the odds of what? the sentence before it didn't contain a quantitative statement....

PHP's shuffle() doesn't play tricks on people, but we hope to put a country balancer into the next version which will make those odds much lower

(But discussing the math behind the odds you give would be interesting. When the probability is calculated properly things which seem anomalous turn out to be business as usual)

The countries are assigned randomly.

Roll a die as many times as you've played games. You'll see you don't get each pip the same amount of times.

You've played Germany 6 out of 21 games. If you treat this as a binomial problem, then:

P(G) = (1/7)^6 * (1-1/7)^(21-6) * (21C6)
P(G)= 4.57%

If anyone disagrees, please let me know what I did wrong.

Just going by the simplistic statement, assuming that you wouldn't be complaining if you were assigned countries in exactly equal ratios, then there must be a country that is played more than others. There is a precisely 1 in 7 chance that this country is Germany.

that calculation is correct, but not statistically very interesting. after all, diplomat would have been just as annoyed if he had had Germany more than 6 times out of 21, rather than exacly 6. He probably just wants to assess the probability of the shuffling system to be fair, so getting any other country more than 5 times out of 21 would seem "unfair" as well.... so the more interesting question might be what the odds are that you can ANY country 6 times or MORE, rather than a SPECIFIC country exactly 6 times.

And diplomat, did your PhD not include a basic course in probability, because that is a standard for all accredited engineering schools.

Giwald,

I agree; however, I'm not sure I can do that calculation. I'll give it a shot, though.

You just sum what you already did for 6..21 times the same country. That gives 6.82%, just for the odds that you'd get Germany 6 times or more.

A rough estimate of the odds of getting ANY country 6 times or more is 7*6.82%=47.7%. I know that isn't exact because I double counted samples in which you get two countries 6 times or more, but that should be a small correction.

... so to get back to the original question. No trick. No anomaly. Just statistics. It's not even that unlikely in the first place.

Random assignment is just like a dice roll. Each roll has nothing to do with the roll before or the roll after. There really is no probability or statistic because it is random. Probability theory assumes trends and factors not necessarily visible to the casual observer. I'm not looking at the code right now, but if it is triggered every five minutes like the turn processing, and if it uses the current time (or some variation there of) to get a random seed, and if it runs through the players either in a preset order (alpha, by profile number, or by sign up order) assigning the nations as it goes, it is possible that it may not be truly random but have a bit of predictability in it. Traditional computers (Macs, PCs, Linux boxes, doesn't matter) aren't ping pong balls in a lottery machine. The random number generator is anything but truly random. If fed the same seed, it will generate the same sequence of numbers.

I don't want to get into random number generators... I presume phpdip uses one that is sophisticated enough to have a fair player shuffle.

Your statement that "There really is no probability or statistic because it is random." makes me extremely confused. The fact that it is random implies that we can exactly calculate probabilities for something to happen.... so what do you mean by this?

@Draugnar,

I'm not sure what you mean by "no probability because it is random?"

The probability of rolling 5 6's in a row on a die is (1/6)^5...

You're right about the pseudo random nature of the code; however for our purposes, it is irrelevant. It is possible to make random number generators that get information from the hardware (which is unique because of temp and manufacturing defects) Although technically pseudo random, it's impossible to find an algorithm for, which is all that's important.

I would figure the probability would be calculated as the product of the chance of getting Germany 5 times (1/7)^5 and the chance of getting anything but Germany for his 15 other games (6/7)^15. This works out to be 9.90% according to my calculator. So just shy of 1 in 10 odds. That's not all that surprising for such a small sample size.

I'm reminded of a coin flip scene from Rosencrantz and Guildenstern are Dead.... I wonder if thats scene is available on You Tube.

llama...we worked with 6 out of 21 instead of 5 out of 20 but we agree on how to calculate these things...

I should have clarified. It's not that there is no porbability, but that the probability of getting a given nation does not change just because you have had that nation previously. Sorry for the confusion. Each draw has just as much chance of producing Germany as it does of producing England.

I guess what I'm getting at is weather countries are chosen randomly or chosen in other ways.

You know diplomat, its not just mods that can answer your questions. Nor do the mods exist to inform you of things you could find out yourself by looking around.

Assuming there are 7 players for a game, the allocation is completely random. Otherwise Italy (and possibly Germany) are set as CD, then the others are randomly distributed.
As pointed out, computers can never truly produce random values, but to all intents and purposes there's no difference.So, treat the allocations as random.

What Kestas said is that there is a conversation ongoing on the dev forum trying to find an efficient algorithm with which to weight the allocation such that you're less likely to be given the same country again and again. If you have an idea, do post it over there

Hmm, 6 out of 21 is no less random than my 5 Russias out of 13 on the FB app.

But, I am slightly bothered about it, in two of the games I set up on FB at the same time, another player I'd never played before joined both just after.

When countries were assigned, I was Russia in both, he was France in both. My previous and next starting countries were also Russia. If we hadn't had the both-the-same-in-both fluke, I'd have never looked at the math at all.

If there could be some pseudo-random but not the same coutnry twice in a row setup, that'd be really cool, but I suspect a bugger to code.

Annoyingly, despite us both agreeing not to meta, it's ended up us as allies in both anyway, and we both tried completely different strategies at start, only to have it all messed up. C'est la vie.

It won't be too hard to code, but we don't want to do that. The idea is that there will be a wieghting, but it can't be deterministic. The thread is here:
http://forum.phpdiplomacy.net/viewtopic.php?f=9&t=145

The real question of probability isn't how many times a person gets a specific country, but why in 22 games I have never been France.

It's just as likely for you to get your sequence of country assignments as a perfectly distributed one. It is for practical purposes, random.

Count me with abgemacht in wondering how someone with a Ph.D. in engineering thinks 1/5! is the probability of getting a country 6 times in 21 games.

Figlesquidge, I notice there hasn't been any activity on the that thread in the developer's forum recently. I'm busy this week, but if people are interested, I might be able to run some experiments with the various proposals next week or so.

Is it possible to create a mode of game-creating where players can choose their country?

You guys should stop giving diplomat a hard time.

I confess that I secretly hacked into his computer and the phpdip servers in order to purposely make him Germany five times.

It seemed like a reasonable thing to do at the time...