Percentiles with just d6s

[Malchor]

Not sure if this is the right place, but here goes.

We know about Korns and Carr's use of d6 to generate percentile results in approximated 5% increments. We also know Arneson was said to have had a thing for percentiles and the Blackmoor players use mostly (if not only) 2d6 somehow. 

This led me to put Korns and Carr on a table to compare (Carr's version is better as it is slightly more accurate and consistently uses 2d6). Then I cast about for some alternatives and found one in an AH golf game that with a tweak can actually accomplish 5% increments, not just an approximation—and for an earlier, if not complete example, Table K in Totten's Stratego.


Here is the spreadsheet if you care to have a look:
docs.google.com/spreadsheets/d/1s5AsYX843bN5lmbtF-0lzw3M8PNkTwBmcD8znf4l-RM/edit?usp=sharing

Found another source, a military War Games book from 1960 (though it was revised in 1966, so hard to tell what was original and what was revised): odd74.proboards.com/post/213347


Edit: Nope the AH golf game system is not an even distribution. Updated this on Google Sheets above.

[Starbeard]

The table you pulled from the AH golf game is great. Not only does it replicate 5% increments, but you also get a special wild card roll (1,1) which can be ignored or reserved for critical or unusual results.

[waysoftheearth]

You can also get precise 5% increments with six-sided side like I wrote up here: odd74.proboards.com/thread/6208

Albeit, you need three dice to do a d20

[Malchor]

Oct 24, 2018 19:01:49 GMT -6 Starbeard said:

The table you pulled from the AH golf game is great. Not only does it replicate 5% increments, but you also get a special wild card roll (1,1) which can be ignored or reserved for critical or unusual results.

I am trying to figure out how to simulate the AH golf game on anydice.com. It might actually be a perfect 5% increment. There are two ways to get 1-2 (a 1 and a 2 or a 2 and a 1) but only one way to get a 1-1.


Edit: figured this out. it is not even distribution, as seen here  anydice.com/program/120e4 SaveSaveSaveSave

[Malchor]

Oct 25, 2018 5:10:46 GMT -6 waysoftheearth said:

You can also get precise 5% increments with six-sided side like I wrote up here: odd74.proboards.com/thread/6208

Albeit, you need three dice to do a d20

Was going to add a 3d6 version to show how close you get with 3d6 to 5% increments, but life got in the way and I realized I need to prove out the  AH golf distribution, it might not be as flat as I first thought.SaveSave

[Starbeard]

Yeah, I looked at the AH one again and noticed the same thing. You can visualize the weighting easily just by listing the possible results:

11
12 = 21
13 = 31
14 = 41
15 = 51
16 = 61
22
23 = 32
24 = 42
25 = 52
26 = 62
33
34 = 43
35 = 53
36 = 63
44
45 = 54
46 = 64
55
56 = 65
66

The doubles all have one chance of popping up, but each other number combination have two chances. You can group the doubles together in pairs (1,1 and 2,2 make 5%, 3,3 and 4,4 make 35%, etc.) but then you only get up to 90%, or a d18. Incidentally, if you ignore doubles then you can simulate a d14.


The only way I can think of to get true 5% increments with a single roll of 2d6 is to ignore 6s on the first die and ignore 5-6s on the second die.

1,1 = 5%
1,2 = 10%
1,3 = 15%
1,4 = 20%
2,1 = 25%
2,2 = 30%
2,3 = 35%
2,4 = 40%
3,1 = 45%
3,2 = 50%
3,3 = 55%
3,4 = 60%
4,1 = 65%
4,2 = 70%
4,3 = 75%
4,4 = 80%
5,1 = 85%
5,2 = 90%
5,3 = 95%
5,4 = 100%

[Malchor]

One OD&D (and Holmes, since that where it first irked me) roll that always had me scratching my head is Wondering Monsters.

Unless I am mistaken, which is quite possible, all other 1d6 checks by the DM are on a 1, 1-2, 1–3 or 1-4, but Wondering Monster show up on a 6.

This is kind of trivial as the result is the same, but from a usability standpoint it makes little sense and is an outlier, all other chance rolls on a d6 starting at 1. So why make people think about it, and no it does not matter if it is just a little extra thought, it is extra cognitive load that a user (aka the DM) should not need to deal with. Since a 6 rather than a 1 serves no functional reason and a conversion of starting at 1 for chance rolls is established, then this looks like a design revision oversight—as in all of the other numbers where adjusted, but this one was overlooked. 6 is also the roll for a 15% chance on both Korns and Carr.

One last note: 5e is still a 15% for wandering monsters, just called a "random encounter" now, rolled on a d20 with 18 or higher.

