Dragonwood dice probabilities

I recently played the dice and card game dragonwood for the first time and loved it! It's not easy to find a game that is both interesting AND can be easily be understood by young kids. It was simple enough to explain in just a few minutes, and it held the attention of four kids ages 7 - 11 for an hour.

It uses six 6-sided dice with numbered faces; but the numbers are not like a normal 6-sided die. Instead, there is one face with a 1, two faces marked 2, two faces marked 3, and the last face is a 4. You need to roll a certain number or better to capture mosters (scoring points) and the number of dice you can use is determined by the cards you hold. So to play well, you need to be able to make decisions like "Should I try to roll that 8 now with three dice, and risk losing a card if I don't get it; or should a take another card now and hopefully be able to use four dice next turn, but risk my opponents getting it first?". The data in the charts below will help you make well-informed decisions to that kind of question. But since getting kids to get a feel for this kind of thing is one of the great things about this game, perhaps you shouldn't print this out, or have your mobile open to this page while you play!

How does it work?

After the game, I thought I should be able to figure out these odds with a pencil and paper; but its been too long since probability class and I didn't make much progress! So instead, I used SQL cross-joins to enumerate all possible results of rolling 1 dice, 2 dice, etc. I then added up the values on the die faces in each possible outcome and counted how many times I ended up with each sum and divided by how many results were possible. This approach should be easy to modify for dice with different face values or numbers of sides.

The Results!

How many dice should I use?

If you want to roll a certain target number; but don't know how many dice you'll need to have a reasonable chance of success, use this table. In the example above, we wanted to roll an 8 to capture a particular monster. Scroll down this chart untill you see 8 in the desired result column. There you can see that while its possible with only 2 dice, the chances are pretty slim at just over 2%. If you can use 3 dice, your chances are an even 50%; but if you can manage a fourth dice, your chances go up to a pretty good 90%. If you don't see a row for your combination of result and number of dice; that means there is no chance! You can't roll a 9 with only two dice for example.

Desired result	Number of dice	Your percent chance of rolling that or better with this number of dice
1	1	100
2	1	83.333
2	2	100
3	1	50
3	2	97.222
3	3	100
4	1	16.667
4	2	86.111
4	3	99.537
4	4	100
5	2	63.889
5	3	96.759
5	4	99.923
5	5	100
6	2	36.111
6	3	88.426
6	4	99.306
6	5	99.987
6	6	100
7	2	13.889
7	3	72.222
7	4	96.836
7	5	99.859
7	6	99.998
8	2	2.778
8	3	50
8	4	90.355
8	5	99.216
8	6	99.972
9	3	27.778
9	4	78.009
9	5	97.094
9	6	99.818
10	3	11.574
10	4	60.108
10	5	91.95
10	6	99.205
11	3	3.241
11	4	39.892
11	5	82.279
11	6	97.404
12	3	.463
12	4	21.991
12	5	67.747
12	6	93.263
13	4	9.645
13	5	50
13	6	85.55
14	4	3.164
14	5	32.253
14	6	73.667
15	4	.694
15	5	17.721
15	6	58.338
16	4	.077
16	5	8.05
16	6	41.662
17	5	2.906
17	6	26.333
18	5	.784
18	6	14.45
19	5	.141
19	6	6.737
20	5	.013
20	6	2.596
21	6	.795
22	6	.182
23	6	.028
24	6	.002

Whats the highest number I have a reasonable chance of rolling?

If you know how many dice you'll be rolling and want to know your chances of rolling a given number, use this chart. For example, this turn you can only manage three dice so you scroll down until you see 3 in the number of dice column then look in the target result and percent chance columns to know that you have an 88% chance of rolling a 6 or better; but only a 27% chance of a 9 or better. You'll still have to decide if captuing that 1 point monster this turn is worth losing your card(s) and having fewer next turn!

Number of dice	Target result	Percent chance of rolling that target or better
1	1	100
1	2	83.333
1	3	50
1	4	16.667
2	2	100
2	3	97.222
2	4	86.111
2	5	63.889
2	6	36.111
2	7	13.889
2	8	2.778
3	3	100
3	4	99.537
3	5	96.759
3	6	88.426
3	7	72.222
3	8	50
3	9	27.778
3	10	11.574
3	11	3.241
3	12	.463
4	4	100
4	5	99.923
4	6	99.306
4	7	96.836
4	8	90.355
4	9	78.009
4	10	60.108
4	11	39.892
4	12	21.991
4	13	9.645
4	14	3.164
4	15	.694
4	16	.077
5	5	100
5	6	99.987
5	7	99.859
5	8	99.216
5	9	97.094
5	10	91.95
5	11	82.279
5	12	67.747
5	13	50
5	14	32.253
5	15	17.721
5	16	8.05
5	17	2.906
5	18	.784
5	19	.141
5	20	.013
6	6	100
6	7	99.998
6	8	99.972
6	9	99.818
6	10	99.205
6	11	97.404
6	12	93.263
6	13	85.55
6	14	73.667
6	15	58.338
6	16	41.662
6	17	26.333
6	18	14.45
6	19	6.737
6	20	2.596
6	21	.795
6	22	.182
6	23	.028
6	24	.002