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Post by NephMakes on Dec 21, 2017 1:31:59 GMT
Okay. You just need a 5 to hit to to win the game. You can either make 2 separate attacks, or boost the first attack. Which do you do and why? What if it's a 4? What if it's a 7? Okay, so this is the ideal case to try out my quick reference card. Let's see.. - 5 to hit looks like ~85% to hit or 15% to miss. Boosted it becomes ~97% or 3% to miss. Two misses would be 0.15 * 0.15 which is between 1% (0.1 * 0.1) and 4% (0.2 * 0.2). I'd say there's no real difference there, in practice.
- 4 to hit: 90% unboosted, ~100% boosted. Two misses on a bought attack would be 1%. Again no real difference in practice.
- 7 to hit: 60% unboosted, 90% boosted. Two misses 0.4 * 0.4 or 16% of the time. Boost to hit.
How'd I do?
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Post by NephMakes on Dec 21, 2017 2:34:04 GMT
Okay. You just need a 5 to hit to to win the game. You can either make 2 separate attacks, or boost the first attack. Which do you do and why? What if it's a 4? What if it's a 7? Putting real numbers to this: - 5 to hit: 17% to miss unboosted, 1.9% to miss boosted. 2.8% to miss two attacks.
- 4 to hit: 8.3% to miss unboosted, 0.5% to miss boosted. 0.7% to miss two attacks.
- 7 to hit: 42% to miss unboosted, 9.3% to miss boosted. 17% to miss two attacks.
The quick-reference plot works well enough for me.
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regleant
Junior Strategist
Sometimes things go right
Posts: 267
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Post by regleant on Dec 21, 2017 3:12:30 GMT
Okay. You just need a 5 to hit to to win the game. You can either make 2 separate attacks, or boost the first attack. Which do you do and why? What if it's a 4? What if it's a 7? Putting real numbers to this: - 5 to hit: 17% to miss unboosted, 1.9% to miss boosted. 2.8% to miss two attacks.
- 4 to hit: 8.3% to miss unboosted, 0.5% to miss boosted. 0.7% to miss two attacks.
- 7 to hit: 42% to miss unboosted, 9.3% to miss boosted. 17% to miss two attacks.
The quick-reference plot works well enough for me. So, per the above math, it is "on average" always better to boost if the attack absolutely needs to hit? That was my initial point. I don't know how many times I've seen the Angelius go in with it's Armor Piercing attack, my opponent saying "okay just need a 5 to hit, and.... *&$&^%"
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crimsyn
Junior Strategist
Posts: 389
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Post by crimsyn on Dec 21, 2017 4:12:48 GMT
Putting real numbers to this: - 5 to hit: 17% to miss unboosted, 1.9% to miss boosted. 2.8% to miss two attacks.
- 4 to hit: 8.3% to miss unboosted, 0.5% to miss boosted. 0.7% to miss two attacks.
- 7 to hit: 42% to miss unboosted, 9.3% to miss boosted. 17% to miss two attacks.
The quick-reference plot works well enough for me. So, per the above math, it is "on average" always better to boost if the attack absolutely needs to hit? That was my initial point. I don't know how many times I've seen the Angelius go in with it's Armor Piercing attack, my opponent saying "okay just need a 5 to hit, and.... *&$&^%" If you need a 3 to hit, then it is better to buy two attacks instead of boosting. Also, if you need a 16 or higher to hit, then it is better to only roll two dice and hope for boxcars on one of your two attempts than to try to actually hit a 16 on three dice.
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Post by Gamingdevil on Dec 21, 2017 8:08:36 GMT
Putting real numbers to this: - 5 to hit: 17% to miss unboosted, 1.9% to miss boosted. 2.8% to miss two attacks.
- 4 to hit: 8.3% to miss unboosted, 0.5% to miss boosted. 0.7% to miss two attacks.
- 7 to hit: 42% to miss unboosted, 9.3% to miss boosted. 17% to miss two attacks.
The quick-reference plot works well enough for me. So, per the above math, it is "on average" always better to boost if the attack absolutely needs to hit? That was my initial point. I don't know how many times I've seen the Angelius go in with it's Armor Piercing attack, my opponent saying "okay just need a 5 to hit, and.... *&$&^%" If I need a five or less and have a backup, I will generally just go for the attack rather than boost, because there's a big payoff (more attacks/spells) for little risk (just trying again gives about the same result). If you absolutely need a 6 to hit, always boost. Of course, if you really need a five and your only option is to boost, like with an AP special attack or a big debuff that you won't have the focus to cast again, then boost.