[derv]

It's likely an extension of the Wilderness Wandering Monster method where you would roll one d6 and consult the matrix. There are variable chances of getting lost or having an encounter based on terrain. In clear terrain there is a 16% chance of getting lost or a 16% chance of having an encounter- a 33% chance of one or the other happening per turn. Encounters occur on rolls of 4-6. Getting lost occur on 1-3.

[Starbeard]

Considering that, according to testimony, wilderness adventuring was added after dungeon expeditions, I'd assume that the wilderness tables were an extension of the WM tables.

Wandering Monsters are encountered on a high roll. This could have carried over into the Wilderness Monsters, which are also encountered on high rolls (but how high is now determined by terrain type).

The roll for getting lost I think was likely influenced by Outdoor Survival, where high rolls are better on the movement table. If you roll low, that's bad and you get lost. The Getting Lost check has the same grades as Wilderness Encounters: 1/6 for easy terrain, 2/6 for moderate terrain and 3/6 for difficult or dangerous terrain, but one is a high roll because that was already being used in the dungeon for encounters, and one is a low roll because 1) it's that's how the other game did it, and 2) it's makes for easy to visually & cognitively differentiate between the roll types by having them shoot for different number ranges (otherwise, they'd look 100% identical).

I do think it's a lot easier overall to keep the rolls similar, so I make all encounters roll low instead of high. A 1 in 6 chance is always rolled on a 1 for me.

[Malchor]

Oct 28, 2018 9:39:17 GMT -6 derv said:

It's likely an extension of the Wilderness Wandering Monster method where you would roll one d6 and consult the matrix. There are variable chances of getting lost or having an encounter based on terrain. In clear terrain there is a 16% chance of getting lost or a 16% chance of having an encounter- a 33% chance of one or the other happening per turn. Encounters occur on rolls of 4-6. Getting lost occur on 1-3.

Ah. That makes sense.SaveSave

[Starbeard]

So I've had a thought: is it possible to reduce the wilderness lost and encounter rolls into a single roll that accounts for both? The answer is yes, using 2d6, and there are only a couple of instances where the chances have to be altered by significantly less than 1%.

…And the best part is that getting lost remains at the low end of the roll, and encounters remain at the high end!

Clear (lost 1/6, encounter 1/6)
Chance to get lost: 13.88%
Chance for an encounter: 13.88%
Chance for both: 2.77%

Woods (lost 2/6, encounter 2/6)
Chance to get lost: 22.22%
Chance for an encounter: 22.22%
Chance for both: 11.11%

River (lost 1/6, encounter 2/6)
Chance to get lost: 11.11%
Chance for an encounter: 27.77%
Chance for both: 5.55%

Swamp (lost 3/6, encounter 3/6)
Chance to get lost: 25%
Chance for an encounter: 25%
Chance for both: 25%

Mountains (lost 2/6, encounter 3/6)
Chance to get lost: 16.66%
Chance for an encounter: 33.33%
Chance for both: 16.66%

Desert (lost 3/6, encounter 2/6)
Chance to get lost: 33.33%
Chance for an encounter: 16.66%
Chance for both: 16.66%

City (lost 0/6, encounter 1/6)
Chance to get lost: 0%
Chance for an encounter: 16.66%
Chance for both: 0%

2d6	Clear	Woods	River	Swamp	Mountains	Desert	City
2	Lost	Lost	Lost	Lost	Lost	Lost	–
3	Both	Both	Both	Both	Lost	Lost	–
4	–	Lost	Lost	Lost	Lost	–	–
5	Lost	–	–	–	–	Lost	–
6	–	–	–	Lost	–	Lost	–
7	–	–	–	Both	Both	Both	–
8	–	–	–	Enc.	Enc.	–	–
9	Enc.	Enc.	Enc.	–	Enc.	–	–
10	–	Enc.	Enc.	Enc.	–	Enc.	Enc.
11	Both	Enc.	–	Both	Enc.	Enc.	Enc.
12	Enc.	Enc.	Enc.	Enc.	Enc.	Enc.	Enc.

Of course, the downside to this table is that it is much more difficult to alter chances on the fly: for example, what if the party is exploring Clear terrain that happens to be overrun by war, or in particularly foggy weather?


Once you have the percent chances, of course you can use whatever die types you like. It's easy enough to turn those probabilities into d20 or d% rolls (which in turn can be simulated using 2d6 or 3d6!), and that would be far easier to modify.

[derv]

Oct 28, 2018 10:34:01 GMT -6 Starbeard said:

Considering that, according to testimony, wilderness adventuring was added after dungeon expeditions, I'd assume that the wilderness tables were an extension of the WM tables.

If you're talking about the original Blackmoor, I don't think either table in the LBB's is a true representation. In the FFC the wilderness encounter matrix appears to use a d20.

