I'd like to state again that I think that the cards "randomness" should be locked and not something map makers can modify. It'll just lead to problems and give something else that needs to be explained for no reason.

Hugh, the line "I have a Phd in Math" would work about as well as my "I have a B.S. in Primatology and B.A.'s in English and Philosophy but if you feel like devolving with me, I promise not to correct your grammar or think too much about it".
P.S. If anyone ever thinks your Math P.h.d is silly, feel free to tell them about my collection of worthless degrees.

RiskyBack wrote:
P.S. If anyone ever thinks your Math P.h.d is silly, feel free to tell them about my collection of worthless degrees.

Hehe, but you use them all everyday in your work right?

As for the cards, ya it could get confusing if map makers do start doing something more complicated, but then they would have to make sure the players understand it.

Yertle Wrote:  As for the cards, ya it could get confusing if map makers do start doing something more complicated, but then they would have to make sure the players understand it.

Yes, we all know how easy that is.

Those are all respectable and interesting degrees Risky! Having taken some philosophy (not as much English and no primatology!), I consider it far more respectable than, say, communications or psychology or (especially) education.

Sounds like we have plan - Good wisdom (Risky + Yertle + tom = consensus) indicates to restore the basic 18/18/18/2 deck as a start. Tom, I'll send you this (message-wise) once I'm done.

-Hugh

Once again, I had 8 men unable to invade a territory with 1 man. As someone previously suggested, if there is a correlation for high numbers for both players, then that would give the defender an advantage. I only mention it, because with real dice, I do not seem to see the same number of unsuccessful invasions with 10 men against 1.

I might run a few simulations with the RNG you are using, even if it's just to satisfy my own paranoia. ;-)

The PHP manual says mt_rand (what tom says he uses) implements the "Mersenne twister", which is supposed to be quite good. Simple issues like seeing more high numbers than low should not occur over the long term with this routine.

If there is an actual issue, which I don't think there is (in spite of my own bad rolling against 1's), it would most likely lie in the sorting of the dice and comparing routine. This is nontrivial for Risk-type games, but I have a hard time believing our fearless leader screwed that up :)

-Hugh

I wouldn't have a hard time believing that if I were you ;)

Once I have the log file analysis online you'll be able to check the attack / defend results yourself which should hopefully alleviate any concerns...

Hugh wrote: The PHP manual says mt_rand (what tom says he uses) implements the "Mersenne twister", which is supposed to be quite good. Simple issues like seeing more high numbers than low should not occur over the long term with this routine.


-Hugh

Hugh,

You say that more highs than lows should not occur over the longer term...but that is exactly my point.  If there is a short term trend, then this would give the defender an advantage as defender '1' beats attacker '1', as does defender '6' beat attacker '6'.  I just find that the attack ratio's that I use to use as rule of thumb (ie, attack with double the men to be sure of a win) jsut don't seem to be holding out here.  But could be my own misconceptions. (most likely!!!!!)

Anyway, as I said, I will peform a simulation when I get a chance, and post the results.

Regards,

Paul.

"over the long term" is simply a statistician-speak way of describing an infinite set while A)avoiding making the unrealistic assertion that we'll be rolling an infinite number of dice and B) acknowledging that probabilities are based on expected behavior that is really only predictable with an infinite number of dice rolls.

Most rolls will be above or below some mathematical expected value, and you may notice a run where a few in a row happen to be low or a run where a few in a row happen to be high. From a human perspective, seeing 20 1's come up in a row may seem like a lot, but statistically speaking it's a short blip 'over the long term.'

And yes, in rolling a same number of dice, the defender has an advantage over the attacker. That's why the attacker gets a third die.

paulharrow wrote:

... (ie, attack with double the men to be sure of a win) jsut don't seem to be holding out here....

The funny thing about randomness is you can never be certain.  99% certain is nice in these games but I've rolled the dice way more than 100 times.  Anyway, I do think few things will ease your concerns more than you performing a simulation, checking for long runs, and seeing the results yourself.  

-Hugh

Hugh wrote:  Anyway, I do think few things will ease your concerns more than you performing a simulation, checking for long runs, and seeing the results yourself.  

-Hugh

Actually, I think the only thing that will ease my concern is when the dice all go my way.  Ha, I'm sitting here just laughing at myself over my own paranoia.  If there was a real issue, then I wouldn't be the only one raising it.  Maybe I just shouldn't expect to have the same % of wins in here as I do when I play my 9 and 11 year old daughters.  ;-)  (*paulharrow blushes*)

Yertle wrote:

I prefer the 0%/100% Probability Rule, everything is either 0% or 100%, there's nothing in between

Lol Yertle... the probability for anything to happen is ALWAYS 50%... (horrible math FTW) it either happens or it doesn't. 

