I went when I was really young. I think I mainly visited resorts and amusement parks.
DAAK
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If you don’t like dice play Chess, or GO or checkers.
What fun would it be if the Japan TRN off KWA never saved itself?
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Singing to the choir Frimmel.
Though I think the example I used was the(actually rather common) super defense of Yukon Jack… the British INF in WCan that routinely seems to survive Japan amphibious assaults… at least he did in Classic for some reason…
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The only problem I have is that 1 infantryman in ADS can successfully hold off 400 attacking infantrymen given the right dice rolls.
Perhaps the best solution is to determine the odds of the battle then roll percentile dice (2 X 10 sided dice or 1 X 100 sided die) Still gives you odds, but at least you know you’ll win 40% of the time when the odds say you will!
And with Frood’s break down, you could jsut figure out where that roll scores on the chart. :)
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It may be abnormal, but it DOES happen.
Let me put it this way…
Many, many years ago, as a group of us were playing AD&D, a d20 stopped ON EDGE. It just sat there, its movement completed, perched on the edge ratehr than falling to put one face flat on the table, and another facing up.
After several moments, someone bumped the table and the die finally fell. But as George said after it happened…
“With all the dice that have been rolled on this table, it was bound to happen eventually”And your “all 5 ones missing, several times” is certainly far more likely than a d20 landing on edge and staying there until the table is bumped.
I’ll bet Frood (or any other Dicey) does not even CONSIDER the odds of a die landing on edge in the sims. But it is an extremely rare option that CAN happen.
When you get screwed by a die that rolls nothing instead of just rolling the 88% likelyhood of non-ones…
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The only problem I have is that 1 infantryman in ADS can successfully hold off 400 attacking infantrymen given the right dice rolls.
And that can happen at your dinner table with real dice not just with a computer program. The odds are long but so are they of getting hit by ligtning or winning the lottery or getting a rare and terrible disease…but people do get hit by lightning and win the lottery and die from rare and terrible diseases.
Try this mantra, say it often while gaming, “They’re dice.” Say it when they are bad for you and when they are good for you. Say it when they are good and when they are bad for others.
“They’re dice.” “They’re dice.” “They’re dice.”
_Think of the story of the scorpion on the fox’s back crossing the river. The scorpion stings the fox. “Why’d you do that? You’ve killed us both.”
“It’s my nature,” answers the scorpion._
“They’re dice.” It’s their nature.
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@ncscswitch:
I’ll bet Frood (or any other Dicey) does not even CONSIDER the odds of a die landing on edge in the sims. But it is an extremely rare option that CAN happen.
That’s an awesome suggestion! I could program it with a 1 in 3 million chance of leaving each die balanced on one corner. The effect of this will be instant nuclear armaggedon on the enemy force. Sweet.
Speaking of odds, I am trying to figure out if there is a better way to calculate them than by running a battle 10,000 times. It should be doable mathematically. Eg. with just one tank on each side, you know that there is a 1 in 3 chance of either side winning, and a 1 in 3 chance of mutual destruction. However, it gets a lot more complicated with more units of different types, esp. with subs and aircraft and opening fire etc. But in principle it should be possible to calculate the percentage of each possible outcome individually just once. I don’t know if it would run faster, because there might be millions of possible ways a large battle could run, but it should be completely accurate anyway.
The question is, does anyone know how to calculate those odds? Even for a single round of 8 armor v. 8 infantry, as a moderately complex example? What’s the formula? Math nerd, anyone?
Also, just wondering if the e-mail format is working for people. Will it work with TripleA? I don’t have that working right now (Java problems), so I don’t know how the PBEM works. Is it just manual entry of the e-mailed results?
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From the tests I have run, it works great with forum play (e-mails)
I have not installed tripleA on my new PC yet, but I think that has a built in combat roller.
As for the 1 in 3,000,000 chance… For d6 that should be about right.
For d20, I have seen 2 land on edge. The second was in a gaming gorup about 6 years ago. But since it was not the first time I had seen it, was not as impressive (you get numb to d20 landing on edge once you have seen it happen) :-D
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It has to be possible. After all, there is AASim for classic that runs a lot more computations, as well as other online diceys. Though, there are two new units on the board which has to exponentially increase the amount of results for any given battle.
Also, I wish you had a picture of a D20 balanced on edge on that table. :( That would make an awesome avatar for this site!
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After about 30 seconds of everyone sitting there with their jaws hanging open, the table got bumped and it fell…
The second time, was on edge far less.
I guess I could stage one and photograph it…
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This reminds me of when playing risk . . .
The attacker would roll three 1’s. He would still request that the defender roll “in case the dice explode” :D -
@ncscswitch:
I have not installed tripleA on my new PC yet, but I think that has a built in combat roller.