I think Gygax was just trying to keep things uniform in the LBB's.

[waysoftheearth]

Oct 28, 2018 9:39:17 GMT -6 derv said:

It's likely an extension of the Wilderness Wandering Monster method where you would roll one d6 and consult the matrix. There are variable chances of getting lost or having an encounter based on terrain. In clear terrain there is a 16% chance of getting lost or a 16% chance of having an encounter- a 33% chance of one or the other happening per turn. Encounters occur on rolls of 4-6. Getting lost occur on 1-3.

Probably, the above point may be worth it's own topic.

I agree the table of U&WA p18 implies what derv wrote. However, the implication of this is that one can never be lost AND meet an encounter, or---in the case of swamp---one will ALWAYS get lost OR meet an encounter. Seems a bit counter-intuitive to me.

On the other hand, U&WA p17 doesn't explicitly state one throw is used to check for both getting lost and meeting an encounter. Actually, the text talks about the chance of getting lost in one section, then the chance of meeting an encounter in the next section. From this alone I don't think it's so wild a stretch to check them independently.

Either way, rolling independently for these events opens up the interesting possibility that one or other or neither or both events can occur. I enjoy the additional variability... YMMV.

[Starbeard]

I've always interpreted them as two separate rolls, partly because I first read AD&D. B/X also uses two rolls and even sticks to the numbers in the original table, but of course that doesn't mean it wasn't a reinterpretation of the original intent.

I agree that the situation is more ambiguous in U&WA, but I'd be surprised if it was actually written intended to be a single roll, where you either get lost, have an encounter, or neither. Page 17 does say, "At the end of each day (turn) the referee will check to see is a monster has been encountered." It then goes on to describe how travelling on a river requires two encounter rolls each day, one while on the river and one while resting on land at the end of the day.

I haven't looked hard, but I'm not aware of any rules for getting lost in Blackmoor, so that doesn't help as a basis of influence. The rules of Outdoor Survival, however, mimic the later B/X and AD&D clarification exactly. In Outdoor Survival you roll at the start of the turn to see how you move, getting variable degrees of lost on a 1-3 depending on the scenario, then at the end of the day you roll again to see if you have an encounter, which occurs on a 5-6.

[derv]

My primary point is uniformity within the rules for wandering monsters. I wouldn't insist that the matrix need be used any particular way. But, if separate rolls are intended, Malchor's point is only more acute. Both results on the matrix could easily be expressed with the common roll low method. And if both encounters and getting lost were meant to occur on the same turn, it could easily be expressed with overlapping results on the matrix with a d6.

Consider that on foot you have a 3 hex allowance. Different terrain impose different costs to enter. You are checking for getting lost before you pay the cost, before you actually move. The encounter occurs based on the hex you end in, after you move.

Let's say you start in a wooded hex (or better expressed you ended the last turn in a wooded hex). You roll d6. You are checking if there is an encounter or if you will get lost before entering the next hex. If you roll a 5-6, resolve the encounter and proceed in the direction of choice. If you roll a 1-2, you are lost. Roll for direction of travel (allow one point of direction change). Now pay the movement costs. Rinse and repeat.

So, in a sense, getting lost and having an encounter can happen on the same turn with a single roll on the matrix. I hope some are having an a-ha! moment here.

[Starbeard]

I think I see what you're saying. The one roll would be made essentially between turns; encounter results are played out before movement, effectively making them an addendum to the previous turn, while lost results are applied during movement of the new turn. So, a lost result followed by an encounter result would place them on the same turn.

[derv]

Oct 29, 2018 17:01:36 GMT -6 Starbeard said:

I think I see what you're saying. The one roll would be made essentially between turns; encounter results are played out before movement, effectively making them an addendum to the previous turn, while lost results are applied during movement of the new turn. So, a lost result followed by an encounter result would place them on the same turn.

Essentially yes. I'll add my additional opinion of why I think a single roll is intended and why the probabilities do not overlap.

If you roll an encounter at the end of the previous turn then the GM would go into a sequence of determining if the encounter can be evaded. If not, flight-pursuit can ensue. The methods of pursuit mimic the methods of being lost. Direction of movement is randomized. The party is moved in directions that are not of choice. This continues until they have evaded or they've been caught. Such a sequence would end with a required rest period and two wandering monster checks per day at rest. Now the party would be free to move any direction it wants.

edit: I'll also add that I think the results of the Matrix for Swamp are intentional. If you end your turn in a swamp hex you will either have an encounter or get lost for the following turn trying to get out. The message is that swamps are to be avoided because they are a dangerous place. Weird things live in the swamp and sometimes people go in and never come out again. It's the only hex type to have this feature.