Quantum mechanics doesn't allow for probabilities to be EITHER 0% or 100%...

-------> This way to derail the thread!

Ender wrote:

Yertle wrote:

I prefer the 0%/100% Probability Rule, everything is either 0% or 100%, there's nothing in between

Lol Yertle... the probability for anything to happen is ALWAYS 50%... (horrible math FTW) it either happens or it doesn't. 

 

Quantum mechanics doesn't allow for probabilities to be EITHER 0% or 100%...

 

-------> This way to derail the thread!

What about AFTER it happened?  Everything either happened or didn't happen yesterday, thus 0% it happened or 100% it happened, not 50% that it happened.

Happen happen happen happen happen happen happen...it's a funny word now.

Right... every event A has two possible outcomes: 1 or 0. The average of those values is 0.5...

Say I am flipping a coin with outcomes heads = 1 and tails = 0 and I have flipped 4 heads in a row. What is the probability that the next coin flip will be heads? 50%! (OMG bad math!)

The actual probability of flipping 5 heads in a row is (0.5)^5 = 0.03125 = 3.125%

Saying what is the probability of something that DID happen made me laugh!

But if you look beyond the event of the 5th coin flip the probability is either 0 or 1 that it was heads, therefore the probability that the event of the 5th coin flip will be heads is 0 or 1. 

Throwing a six sided dice is the same thing, the probability that a 3 is rolled is either 0 or 1, because after the event occurs it was either a 3 or it was not a 3. 

Yertle wrote:

But if you look beyond the event of the 5th coin flip the probability is either 0 or 1 that it was heads, therefore the probability that the event of the 5th coin flip will be heads is 0 or 1. 

Throwing a six sided dice is the same thing, the probability that a 3 is rolled is either 0 or 1, because after the event occurs it was either a 3 or it was not a 3. 

First of all, that last comment makes no sense.

I think what Yertle is trying to say is that he would prefer not to flip a coin at all (or, in other words, he would like to roll a 1-sided die). In that scenario, he would have absolute certainty as to the outcome of each role, as the probability of winning would either be 100% OR 0% depending on how many armies each side has (hence Yertle's 0%/100% comment). What Yertle is saying is that he would prefer that luck not factor at all into his games. Note the difference between this scenario and flipping a two-sided coin.

Personally, I think you are thinking that Yertle is trying to be Yertle and not trying to be a little Risky.

Re-Read his posts and pretend that I wrote them and it will all make much more sense.

I'm with the Turtle on this!!

Kjeld wrote:

I think what Yertle is trying to say is that he would prefer not to flip a coin at all (or, in other words, he would like to roll a 1-sided die). In that scenario, he would have absolute certainty as to the outcome of each role, as the probability of winning would either be 100% OR 0% depending on how many armies each side has (hence Yertle's 0%/100% comment). What Yertle is saying is that he would prefer that luck not factor at all into his games. Note the difference between this scenario and flipping a two-sided coin.

This is the goal of many of my map ideas...

...it hasn't worked out yet.

RiskyBack wrote:
I'm with the Turtle on this!!

Case closed, I win (Bagel Bites???).

Kjeld I was talking about a whole coin and whole dice :).  On a previous roll of a dice, what is your probability that you rolled a 3?  It wasn't 16.7% probability that you rolled a 3, you either rolled a 3 (100%) or rolled any number other than a 3 (0%).  So the probability of your next roll of a dice of rolling a 3 is then still 0% or 100% .

*This is beyond the scope of rolling dice on WarGear :P.

Ender wrote: Right... every event A has two possible outcomes: 1 or 0. The average of those values is 0.5...

Say I am flipping a coin with outcomes heads = 1 and tails = 0 and I have flipped 4 heads in a row. What is the probability that the next coin flip will be heads? 50%! (OMG bad math!)

The actual probability of flipping 5 heads in a row is (0.5)^5 = 0.03125 = 3.125%

Saying what is the probability of something that DID happen made me laugh!

My sarcasm detector is broken, so I'll just go ahead and point out that you're right about both.

The probability that the next coin will be heads is .5. The probability of flipping 5 heads in a row is .03125.

Your use of the word "actual" in there made me unsure if you're making a distinction between the two.