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zich
Junior Strategist
Posts: 690
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Post by zich on Dec 21, 2017 9:32:34 GMT
Here we go (numbers rounded to 4 decimals):
Expected number of hits:
to hit 3 1 attack boosted: 0.9954 2 attacks: 1.9444
to hit 4 1 attack boosted: 0.9954 2 attacks: 1.8334
to hit 5 1 attack boosted: 0.9815 2 attacks: 1.6666
to hit 6 1 attack boosted: 0.9537 2 attacks: 1.4544
to hit 7 1 attack boosted: 0.9074 2 attacks: 1.1666
Chance of at least one hit:
to hit 3 1b 0.9954 2: 0.9992
to hit 4 1b: 0.9954 2: 0.9931
to hit 5 1b: 0.9815 2: 0.9722
to hit 6 1b: 0.9537 2: 0.9228
to hit 7 1b: 0.9074 2: 0.8264
So, what does this mean? If you absolutely know that you only need one hit, you start boosting as soon as you need a 4 to hit. If you know you will need multiple hits you start boosting at 8. If it is uncertain whether you need multiple hits or just one, you might already start boosting at 7. Bun in general, boosting 6 or under really only makes sense when you absolutely only need one hit.
That is of course assuming that buying attacks costs 1. You could also - for example - be casting Arcane Bolts for 2.
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zeffid
Junior Strategist
Posts: 163
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Post by zeffid on Dec 21, 2017 20:45:47 GMT
I'm working on a quick-reference card that will (I hope) show at a glance what I should expect from a roll and how much boosting would help. What would be really helpful is some quick chart/formula to calculate probabilities for cases like: 10 dmg rolls at 2d6-5; probably I want to compare that with 5 rolls 3d6-5.
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Post by NephMakes on Dec 22, 2017 0:40:01 GMT
Plot for the "at least one hit" case that reflects some of the points made in this thread:
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Post by Trollock on Dec 22, 2017 7:34:27 GMT
Oooh! I have a new misconception! The misconception that dice math is super important. When i got in to this game, i came from a Warhammer Fanatasy background. I immediately wanted to make spread sheets and graphs to determine the most efficient mathematical way to play the game. How many guys should i include in a CRA? Will this unit do more damage than that unit and so on. In WHF that type of knowledge was key to building lists, since there you had units that were strictly better than others. You threw enough dice that you could count on averages pretty well and so on. This type of knowledge IS important to have, but the minutia of dice math seldom has any real game impact. You can go through most games by knowing that 2 dice will roll 7 on average, and 3 dice will roll 10.5 on average. Most game decisions revolve around "can i kill that thing in one round?". You can easily calculate how much damage each hit should do, and then calculate how many hits you need. If your warjack needs 6 hits to one round another jack, it is most likely impossible, since most often you wont do more than 4-5 attacks. If you can send in two jacks against the same target (doing 8-10 attacks) and you are likely to hit (maybe you only need to roll a 4 to hit) then two jacks should do the job. If the two jacks are 87% or 95% likely to get the job done is seldom a factor. If you get a good chance, you will go for it, and hope the dice go your way. I suggest to new players to learn these basic dice math skills, because they are VERY important, but the more complex stuff cant be done at the gaming table anyway, and can thus be left to forum discussions. Your job as a player is basically to be able to determine at the table if your plan is ~25% likely to succeed (only desperate players should take these chances) or ~50% chance to succeed (you could take this chance if you are behind and need to make something happen to take control) or ~75% chance to succeed (you will take this chance even if you are ahead, but only if you arent risking losing everything if it goes to hell) or if it is ~100% chance to succeed (things like clearing out once infantry model from your zone to score your final point using your entire army to do it). Learn that rolling 5+ is very likely(but not guaranteed) to happen, but 9+ is very unlikely (but not impossible) to happen. Learn that getting +2 to your roll will make a BIG difference. Learn that rolling multiple 7+ in a row is NOT very likely to happen and you can go to the WTC and do well. Though most of the best players have a good grasp of dice math, there are LOTS of players who are way better at math than them, but still are way worse at the game. Dice math is fun and interesting, but it is not your math knowledge that will win or lose you most games. Model placement and target selection are much more important and subtle concepts
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Post by NephMakes on Dec 23, 2017 3:12:18 GMT
What would be really helpful is some quick chart/formula to calculate probabilities for cases like: 10 dmg rolls at 2d6-5; probably I want to compare that with 5 rolls 3d6-5. This is too much for a quick-reference card, but it gets at your specific case: For automatic hits, boosting and buying are basically equivalent at dice off 3.5. At that point, a basic 2d6 roll averages 3.5 damage, and doing that twice is the same as adding another d6. Dice off more than that, it's better to boost. Dice off less than that, it's better to buy another attack. Being able to miss the bought attack will devalue buying and shift the equivalence point.
