Board Game Arena

There are only 104 dice throws out 1296 possible throws that will bust you. That's a 1 in 12 chance of being busted.

It should be regularly possible to make anywhere from 12 to 20 rolls without getting busted, just as it should be possible to roll a standard 6 sided die up to 10-12 times WITHOUT ever rolling a 6.

However in practice I find the number of occasions where you can survive more than 10 rolls to be quite small. I started to log this very thing this week.

Every time I play I'm now going to push 6,7,8 until I bust and then record how many rolls the system allowed me to have.

My first attempt saw me get 17 rolls. However I'm willing to bet that for the majority of time i will struggle to get 10

In your statistics you should count all the successful rolls after you have established the 6-7-8 ropes.

So if you have rolls 6+7, 7+7, 6+6, 7+7, 7+8 (which establishes the 6-7-8 ropes) and in the next roll you fail then you have to count it as a failure in the first roll.

With this said you have the following probabilities for the early failures:

1st roll: 8.02 % (thus: 8.02% to fail on 1st roll or earlier)
2nd roll: 7.38 % (thus: 15.412% to fail on 1st roll or earlier)
3nd roll: 6.79 % (thus: 22.19% to fail on 1st roll or earlier)
4th roll: 6.24 % (thus: 28.44% to fail on 1st roll or earlier)
5th roll: 5.74 % (thus: 34.18% to fail on 1st roll or earlier)
6th roll: 5.28 % (thus: 39.46% to fail on 1st roll or earlier)
7th roll: 4.86 % (thus: 44.32% to fail on 1st roll or earlier)
8th roll: 4.47 % (thus: 48.79% to fail on 1st roll or earlier)
9th roll: 4.11 % (thus: 52.90% to fail on 1st roll or earlier)

The expected value for failure is approx 12 rolls, but please note that the median value for failure is approx 8.5 rolls. That means that in 50% of all tries you will fail before the 9th roll and in 50% of all tries you will fail after your 9th roll.

CaractacusPots wrote: ↑12 September 2020, 20:43 I started to log this very thing this week.
Every time I play I'm now going to push 6,7,8 until I bust and then record how many rolls the system allowed me to have.

And yet on game 111558427, played 2 days ago (which qualifies as this week), you chose to stop on roll 9. Game 111750071, played yesterday, you also chose to stop on roll 9.

euklid314 wrote: ↑12 September 2020, 21:55 The expected value for failure is approx 12 rolls, but please note that the median value for failure is approx 8.5 rolls. That means that in 50% of all tries you will fail before the 9th roll and in 50% of all tries you will fail after your 9th roll.

Nonetheless, you should regularly be able to push 12+ rolls plenty of times.

Does that actually happen? Hmmm


Here's an interesting thing though.

Should we count the rolls of the players before us? Or just our own throws?

So if the player before you was on 678 and did 7 throws and then stooped/banked I presume that means 7 of the average 678 throws you can expect have already been used up and now your own chances are greatly reduced.

If so it's vital to track what throws your opponents are getting during the game

CaractacusPots wrote: ↑12 September 2020, 22:48 So if the player before you was on 678 and did 7 throws and then stooped/banked I presume that means 7 of the average 678 throws you can expect have already been used up and now your own chances are greatly reduced.

If so it's vital to track what throws your opponents are getting during the game

Sigh. Only if you believe that dice have memory. Or if you believe that all the dice are rolled beforehand on a game that has a wide range of possible total rolls, so the unused rolls would show up as a bias in any randomness analysis.

Also, please define what probability you mean when you say that something can be done "regularly." The term implies more often than not, which is over 50%. 12 rolls of 6/7/8 has a probability significantly less than this.

CaractacusPots wrote: ↑12 September 2020, 22:48 Nonetheless, you should regularly be able to push 12+ rolls plenty of times.

Does that actually happen? Hmmm


Here's an interesting thing though.

Should we count the rolls of the players before us? Or just our own throws?

So if the player before you was on 678 and did 7 throws and then stooped/banked I presume that means 7 of the average 678 throws you can expect have already been used up and now your own chances are greatly reduced.

If so it's vital to track what throws your opponents are getting during the game

With a 1 in 12 failure rate on each roll you should be able to push 12 rolls only about 35% of the time. You can do the maths for yourself, it's (11/12)^12 = 0.35

It's NOT important to track what your opponents get. Unlike Poker, say, where if your opponent has the Ace of Spades it means you DON'T have it, in a dice game every time you roll the dice it's a new random event - the odds of rolling a 6 never change no matter what you opponent rolled, or what you rolled, or what someone in another game rolled.

CaractacusPots wrote: ↑12 September 2020, 22:48Does that actually happen? Hmmm

Yeah, I was often playing with friends and I was way better than them, and I was trying to win in 3/4 players game.
So, most of the time I will not be first (since there is 3+ players), I was taking lots of risks.

Usually, I was loosing, but more often that you can think, I was able to steal a victory with like a one shot of 7 or things like that.

But you should do it at the right time. 6/7/8, 2/7/8, 6/7/12 are really great candidate to take a lots of risks.
Trying to force a 7/9/10 even if you want to take a lot of risks will usually not be worth the one or two steps you can get on that 10.

Btw, my 7/9/10 example seem the perfect counter-example of why that 'rule of 28' seem bad if you apply it without thinking: your chance to bust are really high, and the potential gain of another 10 doesn't make a big difference.

I’ve gone bust after a couple of rolls on the middle three - happened a few times.

CaractacusPots wrote: ↑12 September 2020, 22:48 So if the player before you was on 678 and did 7 throws and then stooped/banked I presume that means 7 of the average 678 throws you can expect have already been used up and now your own chances are greatly reduced.

If so it's vital to track what throws your opponents are getting during the game

The fact you don't understand why this is wrong yet proclaim yourself to be a backgammon expert is telling

FT3 wrote: ↑15 September 2020, 23:28 I’ve gone bust after a couple of rolls on the middle three - happened a few times.

Me too