Using Math to Win Heroscape

[Alex Karasavidis]

One day in math class I was thinking would it be possible for me to use percentages and probability to help me win games of Heroscape. You will be interested to know you can!
Heres an example of using probability for Atlaga thy Kyrie Warrior. Atlaga is facing Braxes with no glyphs and no height advantage and Braxes has full health
Bolt of Witherwood needs to roll a 15 or higher to kill that figure. Or you may attack with four dice what will you do when Braxes has a chance to kill you next round.
You have 25% chance of having bolt of witherwood working or a 50% chance for one die to roll a skull. That means you have 4 50% chances to half kill Braxes or one 25% chance of killing Braxes.
This is one very simple example but there are many other variables effecting the probability such as height, lives, glyphs, and abilities could change the course of the game.
I hope this is making sense feel free to ask questions on it because I know this is hard. If people take an interest in this I will be more than happy to put more figures probability and go even deeper in this. If your someone whose really interested watch a show called beating the Roulette wheel on history channel which shows you probability that I try using and it also inspired me to make this thread.

I hope this proves very effective for the readers,

Alex

[greygnarl]

Atlaga can shoot and Witherwood on the same turn. Other than that, I'd say that this post doesn't really cover much new ground. If you are interested, here is a great post with a whole section of Mathscape threads.

[Heroscaper Guy]

There will always be variables though. Dice won't go your way or your opponent will see your plan and wreck it. You can minimize variables but not completely.

[Alex Karasavidis]

Yea your all right I just thought this would help.

[Aldin]

Originally Posted by Alex Karasavidis

That means you have 4 50% chances to half kill Braxes or one 25% chance of killing Braxes.

To take this a bit further, rolling four dice will be four skulls 6.25% (1/16) of the time at which point Braxas rolls defense dice with a roughly 70% (19/27) chance of getting at least one shield. So your expected damage on the regular attack is roughly 2 wounds, though anywhere from 1-3 would be typical. So on average, if Bolt of Witherwood fails, it will take Atlaga 4 turns to take down Braxas - assuming she doesn't manage to take him down first.

~Aldin, strongly recommending greygnarl's link as a great starting point for further investigation

[wriggz]

It is good that you are thinking about the units in a different way. There are lots of subtitles of various units and how the work together.

Keep theoryscaping, do some research and don't give up.

[El T]

I have been musing to myself recently about creating a sort of formula for determining an overall numerical score for cards, to help come up with a "draft board" and such.

The hard part would be to account for special attacks and vulnerability to opponents' special attacks.

This means that creating a formula would be infinitely easier for the Basic game, but of course basic games are for no0bs and nobody really plays them. Still, might be worth coming up with a formula for basic, and then building off it for the advanced game.

Thoughts?

[wriggz]

Heroscape Card Calculator:

This was some early work I did on the project. Trust me it will drive you crazy.

[ollie]

Probability Notes that use Heroscape as an example. Alex, you might find them helpful in your calculations.

[OEAO]

Originally Posted by Aldin

To take this a bit further, rolling four dice will be four skulls 6.25% (1/16) of the time at which point Braxas rolls defense dice with a roughly 70% (19/27) chance of getting at least one shield. So your expected damage on the regular attack is roughly 2 wounds, though anywhere from 1-3 would be typical. So on average, if Bolt of Witherwood fails, it will take Atlaga 4 turns to take down Braxas - assuming she doesn't manage to take him down first.

~Aldin, strongly recommending greygnarl's link as a great starting point for further investigation

Wouldn't it be 1 wound? Atlaga should roll 2 skulls and Braxas should roll 1 shield. I'm not sure where you are getting 2 wounds.

[Knight of Scape]

Originally Posted by OrcElfArmyOne

Wouldn't it be 1 wound? Atlaga should roll 2 skulls and Braxas should roll 1 shield. I'm not sure where you are getting 2 wounds.

It is not quite as simple as you are thinking. But it is not quite as extreme as Aldin is saying either. The problem with both approaches can easily be demonstrated.

If the average damage was the difference between the average number of skulls and the average number of shields, almost no one would ever be able to wound Deathwalker 9000. Drake would average 3 skulls, DW would average 3 shields, Drake's average damage would be zero. In any case where the defender rolls at least one die, the average damage will be greater than the difference between the average number of skulls and the average number of shields.

What this calculation will actually find is the average difference between the attacker's number of skulls and the defender's number of shields. The problem is, in heroscape, it is impossible to deal a negative number of wounds. If the attacker rolls 1 skull and the defender rolls 3 shields, the damage is not 1 - 3 = -2, it is 0. This means that your calculation is summing wrong values for every case where the defender rolls more shields than the attacker rolls skulls. The magnitude of this error will depend on how high the defender's defense is, relative to the attackers attack.

It actually turns out that, in this case, you are closer than Aldin. A useful tool for these things is Sisyphus' Probability Tables (because calculating this stuff by hand is a pain).

The tables will tell you that the average damage of 4 attack on 3 defense is 1.15 wounds. This is more than 1, as predicted, but a lot less than 2. Also, (this is very useful against squads, where extra damage is overkill) the tables tell you that the chance of inflicting at least one wound with 4 dice on 3 defense is 65.5%.

If you want to simulate a whole matchup in this manner, mathguy's matchup calculator is really nice. It can tell you that Atlaga has a 24% chance of beating Braxas head to head without his witherwood. You have to be careful how you use it, however. It does not take into account things like range and move (although you can somewhat simulate those with initiative bonuses, and sometimes its simulation of special powers is a bit non-optimal.

For example, the default Atlaga vs. Braxas calculation assumes Braxas uses Poisonous acid breath instead of her normal attack every time. But this is not actually her best strategy. If you take away PAB from Braxas' powers, Atlaga's win chance drops to 4.3%!

Moral of the story, probability is hard, so let other people do it for you when you can.

~KoS, who has spent too much time calculating probabilities like 3 attack on 2 defense in his head because he did not have a calculator/computer/table of values handy.

[Bobofdeath's Dad]

Originally Posted by Alex Karasavidis

One day in math class I was thinking would it be possible for me to use percentages and probability to help me win games of Heroscape.

Alex

As a high school math teacher I must ask if you were thinking more about playing Heroscape or the mathematical probabilities involved in the game, while you were in math class?

Of course, if Heroscape was entirely about "theoretical probabilities" then players could choose an army, plug them into a Heroscape percentage calculator and find out who won without playing the actual game. While that would not be much fun it would have saved me a LOT of money for figures and terrain. All I would need is the stats for each figure.

Thankfully there is "experimental probability" which is why Deathwalker 9000 only needing ONE shield to survive an attack while rolling 9 defense dice can still die.