Ask Heroscape math questions here!

[CornPuff]

This thread is simple. Ask a mathy Heroscape question, and I'll try to answer it. Anyone else is welcome to chime in with answers too.

Ever wondered what the probability of some HS thing was? Want to know how to fire the Queglix gun? Thought about whether you should put Thogrim's spirit on Jotun or the Krav Magas?

Here are some sample answers to get the thread rolling....

How many rounds, on average, do I have to wait before the Airborne Elite drop?
2.5 rounds.

Whats the probability of Deathwalker 7000 rolling all blanks on defense?
5.8%

In my game last night. I had Major Q9 in Raelin's aura, giving him 9 defense. Somehow, he died in 4 attacks. 3 shots from Syvvarris on high ground, and 1 attack from Marrden Hound on even ground. What are the chances of that?

Those attacks will kill Q9 4.1% of the time

Q: How do I fire the Queglix gun?

It depends on the defense of the figures you want to shoot.
Against figures with Stealth Dodge orShields of Valor, use 1 die per attack.
Against figures with 0, 1 or 2 defense, use 1 attack die.
Against Heroes or squad figures with 3 or more defense, use 3 attack dice. It is never to your advantage to roll 2 attack dice.
edit: check out mathguys posts below. Desperate times can call for desperate measures....

Also, for math buffs, or people that question my answers, I can go deeper and actually post some equations that I use over in this thread:
http://www.heroscapers.com/community/showthread.php?t=612


On your mark.
Get Set.
Ask me Questions!!!!

[bushi96]

You are a stud. Here is a good one- When exactly does it become more advantageous to use Deadeye Dan's sharpshooter ability over his regular attack?

And what do you plan to do tomorrow?
http://peter.vestergaard.nielsen1.person.emu.dk/lyd%20og%20billede/pb.gif

[ultradoug]

what chance do i have to frenzy?

ok I'm on a train playing heroscape going 40 miles an hour headed towards skyknight whos tied to the tracks...

[Jason]

According to my calculations using 2 dice against a 2 defense unit is not inferior to chooisng 1 die

[mathguy]

...
Q: How do I fire the Queglix gun?

It depends on the defense of the figures you want to shoot.
Against figures with Stealth Dodge orShields of Valor, use 1 die per attack.
Against figures with 0, 1 or 2 defense, use 1 attack die.
Against Heroes or squad figures with 3 or more defense, use 3 attack dice. It is never to your advantage to roll 2 attack dice.
...


Those are good general guidelines, but it also depends on the enemy attack and on the number of enemy units. Here is an example:

Q9 vs 2 squads of 4th Mass guys and give the 4th mass guys height advantage and Wait then fire and Attack glyph +1, that is
Q9 versus 2 squads with squad size 4 (8 figures total) with ATT=5, DEF=3.

Here are the Q9 win probabilities based on strategy (sticking with one strategy throughout the matchup):

333 2223 22221 1x9
3.011% 3.275% 3.301% 2.616%


This is an example where it is best to roll 2 attack dice versus 3 defense. This makes some intuitive sense because against high numbers and high attacks, Q9 is more "desperate" to make more attacks to try to take out more units.

Along this line of thinking, it is not surprising that if you reduce the number to 1 squad in the above example, then Q9 does best with 3 attack dice. But then again, if you increase the enemy attack to say 10 attack dice with just 1 squad, then Q9 does best with rolling 2 attack dice.

One final point, it is even more likely in the above example that a "combination of strategies" is best. That is, start out with one strategy (like the 22221), and as the number of enemy units go down, you might want to switch to another strategy (like the 333).

Yay math!

[toddrew]

According to my calculations using 2 dice against a 2 defense unit is not inferior to chooisng 1 die

True on a single attack, not necessarily for a greater # of attacks per turn, as I assume Corn Puff computed.

And, Corn Puff, please do post the calculations, like all of our math teachers indoctornated us: Show your work! :D

Like mathguy, thanks for your posts.

