Have I missed a new rule that states that on any throw one of the die will have a value of 1? I have tried it, no matter haw many times you throw 2 die you cannot count on getting a 1 eight times in a row. EXCEPT HERE. Please TJ Give your random number generator a nudge, I think it's got stuck. :o)
...but that's all it is. :-) The die roller is indeed quite good at being random, for a computer. I check it periodically, and over any kind of reasonable statistical sample, each roll comes in right near the 2.777777(etc.)% that it should (e.g., each roll happens once in 36 rolls, on average, over time). I did just double-check it now to be sure, but even over a quite short sample period, there's no particular preference for 1s.
Randomness is an interesting thing. The odds of a roll having, say, a 1 in it are 11 in 36 -- put another way, just over 30% of all die rolls have 1s in them. We humans, who seek patterns in things, tend to think that previous results change the odds of future results. Who hasn't said something like, "I've gotten a 1 on my last four rolls, surely I won't this time?!" But of course it makes no difference whatsoever, the odds of a 1 coming up in the next roll are exactly what they always were: 11 in 36 (just over 30%).
But it seems, to us, like it should make a difference. And there's a good reason for that: Say you rolled the dice 1,000,000 times. The odds are that 305,556 of those rolls (call it 30.55%, although really those 5s at the end go on a while -- forever, in fact) will have a 1 in them. Any individual roll in that million rolls had an 11 in 36 (roughly 30.55%) chance of having a 1. BUT! Break that sample up in to 500,000 pairs of rolls. What are the odds of a given pair of rolls both having a 1 in them? 30.55%? Of course not. It's much, much lower than that, specifically, about 9.34% (30.55% x 30.55%). So of that 500,000 pairs of rolls, 46,682 or so would be pairs where both rolls had a 1. And those odds drop very quickly indeed if you consider triplets of rolls (30.55% x 30.55% x 30.55% = 2.85%) or groups of four (30.55% x 30.55% x 30.55% x 30.55% = 0.87%).
And it's that seeming dichotomy that's interesting about randomness. The odds of a given roll containing a given number don't change, no matter how many times it's happened before; and yet, the odds of it happening several times in a row are very low indeed.
It seems like a dichotomy, but it isn't one. And here's why: It's because it depends on when you're looking at the sequence. Let's take an example: Maria and Nitin both have a pair of dice. The goal is to have four rolls with 1s in them. Maria has already rolled her dice three times and gotten rolls with 1s in them; Nitin hasn't rolled his dice at all yet.
What are the odds that Maria will get a fourth roll with a 1 in it? That's right, exactly what they always are: 11 in 36, or 30.55%.
What are the odds of Nitin getting four rolls with a 1 in them? That's right, very low, specifically 0.87%.
But why? Because Maria's already beat the odds on the previous three rolls, and Nitin hasn't rolled at all yet. Maria is already in that very unlikely position of having rolled rolls with 1s in them three times in a row (something that's only going to happen 2.85% of the time); Nitin is still in the position where he hasn't started yet. When he starts, he has a 30.55% chance of getting a 1 in the first roll. If he does, he has a 30.55% chance of getting a 1 in the second roll -- but most of the time (69.45%), there is no second roll because he didn't get a 1 on the first roll. And so it goes.
"But wait!" I hear you say, "That means if I've had a 1 in my last three rolls, and I roll another one, something's happened that only happens 0.87% of the time -- something must be wrong, those odds are nearly zero!" And indeed, those odds are nearly zero. But how many times have you rolled the dice four times on Pocket-Monkey? If you've played a 21-point BG match, on average you've rolled the dice 500 times or so, which is 125 four-roll runs. And on average, during that match, you've had at least one four-roll run with 1s in every roll. And of course, you also (on average) had a four-roll run where there was a 2 in every roll. And a run with a 3 in every roll, etc. So if you're looking for patterns (and we humans are nearly always looking for patterns), you'll find one. :-)
Randomness is an interesting thing.
I've already rambled on quite a bit, but I'll just touch on another thing about we humans that's interesting (well, I think it is) and at least vaguely relevant: We frequently suffer from something my father called "neglect of negative instances". You put your pencil on the table, and it rolls off, and you think "Argh! It's always doing that!" Now, while it may be that it is always doing that (in which case you might consider fixing the table, it' clearly not level), it's much more likely that it only does that sometimes -- it's just you don't notice it when it doesn't roll off the table, because it's a non-event. My mobile phone is always running out of battery power in the middle of an important call. Well, no, probably not, it's just that I haven't noticed the dozens of important calls where it didn't run out of battery power; they were non-events. We humans take note of things that happen that are unusual, and tend to gloss over the usual. With pencils and mobile phone batteries -- and dice rolls! -- this is a fairly innocuous tendency we have. But scientists are taught to be very careful of it, it's an easy trap to fall into. I fell into it just recently here on PM. I was in a game and my opponent was just getting all the rolls, particularly doubles. I was feeling a bit hard done by, to be honest, by the die roller. I hadn't had doubles in ages! But then I thought: Let's go look. And you know what? In that game, my opponent had had six doubles -- and I'd had five. Apparently, to me, his getting doubles was unusual and noteworthy, whereas my getting doubles was just normal. Go figure.
posted by pint of beer (john shields) on 05/07 at 09:09
that is some great reading, i always feel bad done by when my opponant gets lots of doubles and i appear to get none. just go`s to show you forget all the good games you win and focus on the bad losses great explanation (still i guess being human you tend to think some players are just born lucky, lol), keep the good work going T.J. this is the best site i play on
I've always felt this was an interesting topic -- specially the "neglect of negative instances" phenomenon you describe -- and this is the best description of it I've ever seen.
I belive that those statistics are real for T.J. experiments.
But statistics are statistics, for better and for worse. They deppend very mutch on the way we get them.
Are they only in one computer? Are they all automatic, thats meens no different time bettween numbers?
Once i tried to use the values in a real game to do a study, to see if my feeling it was right or not, but to mutch time used in getting those values, i give it up. And one game is no example, its necessary to do many more games to get a good result.
On the same theme, during the first part of the game if I get a piece removed from the board I am not suprised when the dice roll a double 6. It happens a lot.
its funny ppl get doubles all the time in a game its wrong for that..these games are crazy that ppl get them all the time n you know u might have a game won n they end up winning n thats wrong
It's the nature of games with an element of chance, like Backgammon, that that sort of thing will happen every once in a while. In my view, it's not "wrong" or "unfair", it's just the way chance is. It's the same when you're playing in real life with physical dice.
There are lots and lots of games that don't include the element of chance -- pretty much every other game here on PM: Chess, Checkers, Halma, Mill, Reversi...
We all have won or lost games because of doubles and the same complaint that something unfair has happened shows its face on every site you can play backgammon on. Even in real games I've seen people complain that doubles has come up more than it should. Isnt backgammon a mixture of skill, chance, and some luck well use your skill with the roll hope chance gives you a break and pray for some luck.
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