Can You Determine the Randomness in Backgammon?

[RenasontsMan]

If you have played games of chance, you may have seen rolls of the dice, or flops of the cards that did not strike you as being random. I have played many games of backgammon, where the roll of the dice trumps talent. You can be bearing your checkers off, and lightning strikes. You get hit, your opponent fills his prime, and you sit and watch as he merrily rolls the dice and you roll 3-3, and then 3-1, and then 1-1, etc.

My opponent once had three men exposed on his back row. THREE! I was plowing ahead and bearing off, leaving one checker he might hit with a roll of 1-X or X-1. Not to worry. I had three chances to hit him back IF he got me.

Well, he rolled 1-1 and not only hit me, but COVERED every one of his three exposed men in his home row. I was twitterpated. Unfair, I say.

Now this brings to mind a test which I dare say not one of you could pass.

Let me offer up a series of dice rolls as you play backgammon. I will be behind a screen and
roll the dice and then call out the numbers. I may be honest or not.

HOW would you tell, dear physics intellectual, if I were cheating on any given single roll, series of rolls, or all of them? You would have to rely on simplistic statistical tests, as if 6-6 or acey-deucey wouldn't be likely to come up three or four times in a row.

It just so happens that my little girl was playing the acey-deucey variation of backgammon with her cousin some time ago. He was mopping up, going away, whistling a happy tune, if you know what I mean.

I encouraged my little girl, then about 6, "Come on, roll acey-deucey." She did. And with acey-deucey, she got her choice of doubles and another roll. Of course she opted for 6-6. Her cousin yawned, his lead still apparently insurmountable.

I yelled again, "Come on, roll acey-deucey." She did. Double sixes it was.

Her cousin's eyes got wider.

I yelled, "Come on, roll acey-deucey." I swear, it happened. Three 1-2's in a row.

Finally, on her next roll, she did NOT roll acey-deucey. No, she rolled 6-6.
Her cousin, 7, jumped up screaming, and cried as he ran away, utterly beaten.

Twenty-four times four is a significant portion of the number necessary to bear off all your men.

So HOW would you determine randomness objectively while playing backgammon?

Better yet, provide a formula for generating random numbers.

And if evaluating whether or not a given number is indeed random, what claim do any of us have on intellectualism, hmmmmm?

 

[RenasontsMan]

///

HOW would you tell, dear physics intellectual, if I were cheating on any given single roll, series of rolls, or all of them? You would have to rely on simplistic statistical tests, as if 6-6 or acey-deucey wouldn't be likely to come up three or four times in a row.

///
So HOW would you determine randomness objectively while playing backgammon?

Better yet, provide a formula for generating random numbers.

And if evaluating whether or not a given number is indeed random, what claim do any of us have on intellectualism, hmmmmm?

Fifty-six views, and not one offering up a random number generator.
Not one offering up how we could know if a number was random or not.

You may THINK that all thirty-six individual rolls are equally probable, but it sure seems odd when your opponent gets one double after another, and you get squat diddley.

 

[Office_Shredder]

The question of how to generate a number truly randomly, or how to tell if a sequence of numbers is random, is a deep and difficult one.

It's not odd that your opponent gets better rolls than you sometimes. It would be odd if it occurred often, but unless you keep track of every roll you get and every roll your opponent gets, all we can say is that the times when someone rolls four doubles in a row is far more memorable than the times when they don't, so it's not surprising those are the times you remember

 

[Proton Soup]

 

[Danger]

:rofl: :rofl: :rofl:

That pretty well sums it up, PS.
That's what drove me nuts with customers when I was looking after VLT machines in the bars. They'd keep saying, "This machine is due to hit any time now" because it had been dry for a while. Just try explaining to a gambler that every draw is a fresh one.

 

[Hurkyl]

I have played many games of backgammon, where the roll of the dice trumps talent.

Do be careful with this. It is disturbingly common for people to look for scapegoats to rationalize away their own poor play or their opponent's good play, and random chance is a more convenient scapegoat than most.

 

[Danger]

It is disturbingly common for people to look for scapegoats to rationalize away their own poor play or their opponent's good play, and random chance is a more convenient scapegoat than most.