One can't be worried about coming off as wonky, given the setting :)

[CornPuff]

I like your numbers, mathguy.
All my numbers are done with chance to hit against 1 life units, and expected damage against multi life units.
Most of my numbers don't have a 'desperate times call for desperate measures' angle. I figure that as long as you have more units, a slow and steady pace is best, rather than trying for the lottery on every shot.
In other words, my numbers aren't always accurate for one on one situations where you are likely to lose. I'd consider rolling 2 dice with Q9 a sort of 'hail Mary', 'if this doesn't work, nothing will' type maneuver.

[CornPuff]

Now, the first answer from CornPuff! :popcorn:


Here is a good one- When exactly does it become more advantageous to use Deadeye Dan's sharpshooter ability over his regular attack?

That is a good question to start with.

Deadeye Dan has three attacks: Normal, Sharpshooter and Ullar Enhanced Rifle
His normal attack is 1. This can of course be boosted by Height Advantage, Taelord, Finn's Spirit and glyphs.
Ullar Enhanced Rifle can only be used on Medium figures, and only if Deadeye Dan has not moved. Its great for picking off high defense squads
Sharpshooter can only be used if DED hasn't moved. It has a 10% chance of destroying any figure.

Lets focus on how many turns it will take Deadeye to kill an enemy figure. Enemy figures have 2 relevant properties: Life and Defense.

Say we are shooting at a wounded Syvvaris from high ground (Normal Attack = 2). Say he has 2 life left with 4 defense. We check each shot's average damage to find out which will finish off Syvvaris the quickest.
Sharpshooter: Avg. Damage = 0.2
Ullar Enhanced Rifle: Avg Damage = 0.5
Normal Attack: Avg Damage = 0.56

So we would attack Syvvaris with a normal attack.
Bang! Syvvaris only has one life left now. We want the attack that has the highest chance of finishing him off.
Sharpshooter: Chance to Hit = 10%
Ullar Enhanced Rifle: Chance to Hit = 50%
Normal Attack: Chance to Hit = 44%
Looks like its time to switch to the Ullar Enhanced Rifle for the final blow.

This is just an example, I've attached a pdf that shows which attack is best against many combinations of Life and Defense.

I hope this helps. Good luck shooting Charos in the eye! :johnwoo2:

[mathguy]

CornPuff: Indeed "desperate times call for desperate measures" is a good way of putting it. And frankly in that example I posted, it only matter a tiny amount anyway to use the better strategy.

Here is another neat situation, say Q9 with height advantage versus DW9K within Raelin's aura.
Q9 with height win percentages versus DW9K within Raelin's aura.

Q9 vs DW9K Q9 vs DW9K
ATT 5 ATT 4 Gueglix 333 ATT 4
DEF 8 DEF 11 DEF 8 DEF 11
no special

83.452% 80.633%

Q9 does best in this scenario to not use his special attack.

But if DW9K did not have his defense boosted by Raelin, that is with a DEF 9 only, then Q9 does better to use the Gueglix 333 strategy.

It's fun thinking about when and why certain strategies are better.

[CornPuff]

what chance do i have to frenzy?

Venocs Vipers, Elite Onyx Vipers and Aubrien Archers Frenzy on the roll of a 16 or higher.

Every time you roll the D20, you have a 25% chance of rolling a 16 or higher, and Frenzying. On average, you will frenzy once every 4 rolls of the dice. But when you frenzy, you get to go again, so once every 3 turns, on average.

If you draft the Venoc Warlord, you can Frenzy on a 15 or higher. This bumps you up to a 30% of Frenzy. On average you would roll frenzy every 3.3 rolls.

If you also grab a glyph of Lodin, then your vipers will frenzy whenever you roll 14 or higher, or 35% of the time. This means an average of 2.9 rolls until the next frenzy.

So, if you draft the Venoc Warlord, your vipers will Frenzy almost every other turn, as opposed to once every 3 turns.

[CornPuff]

I decided to split the thread. After all, not everyone needs to see our equations :P

Heroscape Math Questions and answers will stay here.

We can do behind-the-scenes math talk over here:
http://www.heroscapers.com/community/showthread.php?t=612

[mathguy]

...
Every time you roll the D20, you have a 25% chance of rolling a 16 or higher, and Frenzying. On average, you will frenzy once every 4 rolls of the dice. But when you frenzy, you get to go again, so once every 3 turns, on average.
...