Yeah, it has a built-in one, but it also offers a PBEM option, that I have not checked out yet. I assume you have to just tell it how many casualties you are going to take, just wondering if anyone had used it. I guess the place to ask would be over at tripleawarclub.org or whatever it’s called.
I just tried to check out DAAK but it won’t let me play without creating a game # or something.
How do I get into a tournament or game here? I’ve never played that way before, in fact, I’ve only played AA about 5 times total. Anyone want to pick on a newbie? Of course, it would be tricky for me to use AACalc (everyone here calls it Frood, but that’s just my domain name), because I could doctor the output and you’d never know. For that matter, I guess anyone who knows how to spoof an e-mail address could impersonate it. I wonder, how could I validate that? I guess that’s maybe why DAAK is used for tournaments, because it actually tracks the game.
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The only problem I have is that 1 infantryman in ADS can successfully hold off 400 attacking infantrymen given the right dice rolls.
Perhaps the best solution is to determine the odds of the battle then roll percentile dice (2 X 10 sided dice or 1 X 100 sided die) Still gives you odds, but at least you know you’ll win 40% of the time when the odds say you will!
Given the same dice roller in both (e.g. a random number generator on a computer), you will have EXACTLY the same odds of having exactly the same outcome in both situations.
If you have a one in a N-illion chance of 1 infantryman in ADS killing 400 attacking ones, then you will have the exact same odds if you “determine the odds and roll a percentile dice”. It won’t change a thing. Only you have a greater suspicion probably when inevitably the single die comes up with a rediculous result.
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Those wild dice, while not common, stick in your memory, where teh common ones do not.
For example, I well remember a particular AD&D battle where 3 PC’s went up against a major Demon that made Orcus look like a pee-on. After hours of gaming, and many, many, turns of battle, the demon’s hordes were dead, and the Demon Lord was really beat up, but so were we. The Paladin was seriously hurt, the Cleric out of healing and offensive spells, and I was down to Magic Missiles (which were nearly useless against his magic resistance. But the Demon Lord was about to get a Heal spell off.
Initiative was rolled for the next round, and only my Magic User would get to act before his heal went off… and I had only a half segment to act, so no time to cast a spell.
So at long range (10 hexes), I pulled out a +4 dart and threw it. Natural 20, a hit. Max damage. Demon Lord is dropped to exactly 0 hit points… and dies.
Had my initiative been anythign less than top of 6’s, had I not rolled tha natural 20 to hit, had I rolled less than max damage, we were all dead. But I beat the odds, rolled the 1 in 12 for initiative, the 1 in 20 to hit, and the 1 in 4 for max damage. I made the 1 in 960 chance of killing that guy.
Closing on 20 YEARS later, that set of rolls is a vivid memory. But what of the hundreds or thousands of other rolls that have long since vanished from memory?
Selective memory leads us to remember the crazy results and forget the normal ones. And with A&A being only d6’s instead of up to d100, the “crazy” results are certainly more likely to occur since any given die has a 17% chance of rolling any given number.
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Yeah, that’s called “observation bias” or “confirmation bias” - I can never remember which though… Both may be at play here. We remember those experiences that confirm our beliefs, etc.
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By the way, frood, to do a purely mathematical calculator for battle outcomes, rather than a simulator, the task would be incredibly complicated if you were going to do ADS.
You’d have to keep an array of all the individual units in the battle, and calculate the probabilities that each one would get a hit or miss. Then do the same for the defending army. Then recursively consider the probabilities for each of the possible resulting outcomes. You perhaps could save a bit of calculations by using a Pascal’s triangle or combination table. It’s probably easier if I gave you an example:
Consider 2 tanks 3 infantry (attacking)versus 5 infantry (defending).
For each attacking armor, there is a (1/2) probability of hitting or missing, and for each attacking infantry, there is a a (1/6) probability of hitting and a (5/6) probability of missing. For each defending unit, there is a (1/3) chance of hitting and (2/3) chance of missing.
