Bringing d100 to 2d6

With the conversion of d20 table-top roleplaying game systems into BITS’s 2d6, I figured we should follow up with another incredibly popular system of d100.

About d100

In d100, two 10-sided dice are rolled, one being the 10s spot on a number, the other being the 1s spot.

A player’s character has stats or attributes that represent how good they are at certain things. These could be numbers from 1 to 99, 0 and 100 reserved for critical failure or success on rolls.

There are two kinds of d100 system: roll target or under, and, roll target or over. Because the latter requires a lot more math for reasons I’ll leave out here, the rest of this post only deals with rolling at a target number or under 🙂

When a roll needs to happen, the rolling player picks their best applicable attribute. When rolling, the value of the roll must be at or under that target. So while the attributes of the character increase as they experience the game, so too do rolls get easier!

That’s d100 at a glance.

Roll %s

To get from d100 to 2d6, we need to talk percentages.

A d100 has an average value of 50.5, or that ~51 and above will happen half the time. Makes sense. 2d6 averages at 7, where any number at or above that comes out 58.33% of the time.

But 58.33% is a significant departure from 50.5%! However, if we consider percentages are rounded down, that 58.33% can become 50%. With that bit of fudging, percentages are back in safe waters.

Ability Score to BITS

This is where the conversion happens.

How can a player know what their d100 stat is in BITS 2d6?

Easy: consider everything below average is a 0 in BITS while dividing everything above into decreasing proportions.

A simple use of the 1-2-3-4 nature of BITS is we invert how much weight is put on each element. A 1 should have 40% ownership of anything next above average, 2 30% after that, 3 20%, and 4 10%.

Starting at the lowest percentage of 10%, 10% of the 2d6 average percent of 58.33 is 5.833. Since it has already been decided rounding down is key here, the value of 4 in BITS will own the last 5% of all scores and 1 will get 20% of the total.

That’s a bit wordy. Here’s a chart:

d100 Value RangeBITS Value
1-500
51-701
71-852
86-953
96-1004
Give or take 1 on the d100 Value Range.

Easy, right?

And, depending on what’s available for a given game, group skills and abilities equally under each BIT (Body, Interaction, Thought) to get that BIT’s value. Average together the values there, round down (if needed), compare with the chart above.

Easy!

Other Considerations

Now I know some d100 systems use additional scores that aren’t based on 100. Some systems use poly-dice.

For those numbers in those systems, I refer you back to my d20 poly-dice conversion post. That can convert Dungeons & Dragons and it can convert here too.

Applicable Games

Any game that uses a d100 system!

(Though I must admit my exposure to d100 systems is much lacking compared to d20s and polyhedrals.)

If it is a weird one with a roll-over mechanic, there shouldn’t be too much fiddling with the values to get things back on track. Set everything below-average to 0, then divide-up the remainder with 40%-30%-20%-10%.

Some games using the d100 system:

Missteps Along the Way

That’s the end of the d100 conversion so you may move on to another article on this site.

If you’d like to know what was was reviewed before the above was settled on, keep reading ~

Don’t think that I had all of the formulas and math pop into my head at once. I looked up dice probabilities and ran multiple graphs to confirm what was both mathematically sound and friendly (i.e. easy) for player use.

However, starting off with the wrong premise can make any outcome moot.

The first failure was looking at the value of 1 as a percentage of 2d6. That’s 14.3% (1/7, the average value). Because it handles better, say 15%. 15% per point of BITS value (best calculated starting at 4 and going down to 1 at 60%.

This looked fine to start:

    • BIT Value – d100 Conversion
    • 0 – top 100%, nothing special.
    • 1 – top 60%, a 40 and above in d100 gets 1, OK.
    • 2 – top 45%, 55+, good.
    • 3 – top 30%, 70+, great.
    • 4 – top 15%, 85+, excellent.

But you can see already that a value of 1 allows below-average performance to attain above-average results. Further, the progression is linear, whereas 2d6 is inherently parabolic (lines and curves don’t mix).

Scrap that.

Next I figured out the value of 1 in 2d6 for above-average values. I.e., what is 14.3% of 41.67% (difference of 58.33% average)?

The answer is 6, but already the premise is wrong – I was using the below-average range to affect the above-average allocation of BITS values.

Lame!

But that didn’t stop me from using 42% with the 40%-30%-20%-10% conversion. This actually got really close to the final result, but I rounded down first (i.e. I stepped by 4% of the total):

    • 0 – >0
    • 1 – >60
    • 2 – >76
    • 3 – >88
    • 4 – >96

Ignoring that these numbers look kind of ugly, if we round up (4.2% is 10% of 42%, rounding up to 5%), we get what turns out to be the final conversion:

    • 0 – >0
    • 1 – >50
    • 2 – >70
    • 3 – >85
    • 4 – >95

So despite starting from the wrong place, we got to the correct answer 🤷‍♂️ Wild how that works!

Anyway, I caught these mistakes before and during writing, so now you can see some of the method that goes into the consideration of BITS and other systems 🙂

The End

Appreciate you getting this far, reader.

For the d100 games you’ve played, what considerations are missing from the above? Did they get handled in last week’s d20 poly-dice blog? How could this all be improved?

Will be writing more on BITS for a while yet, so stick around! Cheers ~

Published by

Jimmy Chattin

Processor of data, applier of patterns.

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