Technically, what it means is that on average you get to go an extra 1/3 turn (move) for every turn of the round (game turns). But you still should expect to frenzy (one or more) only once every 4 game turns. Sorry to be technical.

[CornPuff]

hehe, I guess I meant once every 3 order markers.

[shakey_snake]

This is just an example, I've attached a pdf that shows which attack is best against many combinations of Life and Defense.

I hope this helps. Good luck shooting Charos in the eye! johnwoo2
Nice! What about against Shields of Valor and Tough?

[P_J_Keller]

Can I ask a non-Heroscape probability question?

If so, here is one that has been bugging me for over a year. We're playing Risk Godstorm and I have 11 armies attacking my opponent who has 3 armies. I have my War God with me so I win all ties. Secondly I have my Magic Goddess with me so I reroll all 1s.

I assume you're familiar with Risk's combat system where the attacker can roll up to 3 dice (6 sided) and the defender can roll up to 2 dice (6 sided). One side's highest die is compared to the other side's highest die and and the loser losees one army for that die. I was winning ties as detailed above. This is then repeated with the second highest dice. The advantage for the attacker is rolling an additional die. Defender has lost any advantage because my War God is with me.

Anyway, even with the bonuses above (winning ties and rerolling ones) I lost 4 consecutive turns, losing 8 of my 11 attackers and then having to call off the attack. The defender couldn't seem to roll lower than a 4 and I couldn't roll anything but 2s or 3s.

So, what is the probability of my losing 4 consecutive turns with the defender never losing once?

Thanks for the help in calculating this

[daevablacc]

Thanks a lot for getting this going cornpuff. I love info like this.

[CornPuff]

According to my calculations using 2 dice against a 2 defense unit is not inferior to chooisng 1 die

Huh, I reviewed my numbers, and you are right. But its not superior either :-) Against a sea of endless Blade Gruts, Q9 will do equally well firing 9x1 or 22221.

Good catch.

[AmishBurrito]

Here's a math question.

If i ordered 7 sets from hasbrotoyshop.com on saturday, and they shipped on tuesday, and project 7-10 business days for arrival, what is the probability that i will get them in the mail tomorrow?

[mathguy]

Here's a math question.

If i ordered 7 sets from hasbrotoyshop.com on saturday, and they shipped on tuesday, and project 7-10 business days for arrival, what is the probability that i will get them in the mail tomorrow?
You need to know the standard deviation of their delivery dates. Perhaps their "7-10" days implies that the mean is 8.5 and standard deviation is 1.5. From this, taking 1 day to delivery would be a (8.5 - 1)/1.5 = 5 standard deviation event. Assuming a normal distribution, the probability of this happening is about 0.0000002867. :-)

[AmishBurrito]

no no, they shipped tuesday, it will have been 4 days

[mathguy]

no no, they shipped tuesday, it will have been 4 days
Whoops I read it wrong. I thought you were making a joke. :-)

In that case the event would be (8.5 - 4)/1.5 = 3 standard deviations, and so would have probability 0.0013.

[AmishBurrito]

i would never joke about getting my new heroscape figures :twisted:

[mathguy]

Can I ask a non-Heroscape probability question?

If so, here is one that has been bugging me for over a year. We're playing Risk Godstorm and I have 11 armies attacking my opponent who has 3 armies. I have my War God with me so I win all ties. Secondly I have my Magic Goddess with me so I reroll all 1s.

I assume you're familiar with Risk's combat system where the attacker can roll up to 3 dice (6 sided) and the defender can roll up to 2 dice (6 sided). One side's highest die is compared to the other side's highest die and and the loser losees one army for that die. I was winning ties as detailed above. This is then repeated with the second highest dice. The advantage for the attacker is rolling an additional die. Defender has lost any advantage because my War God is with me.

Anyway, even with the bonuses above (winning ties and rerolling ones) I lost 4 consecutive turns, losing 8 of my 11 attackers and then having to call off the attack. The defender couldn't seem to roll lower than a 4 and I couldn't roll anything but 2s or 3s.

So, what is the probability of my losing 4 consecutive turns with the defender never losing once?

Thanks for the help in calculating this

The probability is 0.0000382968.

