Which are the best numbers to proceed on?

[Murrur]

I've been thinking about this problem lately. I think most people would agree that 6,7,8 is the golden trio which allows players to proceed quite far easily, since those three numbers appear most frequently due to statistics.

However, lately i've been wondering wether some other combination would allow to progress further or safer. Hear me out here, While 6 to 8 are most common to appear, the caveat is, that you have all eggs in one basket. If there's a turn with very low or very high dice, your turn is over. I have also noticed that 5 7 8 would also seem to work exceptionally well. Maybe because 5 catches the smaller dice and therefore there is less risk involved, despite 5 appearing considerably less than the center dice?

Do you think the actual pip amounts (dice number) or just the statistical number? E.g. Is there some golden rule on which dice to choose in your game play?

Which combinations do you think are the best ones and why? If you could choose any 3 corridors to proceed on, which ones would you choose?

[RicardoRix]

It's 678.
https://boardgamegeek.com/filepage/7303 ... -cant-stop

but 2, 12 have shorter routes to compensate.

[SluggerBaloney]

Deleted

[RicardoRix]

Based on my analysis of 1200+ die rolls uncovering the flaws in the RNG, I can say that 2 and 12 are by far the most valuable numbers in the game, given that triples come up more than they should, and the rolls 1, 1, 2, 3 and 6, 6, 6, 5 show up far more than they should

Can we see the source of this analysis, and also your calculations?

[Cheery Dog]

I've had some good runs with 6, 7, 9.

But in general for my opinion it's 7, one of 6 & 8 and the third doesn't really matter. It's still how far you're willing to push your luck.

[Paddles]

Can we see the source of this analysis, and also your calculations?

Already asked and (not) answered at in another thread, https://boardgamearena.com/forum/viewto ... 178#p64178

[sprockitz]

I've been thinking about this problem lately. I think most people would agree that 6,7,8 is the golden trio which allows players to proceed quite far easily, since those three numbers appear most frequently due to statistics.

However, lately i've been wondering wether some other combination would allow to progress further or safer. Hear me out here, While 6 to 8 are most common to appear, the caveat is, that you have all eggs in one basket. If there's a turn with very low or very high dice, your turn is over. I have also noticed that 5 7 8 would also seem to work exceptionally well. Maybe because 5 catches the smaller dice and therefore there is less risk involved, despite 5 appearing considerably less than the center dice?

Do you think the actual pip amounts (dice number) or just the statistical number? E.g. Is there some golden rule on which dice to choose in your game play?

Which combinations do you think are the best ones and why? If you could choose any 3 corridors to proceed on, which ones would you choose?

in terms of probability on a single roll to not bust I believe the best combination is actually 6,7,9 or 5,7,8 as both slightly edge out the 6,7,8 trio (I did the math at one point but don't have the exact probabilities with me).
But as far as getting good progress overall I feel anything with the 7, then either 6 or 8 and then something on the opposite side of the 7 as the 6 or 8. I'm always shocked when people have a choice and will go with 5,6,7 over 6,7,9..putting both on the same side of the 7 knocks your odds down a good bit.

[whatshisbucket]

Here are the number of possible rolls (out of 1296) that cause failure for each combination:
104 6 7 8
111 5 7 8
115 4 6 8
126 4 7 8
136 5 6 8
139 3 7 8
139 4 7 9
142 2 7 8
147 5 6 7
148 4 6 7
151 2 6 8
151 4 6 10
160 4 7 10
173 5 6 9
175 3 6 7
176 2 6 7
176 4 6 9
178 4 8 9
178 5 6 10
190 3 6 8
190 5 7 9
197 4 5 7
200 4 5 8
204 3 7 9
213 2 7 9
213 3 7 10
213 3 8 9
216 2 6 9
216 2 7 10
216 3 8 10
216 4 6 11
222 2 5 8
225 3 6 9
230 2 8 9
230 3 6 10
230 4 5 10
239 2 4 8
239 2 8 10
245 2 6 10
247 2 5 7
249 3 5 8
250 2 4 7
261 4 5 9
264 3 4 8
264 4 5 6
271 3 4 7
276 3 5 7
284 2 7 12
287 2 7 11
287 3 4 9
287 4 5 11
290 3 5 9
290 3 7 11
297 3 5 6
298 2 5 6
311 2 5 9
313 2 4 6
313 3 5 10
313 3 6 11
316 2 3 8
316 2 4 9
316 2 5 10
316 2 6 11
316 3 4 10
321 2 3 7
334 3 4 6
339 2 4 10
339 2 6 12
342 2 8 11
342 3 6 12
373 2 3 9
373 2 5 11
376 2 9 10
376 3 5 11
376 4 5 12
410 2 3 6
429 3 4 5
444 2 4 5
445 3 4 11
471 3 5 12
474 2 3 10
474 2 4 11
474 2 5 12
539 2 3 5
546 3 4 12
581 2 4 12
615 2 3 11
620 2 3 4
728 2 3 12

They should really make spoiler tags possible on the forum. Sets with sum >22 can be found by symmetry (for example, 789 and 567 are the same). So according to my code, sprockitz is slightly wrong, although the difference between the top 3 is quite small.

Things that are notable:
The value of having even numbers cannot be understated. It was always clear to me that having all odd numbers is bad, as there is a 1/8 chance that all possible sums will be even, but that the best all-odd combination (5 7 9) is significantly worse than even, say, 4 7 10 is surprising to me.
278 seems to be hugely valuable due to the potential to make progress in relatively few rolls with a small probability of failure.

[Jest Phulin]

For all the numbers....
This document in my google drive (Hopefully this link works. If not, lemme know and I'll try to fix it. It's a bit big to toss into the forums.)

It is broken down by individual numbers, a group of 2 columns (for late in the game when even having an unassigned temporary marker may not be a guaranteed safe since some columns will be locked out), and groups of 3 columns.

In this document, a column or group of columns is considered "safe" with a roll if at least one number can be created. So, for example, rolling 1-1-2-3 will be safe on 2, 3, 4, and 5, and any groups that include those ([3,7,8] or [5,11,12] for example)

Note that individual column results can't simply be added. 1-1-2-3 will count as a safe on 2, and a safe on 3, but only a single safe on [2,3].

This report was generated creating all 1296 possible rolls, and counting the safe ones. So, 1-1-2-2 is actually a different roll than 1-2-1-2.

[sprockitz]

So according to my code, sprockitz is slightly wrong, although the difference between the top 3 is quite small.

Things that are notable:
The value of having even numbers cannot be understated. It was always clear to me that having all odd numbers is bad, as there is a 1/8 chance that all possible sums will be even, but that the best all-odd combination (5 7 9) is significantly worse than even, say, 4 7 10 is surprising to me.
278 seems to be hugely valuable due to the potential to make progress in relatively few rolls with a small probability of failure.

Whoops, looks like I was wrong. Must remember them being close to equal, still a 0.5% difference. The 278 or 6712 are great combos. If anything one thing can help you is evens are better than odds. Take 4 6 10 versus 5 7 9, with 2 dice each one in the first group is worse than it's counterpart in the 2nd group, yet with 4 dice the first group becomes substantially better than the second.