"Best" column combination

[thg0724]

First turn of the game, if the strategy is to roll until you either complete a column or lose all progress, what is three column combination most likely to produce a completed column?

Again, the strategy is to roll until you either complete a column or lose all progress: if your three columns are 6-7-9 and you're on the bottom-most space in each column, the roll allows for a single space advance on either column 7 or 9, which do you choose? A single advance on 6 or 9? 6 or 7?

If your answer is not 9 for either case when it is a choice, would you pick the outer most column with 6-7-10? 6-7-11? 6-7-12?

[ainaki100]

It surely would be cool to see someone do the maths behind this question as I certainly am not that good with the numbers

[Archisian]

First turn of the game, if the strategy is to roll until you either complete a column or lose all progress, what is three column combination most likely to produce a completed column?

Again, the strategy is to roll until you either complete a column or lose all progress: if your three columns are 6-7-9 and you're on the bottom-most space in each column, the roll allows for a single space advance on either column 7 or 9, which do you choose? A single advance on 6 or 9? 6 or 7?

If your answer is not 9 for either case when it is a choice, would you pick the outer most column with 6-7-10? 6-7-11? 6-7-12?

I'd probably actually say 2 or 12. 2s and 12s, while the most difficult number, appears rather often and needs only 3 spaces to complete. 6-7-8 are the easiest, and obviously, the most competitive ones. You most likely will only get one of them. Maybe none, depending on your opponents rolls. But 2 and 12 aren't that competitive. If you focus on them, you can complete them fairly easily.

[euklid314]

Interesting question which is practically impossible to answer mathematically without Monte Carlo random simulation.

If I may chose the starting numbers, I would choose 6-7-12. These numbers have a high probability not to bust (over 90%, if I remember correctly) and getting two more 12s has some decent chances...

If I would start with 6-7-8 and I am not allowed to stop, I would definitely take all double numbers first and look which number gets into the lead. If in doubt probably take the 7.

[thg0724]

Interesting question which is practically impossible to answer mathematically without Monte Carlo random simulation.

If I may chose the starting numbers, I would choose 6-7-12. These numbers have a high probability not to bust (over 90%, if I remember correctly) and getting two more 12s has some decent chances...

If I would start with 6-7-8 and I am not allowed to stop, I would definitely take all double numbers first and look which number gets into the lead. If in doubt probably take the 7.

6-7-12 (or 2-7-8) is 89.8% to be successful (on each roll).

Given that you are starting with this triple, you have already achieved one 12 space and only need 2 more to complete the column. There are 0.13 twelves per roll, so 15.1 rolls are needed to complete the column (on average). That's fewer rolls than you need to complete 10 sixes (16.4) or 12 sevens (16.8). Also, the 12 column, once started, can be completed in two rolls (or rarely 1) whereas the middle columns require at least five (for column 6) or six (for column 7) rolls.

Does the reduction in success from 92.0% (for 6-7-8) to 89.9% (for 6-7-12) offset the advantage of being able to complete 12 with fewer rolls (on average and in ideal situations)? I doubt it. I think your 6-7-12 (2-7-8) guess is probably right.

[podemico]

I did the maths myself before reading this post (maybe I should have done the opposite to save time)

I got surprised on how theoretically difficult is to bust.

There are a bunch of combianations (including the golden 6-7-12) that have about 90% probability of success

In real life I barely survive 3 rolls

[euklid314]

I did the maths myself before reading this post (maybe I should have done the opposite to save time)

I got surprised on how theoretically difficult is to bust.

There are a bunch of combianations (including the golden 6-7-12) that have about 90% probability of success

In real life I barely survive 3 rolls

I am not sure if we are talking about the same problem. If you start with column 6-7-12, then you have a 90% probability to survive the next roll, not a 90% probability to finish a column!

[Jellby]

90% chance of surviving the next roll means 27% chance of not surviving 3 rolls.

[thg0724]

90% chance of surviving the next roll means 27% chance of not surviving 3 rolls.

For the optimists amongst us, it means a 73% chance of surviving three rolls.

[Dreamy T]

4-6-8 or 6-8-10 !
Underrated, but really great !