I have two screen shots. One is I rolled three double ones in a row. The other screen shot is a 5 and a 3 three times in a row. This is statistically huge. What is a good setting for the rolls? I would be glad to share them if someone could explain how to do it. The insert image icon brings up a url to point to.

Obviously it’s rigged. A sequence of three 1/36 probability events can’t possibly happen randomly. Of course that’s what we call sarcasm. Casinos are built on the fact that given enough trials, some very improbable things can and do occur. For example, by proper betting you can reduce your probability of losing money on a series of bets to very low values. Consider a simple Martingale system — you bet $1 on an even money bet. If you win you’re up a dollar, if you lose you bet $2 on the next bet. Win and you’re up a dollar, lose and you bet $4. Keep doubling until you win and are up a dollar. How can casinos stay in business with this weapon bettors have? Well, it’s simple — once in a while someone will lose 10 or so bets in a row and give up. That tenth bet is $512 and the total loss is $1023. That will more than offset all the one dollar wins.

Besides, in your case it really wasn’t a 1/36 sequence that caught your eye. I would guess you’d be posting similar if you saw any double three times in a row. That’s six times more likely than seeing 11. I’d also guess that sequence of three non doubles in a row wasn’t specific to the roll you saw. That makes it 15 times more likely you’d see such a sequence.

Dean, just a quick hypothetical follow up question. I tell you that I flipped a coin 10,000 times. I show you a list of my claimed results. You look at my results and see at least one sequence where there were 10 heads in a row. You exclaim that my coin must be rigged. I say ok, give me a coin you know is fair and I’ll do it again. This time I give you results that show no more than 4 heads in a row at any point. I tell you that I did in fact flip one fair coin 10,000 times for one set and a rigged coin for the other. Which set of results was rigged and how was it rigged?

Thank you all for the responses. What I am looking for are the best settings for a truly random roll? There is seed, trails and things I do not understand.

The seed is a starting long number on which complex mathematical calculations are made, and that creates a long sequence of numbers
which are used as the numbers to generate the dice rolls. It auto generates randomly when you enter the program, so you don't have to touch it.

If you write down this seed and start a new game with the same seed, you will see that the same sequence of dice rolls come up again,
and that itself should be proof enough that the program doesn't cheat.
You could then still argue that the program changes it's playing strategy by knowing the future dice rolls based on the seed.
This can be proven wrong by setting the dice manually after each turn,
or simply seeing that the evaluation of each position is basically the same every time, regardless of the seed.

For practical purposes the random number generators are enough for the gameplay, but if you are not satisfied with it you can change the method.
For example there is an option to import number from an external site called random.org, which generates it's randomness from atmospheric noise.
It's interesting, I haven't tried that option but I think it should work.

And regarding the trials, it's a setting related to rollouts. It's the number of times the game will be played out starting from the position
you want to evaluate, and you can use it to compare equities of positions. The default value is 1296.

Thank you so much John567. I looked in the manual, but there wasn't as good explanation as yours. I never accused the game of cheating. It cant cheat. It is a program. I would expect a roll of a 5 and a three three times in a row eventually. I downloaded and played less than a hundred times so it was a little surprising I am going to try the atmospheric noise.That is the most fascinating thing I have heard in a while. Maybe I could harness the noise into an unstoppable weapon. You know, get bored of backgammon and conquer the world.

today I rolled a 5 and a 2 (in that order) three times in row. I have played this game about a 100 times. Somehow I have managed to screw up some settings somewhere. Will post when I figure it out.

I just rolled 4 and 3 (in that order).
How odd? I only had a 1/36 chance to roll this.

You rolled a 4 and 3 (in that order) three times in a row?

No, one time in a row.

4 , 3
no way
under 10% chance this could happen

I know! I threw away those dice, knowing they were crooked.

If your not going to address the topic of this thread, please do not respond. If you want to discuss the odds for any roll, do so under your own thread. Something is wrong with my game. I dont know weather to reinstall or what. I am trying to figure this out and would like to know what is wrong.

What we are trying to tell you is that rolling a particular pattern of rolls may just be randomness, and nothing at all wrong with your program. It would take quite a bit more than just one instance where you roll three identical rolls in a row to conclude something is wrong with gnubg. Maybe you find that hard to believe but that’s the truth.

The probability of the event you describe is 1 in 5832 (unless you have some way of distinguishing the two dice that gnubg rolls — then it’s 1 in 46,656). Either way, with gnubg generating many thousands of rolls by all the people who use it, it isn’t really surprising that it generated the event you saw. It’s unlikely that YOU would see that, but not that SOMEONE would — in this case you’re the someone.

It’s also quite a bit less unlikely than you think. You posted about a particular roll occurring three times in a row. I suspect there’s nothing special about that particular roll that caught your eye; ANY roll happening three times in a row probably would have made you post what you did on here. If you look at any roll, then the first roll is irrelevant; it only matters that the next two match. In that case (with normal dice) the probability is 1 in 18*18 = 1 in 324, somewhat improbable but not really ridiculously so, especially over 100 or so trials. There’s about a 27% chance of seeing at least one such occurrence in 100 trials. For distinguishable dice it’s 1 in 36*36 = 1 in 1296, or about a 7.5% chance in 100 trials. Somewhat unlikely, but certainly not sufficient to rule out sheer randomness.

For indistinguishable dice, isn't it 1 in 21*21 instead of 1 in 18*18? Where does the 18 come from?

Thank you stremba70 for the reply. if a number is rolled three times in a row (say 4), I would say it happens. Rolling a 3 and a 1 (in that order) three times is much harder to understand. Am I reading your post correctly that rolling a 3 and a 1 (in that order) three times is 1 in 324? I have not played the game a 100 times when these rolls came up. What are the odds of Rolling a 3 and a 1 (in that order) three times in a hundred rolls? What are the odds of rolling the same in (order) combination, three times in a row and a total of 3 times in 100 games? Long sentence there. Maybe I'm making to much out this. Again, Thank you.

You're making way too much of this. Happens all the time.

Not sure what a developer would have to prove or gain by creating a Backgammon program that cheats. If it was truly programmed to cheat, you would never win a game. Why would the 'cheating' be inconsistent to allow you to win a few games every now and then? One should play a computer opponent to learn rather than to win. If you want to have a chance to win, play another human.

uberkuber

For indistinguishable dice, the odds of throwing a given non-double roll, such as 43, are 1 in 18. That’s because there are 36 possible combinations that can be rolled using distinguishable dice (6 rolls on one x 6 on the other), but, since the dice are indistinguishable, there are two combos that give the same non-double roll. Ie if I rolled one die twice, but only told you the combo I rolled, if I said it was 31,
I would say that regardless of whether I rolled 3 followed by 1 or vice-versa. Hence 2 out of 36 possible rolls give that combo, or equivalently 1 in 18.

Your 1 in 21 undoubtedly comes from the fact that there are 21 combos possible. However that assumes that all combos are equally likely. That is not true, however. Each double is half as likely as any non-double. If you think about my sequential rolling above, it’s easy to see why. I can only report rolling 66 in one way, namely rolling 6 followed by another 6.

Dean, long story short, if we assume 40 rolls for an average game, you get just over 8% as the probability of rolling a specific combo in a specific order at least once in 100 games. If you admit that you would have been equally impressed had you rolled 6 and 5 in that order (or any other such combo), the probability of at least one occurrence of three straight rolls of SOME combo is around 95%.

You didn't specify for non double rolls.