# PLS help me compute the odds!

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questccg
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Joined: 04/16/2011

Okay,

So I spent a couple of hours pondering more about my current Work-In-Progress (WIP) "Tradewars - Homeworld".

What has been bugging me is the point values on the cards. Obviously lower scoring ones can benefit from bonuses making each card relevant.

But when using the cards as Starships (not trade), weaker cards are left by the wayside as the game progresses. So I needed to find a NEW BALANCE. And this quick table summarizes what I am proposing to change:

1 value, roll +1d12 = values 2 to 13. Very random. Average roll = 7.5
2 value, roll +1d10 = value 3 to 12. Very random. Average roll = 7.5.
3 value, roll +1d8 = value 4 to 11. Less random. Average roll = 7.5.
4 value, roll +1d6 = value 5 to 10. Less random. Average roll = 7.5.
5 value, roll +1d4 = value 6 to 9. Even less random. Average roll = 7.5

As you may notice the Average rolls are IDENTICAL. This formulation makes the game "PERFECTLY BALANCED"!

My problem?

I need help computing the various ODDS for each encounter. Like is it true that a 5 value which varies between 6 to 9 is more advantageous ODDS-wise than a 1 value having values between 2 to 13...

So say 5 value (6 - 9) vs 1 value (2 - 13). What are the odds a 5 will beat a 1 and vice versa.

If someone can explain to me HOW to do the math, I can go on my Merry way and compute all the other possibilities like 3 vs 2, etc.

Many thanks!

stevebarkeruk
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Joined: 07/26/2008

Because you've made all the averages the same, these units will all effectively be equal when matched against each other.

There is a 50% chance of rolling higher or lower than average in every case (obviously) and just because the range on either side of average is different, that doesn't make one unit better than the other.

The only way the the higher value units could be more valuable would be if rolling close to the average result was good. E.G. If a roll of 7 or 8 is a critical hit and the further you are away from that, the worse you are, then the higher value units are stronger because they roll those numbers more often.

In the example of a 1 vs 5 fight, there is a 4/48 chance of a tie (i.e. 1/12 or 8.3%) and an equal 45.83% chance of either die "winning".

This is calculated from there being 4 x 12 possible outcomes, meaning 48. Of these, 4 would be the same value on each die (4/48), 22 would be die A being higher and 22 would be die B being higher. You can write out all the possible outcomes on a piece of graph paper or a spreadsheet; here's a link to a Google spreadsheet I put together to illustrate the point:

questccg
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Joined: 04/16/2011
So statistically...

Are you saying that "statistically" ALL the cards would be the SAME (odd-wise)?

I'm not 100% sure this is true. Using exhaustive listing I get DIFFERENT results (for outcomes - beats in the following table).

• 5 vs 1: 22 (45%) / 26 (55%) = 48 (100%)
• 5 vs 5: 6 (35%) / 10 (65%) = 16 (100%)

What this sample says is that it would be MORE advantageous to use a smaller starship to battle a big one (when attacking). Does this make any sense? IDK...

Note: this assumes that ties go to the defender...

stevebarkeruk
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Joined: 07/26/2008
Ties going to the defender

Ties going to the defender does make a difference, yes, because then there are no ties. But the chances of a tie are the same between any pair of dice, regardless of who is the attacker, and who the defender. i.e. in a 5 vs 1 scenario there is a 1/12 chance of a tie, no matter which die is the defender.

It's worth noting that ties would occur more frequently if the dice are both smaller. i.e. two D4s rolling off will tie 1/4 of the time whereas two D12s will only tie 1/12 of the time.

In any case, yes, I am saying that all of these are effectively equal, if we assume they all act as attacker and defender as much as one another.

questccg
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Joined: 04/16/2011
I think,,,

I'm not going to implement this change. Although it could be interesting, it makes each starship capable of defeating any opponent starship (with a little luck).

I was hoping the extra balance would make the game MORE strategic. And from the looks of things - that is simply not the case.

Thank you!

Update: Even if I was to add things to the "Red Alert" Expansion, I still feel that a mechanic using more LUCK is NOT the way to go... I think with the current mechanics, starships are more tactical than before.