Number improbability

[pjt33]

All posibilities are considered in one formula or another, so it naturally follows that they add up to 100%.

Not really. That's a rather unnatural normalisation in this context. Naturally they should add up to 300% because each throw generates three outcomes.

[King_Taravangian]

If I roll 2 dice, the probability that I'll see at least one 3 is 11/36: there are 11 possible outcomes with at least one 3 out of the 36 possible (and equally probable) rolls. The "average number of 3s" is, however, is 12/36 = 1/3

Agreed. I will use 12/36, since you can activate sector 3 two times if you roll a 3-3.

Not really. That's a rather unnatural normalisation in this context. Naturally they should add up to 300% because each throw generates three outcomes.

Agreed, but you cannot leave it at that. You normalize to 100% by dividing by 3.

So I propose this:


Column M shows the probabilities proposed by Jellby for individual dice, to which I add the probabilities for the sum of dice (which I think we agree on) and on column O restul the probabilities that pjt33 mentioned. But you can't say that you have a chance of 108% to get a 1, a 2 or a 3 (which is what you get if you add those up), you need to normalize to 100% and you get the same results.

Do you think that we should stop at the results in column O?

[Jellby]

But you can't say that you have a chance of 108% to get a 1, a 2 or a 3 (which is what you get if you add those up)

The problem here is that adding the probabilities of "getting a 1", "getting a 2" and "getting a 3" is NOT the probability of "getting a 1, a 2 or a 3", because those events are neither exclusive nor independent.

Again, if your goal is computing the probability (in the sense of how likely it is that it will happen in a specific roll) of being able to choose a particular number, then neither column is correct, but something like this:

Code: Select all

      single die     sum of dice    total / 36
 1        11                          30.6%
 2        11             1            33.3%
 3        11             2            36.1%
 4        11             3            38.9%
 5        11             4            41.7%
 6        11             5            44.4%
 7                       6            16.7%
 8                       5            13.9%
 9                       4            11.1%
10                       3             8.3%
11                       2             5.6%
12                       1             2.8%

I don't count a number twice if you roll a double. You activate a sector twice, but that doesn't mean that you can choose a number more often per roll. And the total is more than 100% (283%) because each roll you can choose at least two different numbers, but not always three different numbers.

[pjt33]

Not really. That's a rather unnatural normalisation in this context. Naturally they should add up to 300% because each throw generates three outcomes.

Agreed, but you cannot leave it at that.

I can and would.

But you can't say that you have a chance of 108% to get a 1, a 2 or a 3 (which is what you get if you add those up), you need to normalize to 100% and you get the same results.

No, but nor is the chance of getting a 1, 2 or 3 a mere 36.1%. The probability of activating at least one of 1, 2, 3 at least once is 75%.

Do you think that we should stop at the results in column O?

Yes-ish. Actually I think you should stop talking about probabilities and instead talk about frequencies. E.g. in 36 rolls you can expect on average to activate the number 6 slot 17 times, assuming that that slot is your top priority.

[TwoFistedTales]

Finally had my first game where 7 didn't roll but 9 rolled ridiculously. It seems like the winner is predetermined sometimes. I played a game where the last 3 rolls were all 11s to come in second. It just seems like the algorithm for this game is really bad.

[Solarman9]

Finally had my first game where 7 didn't roll but 9 rolled ridiculously. It seems like the winner is predetermined sometimes. I played a game where the last 3 rolls were all 11s to come in second. It just seems like the algorithm for this game is really bad.

To quote John Maclean "Welcome to the party pal"

I quit playing a couple weeks ago when the 6 rolled 30 times and the 4 rolled 3. Combine that with the fact the top players rarely if ever play so once you get to 1700ish, everyone quits because they are satisfied being top 20? At 1700 you lose 28-31 points for third, lose 8-13 points for second, and win 6-8 because you never get to play any top players. If you are lucky you get 12 points from playing someone 1650+. I thought playing elite would be better competition, but it's the same people hoping the algorithm picks them for the winner. I am sure you have had that game where a guy starts with say 4 on 11 and in the first 10 rolls 11 has rolled 4 times already.

[Jellby]

Finally had my first game where ...

Sounds like cherry picking?

[Silene]

Funny how people call the game result "predetermined" when all they wanted to actually say that one player was very lucky, so much that they won easily. That's a strange way to use the term. "Predetermined" sounds like you want to say the winner was picked in advance - the game looked up what players had, calculated what are favourable rolls for whom and then rolls were picked that favoured the "selected winner". So someone wrote an AI that will do all these calculation and then... the player that should be in favour this time would be randomly picked? That sounds like a rediculous amount of work for... nothing of relevance.

Results just happen. And as it is common for propability, they are often not very smoothly distributed on a small number of rolls (like 100-500). Sometimes players are heavily on the receiving end and sometimes on the unlucky side. That's not predetermination - it's just random and a normal thing to happen.

And there are also games where randomly both players get about an equal amount of good and bad rolls. Those are the more interesting games - because in these games, skill actually matters a lot and with good decisions you can tip the result in your favour. Unfortunately nobody is looking at these games although they are much more interesting to look at.

[Cile]

Finally had my first game where 7 didn't roll but 9 rolled ridiculously. It seems like the winner is predetermined sometimes. I played a game where the last 3 rolls were all 11s to come in second. It just seems like the algorithm for this game is really bad.

Unpredictable results? In a dice game?! Unheard of!

It's not the algorithms fault, you don't like dice games and game where the end result can be decided by this amount of randomness. There's nothing wrong with that, different people have different preferences. The sooner you realize it's the amount of randomness you don't like, and it's not the algorithm being programmed to mess with you, TwoFistedTales, specifically, the happier you will be when you play games more to your taste.

[Solarman9]

Twofisted, the funny thing about these guys commenting on the numbers and you is that they don't actually play space base. Ask other people who play. They don't have to play enough to be a guru (i am) but they should at least have some experience with the game before shouting you down. But they'll keep doing it because it's the internet and they are experts at internet posting.