Now that you mention it... I played backgammon once over 20 years ago, and was being taught the game as I played. I seem to recall, however, that there was some element of strategy involved, as opposed to a purely random dice roll. That would be about the same as the difference between playing 5-card draw poker as opposed to 5-card stud. The randomness can be alleviated by the player's "savvy".

 

[RenasontsMan]

Do be careful with this. It is disturbingly common for people to look for scapegoats to rationalize away their own poor play or their opponent's good play, and random chance is a more convenient scapegoat than most.

How "good" is your opponent's "play" when they roll 6-6, followed by 4-4, and then 3-3, while you roll 1-4, followed by 1-2, and then 2-3?

You then get hit, put on the bar, and your opponent proceeds to prime, bear off for roll after roll, even as you get only low numbers and remain on the bar.

Tell me ALL about the "good play" involved, please, as if chance played no part...

 

[RenasontsMan]

/// I seem to recall, however, that there was some element of strategy involved, as opposed to a purely random dice roll. /// [/ QUOTE]

1. Nobody has made any effort to determine what is "purely random" and what is not.

2. I have yet to see a formula offered up to generate random numbers.

3. If you have spent any time watching professional poker championships, you should know that the "best" players don't always win. Sometimes it's the schlep who pulls the flush on the river card - you know, the guy who went "ALL IN" on his 3-4, and beat the "best" player who had pocket aces.

There is a well known saying: "Luck beats skill every time."

By the way, Danger, any pilot who mistakes a tennis court for a runway would also be likely to make the mistake of
going for full flaps before full power. Not the right move.

RenasontsMan, licensed to fly

 

[Office_Shredder]

1. Nobody has made any effort to determine what is "purely random" and what is not.

That's not true. A lot of thought has been put into what purely random means, the problem is that it's impossible to decide on what it is

2. I have yet to see a formula offered up to generate random numbers.

Because formulae, by definition, are formulaic, not random. That doesn't seem terribly surprising

3. If you have spent any time watching professional poker championships, you should know that the "best" players don't always win. Sometimes it's the schlep who pulls the flush on the river card - you know, the guy who went "ALL IN" on his 3-4, and beat the "best" player who had pocket aces.

That happens about as often as the odds say it should happen. You seem to be of the opinion that in games that involve an element of luck, it's shocking that the lesser player occasionally wins by luck.

 

[granpa]

random=unpredictable

 

[russ_watters]

How "good" is your opponent's "play" when they roll 6-6, followed by 4-4, and then 3-3, while you roll 1-4, followed by 1-2, and then 2-3?

In any game with some probabilistic component, there will be times when you will lose based on nothing other than bad luck. No player, regardless of skill, will win such a game every time. What skill does is increase the ratio of wins to losses.

 

[Hurkyl]

There is a well known saying: "Luck beats skill every time."

I know it as "better lucky than good".

This is countered by "make your own luck". Also, by being both lucky and good.

I've watched some good backgammon players play. When choosing between moves, they do things like count through each of the numbers 1 through 6 and try to arrange things so that, on their next turn, as most or all of them will be useful moves. Sometimes, they do the same with their opponents moves, except try to ensure that most of them will not be useful.

Sometimes you get lucky through pure chance. But you get lucky far more often when you create opportunities to be lucky and eliminate opportunities to be unlucky.

 

[Jack21222]

PokerStars and similar websites have found a very robust way to generate random numbers.

From http://www.pokerstars.com/poker/room/features/security/:

We understand that a use of a fair and unpredictable shuffle algorithm is critical to our software. To ensure this and avoid major problems described in [2], we are using two independent sources of truly random data:

* user input, including summary of mouse movements and events timing, collected from client software
* Quantis [3], a true hardware random number generator developed by Swiss-based company ID Quantique, which uses quantum randomness as an entropy source

Each of these sources itself generates enough entropy to ensure a fair and unpredictable shuffle.

