The "Bloodybacks" rules mechanism

The recent versions of my Bloodybacks AWI rules use a very specific die rolling mechanism and I thought it might be of use or interest to include a bit more information on the probabilities associated with this. In version 9 of the rules, this "136=123" mechanism has only been retained for unit activation.

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1. Activation rolls

I'll start with a look at the version of the system that deals with unit activation (and which was also used to resolve shooting in Bloodybacks 8)

The essence of the system is to roll a "hand" of six dice. I use d12s. The hand can be reduced or increased in size. Each of the dice rolled needs to score a "to succeed" number or under. The number of successes are totalled and this is translated into a number of orders, hits or whatever the outcome measure may be.  Let's describe them as "hits" for now. This translation as based on a triangle meaning that one success gives one hit, three successes are needed for two hits and six or more successes for three hits. With a larger hand of dice ten successes would produce four hits and so on, however there is a practical limit to the sensible size of the hand of dice I find.

Mechanisms such as this permit the game designer to control the range of possible outcomes. In this case it is zero to three. This level of control can be very helpful. As an example, I find this a preferable method of determining results in order systems such as seen in Warmaster or Black Powder as it tends to result in fewer absolute failures and better engagement for the players.

Below I present a series of tables that show the range of outcomes for various numbers of d12s and "to succeed" values. These were determined by creating a model within an Excel spreadsheet that simulated 10,000 hands of dice being rolled, so they are not absolute but give a fair impression of the expected probabilities. Where a value of 0% is indicated, this is a possible outcome but very unlikely. 

To succeed = 1
	3d12	4d12	5d12	6d12	7d12	8d12
zero hits	76%	70%	64%	59%	54%	49%
one hit	23%	30%	36%	41%	45%	48%
two hits	0%	0%	0%	0%	0%	0%
three hits	Not possible			0%	0%	0%

To succeed = 2 or less
	3d12	4d12	5d12	6d12	7d12	8d12
zero hits	58%	48%	40%	34%	28%	23%
one hit	42%	51%	57%	61%	62%	63%
two hits	0%	1%	3%	6%	10%	14%
three hits	Not possible			0%	0%	0%

To succeed = 3 or less
	3d12	4d12	5d12	6d12	7d12	8d12
zero hits	43%	32%	25%	18%	14%	10%
one hit	56%	63%	65%	65%	63%	58%
two hits	1%	5%	10%	17%	24%	31%
three hits	Not possible			0%	0%	0%

To succeed = 4 or less
	3d12	4d12	5d12	6d12	7d12	8d12
zero hits	30%	20%	13%	9%	6%	4%
one hit	67%	69%	66%	59%	51%	43%
two hits	4%	11%	11%	32%	42%	51%
three hits	Not possible			0%	1%	2%

To succeed = 5 or less
	3d12	4d12	5d12	6d12	7d12	8d12
zero hits	20%	11%	7%	4%	2%	1%
one hit	73%	69%	59%	48%	36%	27%
two hits	7%	20%	35%	48%	59%	65%
three hits	Not possible			0%	2%	6%

To succeed = 6 or less
	3d12	4d12	5d12	6d12	7d12	8d12
zero hits	13%	7%	3%	2%	1%	0%
one hit	75%	63%	47%	33%	22%	14%
two hits	12%	31%	49%	63%	71%	72%
three hits	Not possible			1%	6%	14%

To succeed = 7 or less
	3d12	4d12	5d12	6d12	7d12	8d12
zero hits	7%	3%	1%	1%	0%	0%
one hit	73%	52%	33%	20%	11%	6%
two hits	20%	45%	65%	76%	75%	66%
three hits	Not possible			4%	13%	28%

To succeed = 8 or less
	3d12	4d12	5d12	6d12	7d12	8d12
zero hits	4%	1%	0%	0%	0%	0%
one hit	67%	39%	21%	10%	4%	2%
two hits	29%	59%	79%	81%	70%	51%
three hits	Not possible			9%	26%	47%

To succeed = 9 or less
	3d12	4d12	5d12	6d12	7d12	8d12
zero hits	1%	0%	0%	0%	0%	0%
one hit	56%	25%	10%	4%	1%	1%
two hits	43%	74%	90%	78%	54%	32%
three hits	Not possible			18%	45%	68%

To succeed = 10 or less
	3d12	4d12	5d12	6d12	7d12	8d12
zero hits	1%	0%	0%	0%	0%	0%
one hit	42%	13%	4%	1%	0%	0%
two hits	57%	87%	96%	66%	33%	14%
three hits	Not possible			33%	67%	86%

To succeed = 11 or less
	3d12	4d12	5d12	6d12	7d12	8d12
zero hits	0%	0%	0%	0%	0%	0%
one hit	23%	4%	1%	0%	0%	0%
two hits	77%	96%	99%	41%	11%	2%
three hits	Not possible			59%	89%	98%

2. Melee rolls

The mechanism for resolving melee also involves a hand of 6 d12. In version 8 of Bloodybacks there was no modifier to the number of dice rolled and results were calculated in the same "136=123" way as activation and shooting. The attacker again has a "to succeed" number starting at a basic 6 which is modified upwards in the attacker's favour or downwards in the defender's favour. As with the other mechanism this constrains the range of possible outcomes while adjusting the probability of each. The following table demonstrates this:

Outcome
	Major win	Minor win	Draw	Minor loss	Major loss
Attacker loss:	0	1	2	2	3
Defender loss:	3	2	2	1	0
To succeed #:
1	0%	0%	1%	40%	59%
2 or less	0%	1%	5%	60%	34%
3 or less	0%	4%	13%	65%	18%
4 or less	0%	10%	21%	60%	9%
5 or less	0%	20%	29%	47%	4%
6 or less	1-2%	33%	31%	33%	1-2%
7 or less	4%	47%	29%	20%	0%
8 or less	9%	60%	21%	10%	0%
9 or less	18%	65%	13%	4%	0%
10 or less	34%	60%	5%	1%	0%
11 or less	59%	40%	1%	0%	0%

As with the previous tables, probabilities were estimated from a model created in Excel to simulate around 10,000 hands of dice being rolled. Probabilities of "0%" actually represent unlikely but still possible outcomes.

I hope that at least someone finds this interesting and possibly useful in your own games design projects.