Considering the defender, the respective probabilities are as follows:
5 hits: (1/3)^5
4 hits: (2/3) * (1/3)^4 * 5
3 hits: (2/3)^2 * (1/3)^3 * 10
2 hits: (2/3)^3 * (1/3)^2 * 10
1 hit: (2/3)^4 * (1/3) * 5
0 hits: (2/3)^5(because there are 5 ways that 4 units can hit and 1 miss, 10 ways that 3 can hit and 2 miss, etc)
Then considering the attacker, things get a bit more complicated:
5 hits: (1/2)^2 * (1/6)^3
4 hits: (2 * (1/2)*(1/2) * (1/6)^3) + ((1/2)^2 * 3 (1/6)^2 * (5/6))
3 hits: ((1/2)^2 * (1/6)^3) + (2 * (1/2)(1/2) * 3 (1/6)^2 * (5/6)) + ((1/2)^2 * 3 * (1/6) * (5/6)^2)
2 hits: ((1/2)^2 * 3 (1/6)^2 * (5/6)) + (2 * (1/2)(1/2) * 3 * (1/6) * (5/6)^2) + ((1/2)^2 * (5/6)^3)
1 hit : ((1/2)^2 * 3 * (1/6) * (5/6)^2) + (2 * (1/2)(1/2) * (5/6)^3)
0 hits: ((1/2)^2 * (5/6)^3)And you know what if you can’t figure out how I came up with that last part I don’t think I’m going to bother to explain it because you need to have some background in probability and combinatorics and I don’t have time to give you a course. The brief explanation is, for 5 hits it was just the chances that both tanks would hit and all 3 infantry would hit, then for 4 hits it was the chance that both tanks would hit and 2 infantry would hit PLUS the probability that only one tank would hit but all 3 infantry would hit, and so on.
The coefficients being used in all cases are the values of the combinations which can be pulled from Pascal’s triangle as I mentioned above. It’s the number of ways of picking k distinct combinations from n items. The standard formula for that is n!/((n-k)!k!) [! = factorial]. So for instance the number of ways 6 units can get 3 hits is 6!/(3!*3!)=20.
Ok, so then anyway, you calculate all those values for the number of hits for each army, then you multiply all that together to get the probabilities for all the outcomes on that round. So for instance, the probability that the outcome of the first round will be 0 units remaining on both sides is the product that both sides will get 5 hits: (1/3)^5 * (1/2)^2 * (1/6)^3.
Now that you have all the respective probabilities of the results of that round, you take those outcomes that don’t result in the end of the battle and you recursively analyze them as if the battle were starting with that. But you see that this is beginning to get extremely computationally intensive, since there are already 36 different outcomes from the first round, only 3 of which result in the battle ending, so you have 33 different things to analyze recursively!
A further problem occurs when you consider the case that one of those 36 outcomes is that no one got any hits. This will always be a possible outcome of every position you analyze, so we face the prospect that our recursion will NEVER terminate. It is always possible that even if we have had 500 rounds of battle and no one has had any hits yet, that for the next round of battle no one will get any hits again.
To force our program to always terminate, we will then have to “eliminate” the case that no one gets any hits, because the situation ends up identical to the previous situation. So what you do is that for all the other 35 outcomes given above, divide the probability of their occurence with 1 minus the probability of no hits. So the “adjusted” probability then for 5 hits on both sides then is:
((1/3)^5 * (1/2)^2 * (1/6)^3) / (1 - ((1/2)^2 * (5/6)^3 * (2/3)^5) )
Got all that?
Anyway, even ignoring all the calculations about probabilities, which is simple enough to do for a computer once you’ve got it programmed, the recursion is still exponential and that is a huge problem. Calculating the outcome of a battle of 5 units against 5 units would probably take several seconds even on a fast computer. Actually probably more, given that after only 5 rounds of battle you already have on the order of 60 million possible threads of recursion, although most of those are probably going to be duplicates. Calculating 10 on 10 would probably take hours. Forget about doing a Karelia vs Eastern Europe scaled battle - it could well take decades for the computation to complete. Such is the nature of exponentially complex functions.
Now if you were trying to do the calculator for LowLuck though, that’s a different issue altogether. That’s easily doable in my opinion, and I made some posts on it a while back on the Axis and Allies forum here in response to someone who was trying to do just that. The reasons that it’s much simpler is that you can ignore the exact composition of units - only the total strength of each army matters. Furthermore, there will always be at most only 4 different outcomes for each round of battle, which shaves the recursion down considerably. Due to the nature of it also, there will be significant overlap after two rounds or more. Large battles also reduce in size much faster since each player is guaranteed to get a certain number of hits.
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Or just run the sim in your head and allow for some variations. If you get a set of rolls that are abnormal, deal with it :-P
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Well he was the one asking how you would calculate the odds mathematically. My last post was in response to frood’s query:
The question is, does anyone know how to calculate those odds? Even for a single round of 8 armor v. 8 infantry, as a moderately complex example? What’s the formula?
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I am sending Dan a few bucks to help maintian the site… I am not going to buy him a Cray to run the calcs :-D
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@ncscswitch:
Or just run the sim in your head and allow for some variations. If you get a set of rolls that are abnormal, deal with it :-P
Or just assume you’ll get 20% of your expected hits, the defender will get 160% of his expected hits and plan accordingly.
(Don’t assume a win unless your odds show 97% or better, works too.)
(Always bring 4:1 odds, works well too!)
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(Always bring 4:1 odds, works well too!)
Is there any other way? (unless playing LL?)
You ALWAYS use 3-1 odds as a minimum, 4-1 prefered. And when you can get 20-1, you bring ALL of it.
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