It then continues:

* A deck of 52 cards can be shuffled in 52! ways. 52! is about 2^225 (to be precise, 80,658,175,170,943,878,571,660,636,856,404,000,000,000,000,000,000,000,000,000, 000,000,000 ways). We use 249 random bits from both entropy sources (user input and quantum randomness) to achieve an even and unpredictable statistical distribution.
* Furthermore, we apply conservative rules to enforce the required degree of randomness; for instance, if user input does not generate required amount of entropy, we do not start the next hand until we obtain the required amount of entropy from the Quantis RNG.
* We use the SHA-1 cryptographic hash algorithm to mix the entropy gathered from both sources to provide an extra level of security
* We also maintain a SHA-1-based pseudo-random generator to provide even more security and protection from user data attacks
* To convert random bit stream to random numbers within a required range without bias, we use a simple and reliable algorithm. For example, if we need a random number in the range 0-25:
o we take 5 random bits and convert them to a random number 0-31
o if this number is greater than 25 we just discard all 5 bits and repeat the process
* This method is not affected by biases related to modulus operation for generation of random numbers that are not 2n, n = 1,2,..
* To perform an actual shuffle, we use another simple and reliable algorithm:
o first we draw a random card from the original deck (1 of 52) and place it in a new deck - now original deck contains 51 cards and the new deck contains 1 card
o then we draw another random card from the original deck (1 of 51) and place it on top of the new deck - now original deck contains 50 cards and the new deck contains 2 cards
o we repeat the process until all cards have moved from the original deck to the new deck
* This algorithm does not suffer from "Bad Distribution Of Shuffles" described in [2].

Would the OP consider this truly random?

 

[xxChrisxx]

Would the OP consider this truly random?

I wouldn't, as any RNG is based on 'something' and is therefore not in the purest sense random. However it's probably as close as you are going to get.

Addendum: Bad example - Stars is rigged


Also to the OP, it's time you learned that variance is a *****.

 

[Jimmy Snyder]

3 is a random number.

 

[xxChrisxx]

3 is a magic number.

fyp.

 

[Danger]

By the way, Danger, any pilot who mistakes a tennis court for a runway would also be likely to make the mistake of
going for full flaps before full power. Not the right move.

It was a dead-stick approach, and it was actually a friend's back yard rather than a tennis court. So, I use a bit of hyperbole now and then. Just because this is a science site doesn't mean that you have to park your sense of humour at the front door before entering.

 

[RenasontsMan]

///


You seem to be of the opinion that in games that involve an element of luck, it's shocking that the lesser player occasionally wins by luck.

I said nothing of the sort. My original point was that IF we have such a difficult time determining what is random and what is not, then perhaps - PERHAPS we should not be so cock sure that we know this or that to be absolutely factual.

"SHOCKING" was YOUR word, not mine.

Another contributor here opined that luck plays almost no part. Pure poppycock.

That he and you continue to repeat your opinions so forcefully rather confirms my point, that maybe truth is sometimes more elusive than some pretend.

 

[xxChrisxx]

Another contributor here opined that luck plays almost no part. Pure poppycock.

see: law of large numbers.

 

[RenasontsMan]

It was a dead-stick approach, and it was actually a friend's back yard rather than a tennis court. So, I use a bit of hyperbole now and then. Just because this is a science site doesn't mean that you have to park your sense of humour at the front door before entering.

I have an extremely good sense of humor. However, my taste for humor runs toward the somewhat plausible, not in the direction of compounded nonsense.

It was humorous to me that someone could possibly think any pilot would seriously contemplate trying to land on a tennis court. Nobody would. Quite impossible.

Secondly, the passenger would be screaming out the warning. Pilots don't generally yell
at themselves to take some action. And in this case, the passenger's advice would not be optimal.

Third, one assumes that the pilot in command is the more competent of the two, and therefore he is better equipped to take appropriate steps.

So your attempt at "humour" overlooked a bundle of things that was so amusing I had to comment on it. That you got all churlish instead bespeaks your own poor sense of humour.

Suck it up. Take it like a ... werewolf, or whatever it is you are.

Irish Airline Captain on final approach: "Damn, mate, but that's a short runway"
His Copilot: "Yeah but it's WIDE!"