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Subject: Math Crusade rss

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Benjaymun Benjaymun
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A few observations from running a Monte Carlo program on various space crusade math situations:

Each light weapons die averages ".5". So a bolter marine without targeter can reliably shoot just gretchin.
Each heavy weapons die averages "1". This means that a heavy weapons marine without targeter can reliably shoot and kill orks.
A reroll is almost statistically identical to adding another die of the largest type rolled. This means that a heavy weapons marine with targeter can reliably shoot and kill chaos marines.

This means that a heavy weapon with targeter has equivalent performance to an extra heavy weapon. The upshot of that is that it may only be worth taking extra heavy weapons if you either run out of targeters, or are unwilling to spend equipment slots on them.

I'll add some more I've discovered later.
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Paul Dale
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Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn
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No need for a simulation here, the averages of various attacks can be worked out exactly. I did this years ago and have a note somewhere with the various probabilities.

You missed the variance -- a white die has a 2 in 3 chance of rolling a zero e.g. With two white dice, you've a 4 in 9 chance of rolling a zero total i.e. about 44% and a 5 in 9 of killing that Gretchin (about 56%). Not exactly reliable :-)

There is a nice probability table in the files section too.


- Pauli
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Benjaymun Benjaymun
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Heh, true. What I meant when I said "reliably" is what target choice the weapon can most optimally be relied upon to take out, without overkill or underkill - I offer no guarantee that it will!

In other words, a bolter marine without targeter should probably choose a gretchin to shoot at if given a choice between it and harder targets, such as orks or chaos marines. He's probably going to roll too low to take out those targets, and waste a shot that might have taken down a grot.

The real surprise for me was the reroll's equivalency to adding another die, under most scenarios. That I did not expect. It makes targeters and the various commander reroll items even more "must-takes" than they already were.

On a related note, that table needs updating to include rerolls. I think they've been excluded because the probability math is not straightforward (involving if...then...else clauses), thus my use of a monte carlo simulation to derive the chances.

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Benjaymun Benjaymun
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As those who analyse the probabilities know, it's almost always in the alien player's interest to seek close combat. This leads me to wonder whether the "blood angels bolter squad" could be played in a way to shutdown, or at least penalise this mode of play from the alien player. I theorise that most people are playing the squad wrong. Perhaps it can be made viable with the following ground rules:

1) Run from and shoot all orks and gretchin. Do not allow them to close and engage in close combat. The 6 move of the bolter marines gives them a fighting chance of outrunning them. If there's unknown blips to be revealed, then the force fielded commander can do that.

2) Engage with combat blades hard targets that targeter'd bolters cannot be relied upon to take out, such as genestealers, chaos androids and chaos marines, but do not leave a marine in a position where he can be close assaulted by other aliens (unless it's the commander).

3) Leave the dreadnaught to the commander.

I suspect that marine players who take the full bolter loadout (bolt pistols, close assault blades, and targeter on bolters) make the mistake of mixing it up in close combat with orks and gretchin, which is a recipe for getting killed. Saving the close combat risk for the harder targets may work. Will have to try this.
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Paul Dale
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I suspect the squaddies will still die horribly..... Hand to hand is simply too dangerous.

A reroll is almost exactly an extra die -- look at the number of zeros on the dice.


- Pauli
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Old Gamer
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Benjaymun wrote:
Heh, true. What I meant when I said "reliably" is what target choice the weapon can most optimally be relied upon to take out, without overkill or underkill - I offer no guarantee that it will!


Yes, but the mean is of very little use in this case. The mode would be appropriate for identifying which target you can kill exactly.
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Robert Stewart
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Benjaymun wrote:
I suspect that marine players who take the full bolter loadout (bolt pistols, close assault blades, and targeter on bolters) make the mistake of mixing it up in close combat with orks and gretchin, which is a recipe for getting killed. Saving the close combat risk for the harder targets may work. Will have to try this.


Taking on Gretchin diagonally with three white dice against none is entirely equivalent to shooting at them with two white dice and a reroll against 0 armour.

Three white dice against one (diagonal against an Orc or Chaos Marine/Commander) gives a roughly 1/8 chance of dying, and a better than 50% chance of a kill, meaning you only face another attack less than half the time. Meanwhile, shooting at an Orc with two white dice and a reroll, you have a precisely 1/3 chance of a kill and a 2/3 chance of them getting to attack you back.

I haven't run the numbers on the counter-attack (which also depend on whether the Orc attacks the Bolter or can engage a Heavy Weapon instead) but I suspect that in a target-rich environment, the quicker kills favour the Marines, while with a lone Orc against an entire squad, the Marines should at least start out shooting.
 
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