Wow, that's rarer than 3 mindshackles in a row (unenhanced). And I have yet to see a successful mindshackle in a game.

Here is the calculation.
For one round, there are 6^2 * 5^3 = 4500 possible outcomes (just treat your dice as being 5-sided dice since you can reroll 1s).
Of these 4500, there are 354 of them which lead to the attacker losing two units.
So the probability is 354/4500 = 59/750 = 0.0786667.
For this to happen 4 times in a row is (0.0786667)^4 = 0.0000382968.

[P_J_Keller]

Thank you, I knew it was so far fetched as to be unbelievable and it's been eating at me for over a year.

BTW - I've only seen mindshackle work twice - and not in the same game

[mathguy]

It really was unbelievably rare, wasn't it? It's like 1 in 26000. I mean, have you done anything gamewise 26 thousand times?
Well, in a game of HS, maybe you roll dice 100 times?
So, in 260 games of HS, you might see an event as rare as 1/26000?

[Jason]

A better way to think about it is that assume there are 26,000 games played of it per day (not unfathomable with the world having 6+ billion people). In that case it would occur in someone's house every day on average

[AmishBurrito]

omg i got my stuff on saturday (they shipped tuesday) and claimed 7-10 business days, way to go hasbro :lol:

[jcb231]

I'd love a table that had across the top numbers of attack die (one, two, three, etc) and downt he side numbers of defense die (zero, one, two, etc) and when you read the table it showed the chance to hit each combo had....so I could scan down the column of "one attack die" to "zero defense dice" and see that my chance to hit is 50%. Or what my chances of hitting a five defense figure are with four dice. Or so on....the box that shows my chance of hitting could tell me what chance I have of getting at least X number of wounds. So In the 1vs0 case, I have a 50% chance of getting one wound. What about 3 vs 2? What are my chances of hitting for at least one, at least two, or at least three?

The chart could also have a quick addendum for Tough, Shields of Valor, Stealth Dodge, and Deadly Strike/Shot.

That would be the ultimate chart. I would talk of the awesomeness of such a chart for many a year....in story and song and spectacle.

[CornPuff]

heh, that would be many many charts.
But, I do have this chart I found on HQ that I find to be accurate and very very helpful.

[netherspirit]

If I have 2 Squads of Mardden Hounds adjacent to 2 squads of Microcorp Agents. What are the odds that all the Microcorp agents will die on the Mardden players turn, assuming he activated a squad?

You would roll for all 6 hounds, not just three :)




983rd! POST!!! 18 more for a winner..

[shakey_snake]

This is just an example, I've attached a pdf that shows which attack is best against many combinations of Life and Defense.

I hope this helps. Good luck shooting Charos in the eye! johnwoo2
Nice! What about against Shields of Valor and Tough?

[ReverendBayes]

I'd love a table that had across the top numbers of attack die (one, two, three, etc) and downt he side numbers of defense die (zero, one, two, etc) and when you read the table it showed the chance to hit each combo had....so I could scan down the column of "one attack die" to "zero defense dice" and see that my chance to hit is 50%. Or what my chances of hitting a five defense figure are with four dice. Or so on....the box that shows my chance of hitting could tell me what chance I have of getting at least X number of wounds. So In the 1vs0 case, I have a 50% chance of getting one wound. What about 3 vs 2? What are my chances of hitting for at least one, at least two, or at least three?

The chart could also have a quick addendum for Tough, Shields of Valor, Stealth Dodge, and Deadly Strike/Shot.

That would be the ultimate chart. I would talk of the awesomeness of such a chart for many a year....in story and song and spectacle.


No Shields of Valor, but Deadly Strike/Shot, counterstrike, and Tough are all taken care of in the comprehensive charts I've posted below.

I originally posted these on .net, and will update them after wave 5 to include all new wrinkles.

Hope these enhance your HeroScape enjoyment!

EDIT: Tough *is* taken care of with these tables, just shift the # of unblocked skulls up accordingly.

[jcb231]

heh, that would be many many charts.
But, I do have this chart I found on HQ that I find to be accurate and very very helpful.

Damn...can't open it. Anyone want to convert it to something other than a PDF?

[NiteRaider]

What are the odds that a Venoc Viper will be killed when attacked (rhetorical question)?