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zich
Junior Strategist
Posts: 690
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Post by zich on Dec 23, 2017 8:47:50 GMT
I'm working on a quick-reference card that will (I hope) show at a glance what I should expect from a roll and how much boosting would help. What would be really helpful is some quick chart/formula to calculate probabilities for cases like: 10 dmg rolls at 2d6-5; probably I want to compare that with 5 rolls 3d6-5. Just compare 1 roll with 3d6-5 (roughly 6) to 2 rolls with 2d6-5 (roughly 5). Then multiply by 5.
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Post by NephMakes on Dec 25, 2017 16:16:39 GMT
Here's something I came across in the comments of some blog post. Consider this example (simplified from the original): You need to roll a seven to hit (58%), the damage roll is dice minus two (2d6 average 5, or 3d6 average 8.5), and you have one focus to spend. Should you boost damage or buy a second attack? The commenter calculated their expected damage: - Boost damage: 0.58 * 8.5 = 4.9 mean damage
- Buy attack: 0.58 * 5 * 2 = 5.8 mean damage
Therefore, they wrote, buying an attack is the better option. But let's say you hit the first attack and now it's time to make the choice. You can again calculate your expected damage: - Boost damage: 8.5 mean damage
- Buy attack: 5 + 0.58 * 5 = 7.9 mean damage
Now it looks like boosting damage is the better option. What's going on here? Is this some wierdness with conditional probability like the Monty Hall Problem? No. The commenter's calculations were wrong. The 42% of the time that the first attack misses, you're not going to just throw away the focus you were going to use to boost. You're going to buy another attack. The correct calculation should be: - Boost damage: 0.58 * 8.5 + 0.42 * 0.58 * 5 = 6.1 mean damage
- Buy attack: 0.58 * 5 * 2 = 5.8 mean damage
For this example, boosting damage (when you can) is the better option no matter when you make the calculation. So I guess the moral of the story is: Make sure you've thought through all the possibilities.
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zeffid
Junior Strategist
Posts: 163
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Post by zeffid on Dec 26, 2017 9:28:56 GMT
Great example there!
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Provengreil
Junior Strategist
Choir Kills: 12
Posts: 850
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Post by Provengreil on Dec 28, 2017 14:00:32 GMT
Putting real numbers to this: - 5 to hit: 17% to miss unboosted, 1.9% to miss boosted. 2.8% to miss two attacks.
- 4 to hit: 8.3% to miss unboosted, 0.5% to miss boosted. 0.7% to miss two attacks.
- 7 to hit: 42% to miss unboosted, 9.3% to miss boosted. 17% to miss two attacks.
The quick-reference plot works well enough for me. So, per the above math, it is "on average" always better to boost if the attack absolutely needs to hit? That was my initial point. I don't know how many times I've seen the Angelius go in with it's Armor Piercing attack, my opponent saying "okay just need a 5 to hit, and.... *&$&^%" yeah, but what about when it's more than one roll, in a scenario with more outcomes? Consider the following:
My sanctifier rolls up to an ironclad. it's gotten battle, charged, and has a full load of focus (that's one PS 16, one charging PS 18, MAT 6 onto DEF 12, ARM 18, 2 focus remaining). Killing the ironclad doesn't end the game, but the rest of the table is such that it allows a win this turn. If the ironclad lives and is capable of destroying the sanctifier alone, I'll probably lose. If neither can kill the other alone, play will continue further. Ironclad does not have any buffs.
What are my chances of winning this turn, and how do I maximize them? If those rolls go wrong, does that increase my chances of losing?
This is the real test for that card.
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Post by jisidro on Dec 28, 2017 14:34:08 GMT
This is a game were players are encouraged to do the optimal play and where you can choose to boost/buy/CRA/CMA/Combo knowing what to do in the grey areas or at least be confortable with your decision is important for performance and enjoyment. Is it relevant to go for the 51% option when you took the 49% one? Well, 2% of the time it is. Is it worth doing math when the clock is ticking? Probably not but if it's an assassination... What I mean to say is that when people protest because abilities are not usefull 100% of the time (Unwielding, for example) and the rule gets looked that you are in a min/max game. Because it is a great ruleset that does not dominate the decision process but it doesn't mean the mind set is not there. TL; DR: Know the math or you will end up blaming the dice and no good plays come off that.
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