper, and so you're often rolling /more/ of them. You may notice that you roll much more "average" with 4+ saves than with 2+ saves; this is why. Automatically Appended Next Post: It occurs to me that I didn't actually talk much about rolling groups of dice and seeing lucky or unlucky results.
Let's say you're rolling 60 4+ saves (over a game). You expect to make 30. And you'll actually save 27-32 of them in half of all games. You'll save 25-34 of them in 75% of games. So it's pretty rare for you to see more than about 16% more or fewer failed saves than you expect.
But what if you're making 60 2+ saves? You expect to make 50 of them - or fail 10 of them, which is probably the number you're paying more attention to. The ranges here are similarly broad - you fail 8-11 saves ~50% of the time, and fail 7-14 ~75% of the time. These ranges look similar, but the expected number of failed saves is lower - now you're commonly seeing up to 40% more or fewer failed saves than you expected.
Consider also that you're generally rolling /fewer/ 2+ saves, because 2+ wounds are more expensive, and that this is going to produce even bigger ranges relative to the expectation.
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This message was edited 3 times. Last update was at 2013/07/13 03:59:07
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![[Post New]](/s/i/i.gif) 2013/07/13 05:50:21
Subject: Math and 40k
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Dakka Veteran
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Thanks for posting this. Statistical variance is something that's almost never talked about when discussing mathhammer, when I think it should be as or more important to talk about than just your base % probabilities that get banded out (because they're easy I guess). As a non-math person that is aware of it, you've explained it well and far better than what I could have. That Archon/Shadowfield example is very good.
I've had many a game where there was rage because opponent didn't get his exactly expected fraction of successful armour saves or hits or what have you, when whatever they rolled was still a very reasonably possible outcome.
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![[Post New]](/s/i/i.gif) 2013/07/13 06:31:17
Subject: Math and 40k
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Resolute Ultramarine Honor Guard
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DO:70S++G++M+B++I+Pw40k93/f#++D++++A++++/eWD-R++++T(D)DM+
Note: Records since 2010, lists kept current (W-D-L) Blue DP Crusade 126-11-6 Biel-Tan Aspect Waves 2-0-2 Looted Green Horde smash your face in 32-7-8 Broadside/Shield Drone/Kroot blitz goodness 23-3-4 Grey Hunters galore 17-5-5 Khan Bikes Win 63-1-1 Tanith with Pardus Armor 11-0-0 Crimson Tide 59-4-0 Green/Raven/Deathwing 18-0-0 Jumping GK force with Inq. 4-0-0 BTemplars w LRs 7-1-2 IH Legion with Automata 8-0-0 RG Legion w Adepticon medal 6-0-0 Primaris and Little Buddies 7-0-0
QM Templates here, HH army builder app for both v1 and v2
One Page 40k Ruleset for Game Beginners |
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![[Post New]](/s/i/i.gif) 2013/07/13 09:00:11
Subject: Re:Math and 40k
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Brigadier General
The new Sick Man of Europe
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The combat calculator at Heresy Online is good.
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DC:90+S+G++MB++I--Pww211+D++A++/fWD390R++T(F)DM+
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