Improving the Odds in RISK

[tahitiwahini]

Recent analyses reveal that the chances of winning a battle are considerably more favorable for the attacker than was originally suspected.

"The logical recommendation is . . . for the attacker to be more aggressive," says statistician Jason A. Osborne of North Carolina State University in Raleigh, who presented his findings in the April Mathematics Magazine.

Based on his analysis, Tan concluded that, when both attacker and defender have the same number of armies, the probability that the attacker wins is less than 50 percent. When there are twice as many attackers as defenders, the winning probability exceeds 80 percent. Moreover, the expected loss by the attacker is slightly lower than the number of defending armies. For example, if an attacker has 20 armies and a defender has 10 armies, the attacker would win the war with a probability of 98 percent and lose about 9 armies doing so.

Keeping in mind the need to defend a newly conquered territory, Tan formulated the following rule of thumb: Based on how many defending armies you want to leave on a territory that you want to conquer, attack if you have twice as many armies on a neighboring territory and also if the number of armies your opponent has is at most half of the number of your armies.

The new results point to a bigger advantage for an attacker over the long run than suggested by Tan's analysis. For instance, even when the number of attacking and defending armies is equal, the probability that the attacker ends up winning the territory is actually greater than 50 percent, provided that both sides have at least five armies each. The attacker also suffers fewer losses on average than the defender.

http://www.sciencenews.org/articles/20030712/mathtrek.asp

[Kugelblitz22]

It always amazes me to see these games with 1000 armies on the board. You'll never see me in a game like that. I want that attacking bonus!

[silvanthalas]

I just had a 16v7.

Worst case scenario should be that I lose 7, best case that I lose 5.

I lost 12.

If I find that statistician, I'm going to slap him.

[tahitiwahini]

I just had a 16v7.

Worst case scenario should be that I lose 7, best case that I lose 5.

I lost 12.

If I find that statistician, I'm going to slap him.

Of course, such results are useful only over a long sequence of many battles. Depending on the turn of the dice, you can still lose no matter how overwhelming your forces may be in any given instance. And small variants in the rules—such as whether you can withdraw from an attack if you so choose or the number of dice a defender is allowed to roll—can strongly affect the expected results.

Congratulations! You defied the odds. Happens all the time.

Wouldn't it be better if you defied the odds in your favor though?

[AAFitz]

I just had a 16v7.

Worst case scenario should be that I lose 7, best case that I lose 5.

I lost 12.

If I find that statistician, I'm going to slap him.

thats only losing 6 rolls in a row...when the defender wins ties....thats not surprising at all

ive lost many more in a row....ive also attacked with 7 to 12 and won with some left over....

and i am a big fan of being the attacker than the defender...but like anything else...you have to be careful

[dividedbyzero]

I just had a 16v7.

Worst case scenario should be that I lose 7, best case that I lose 5.

I lost 12.

If I find that statistician, I'm going to slap him.

Buy a lottery ticket. Stat!

[silvanthalas]

Happens all the time.

Yes, it does. It happens to me all the @#$% time.

I did win a 6v13 once, only losing two. But it is far more common for me to lose much more than the 'worst case scenario' would predict, even compared to a 'base case scenario' of underwhelming odds, such as the 6v13, and I'd love to know why.

Oh, look, now a 12v2 and I lose 10 armies in a row. When's the last time I defeated 10 armies in a row? You know, I can't remember. I wonder why that is...

And to see the defender get double 6's once again, after having gotten back-to-back double-6's in that 16v7 a little earlier. Double-6's, a 1:36 odds, 3 times in the last dozen 3v2's I've rolled.

How wonderful.

[tahitiwahini]

Happens all the time.

Yes, it does. It happens to me all the @#$% time.

I did win a 6v13 once, only losing two. But it is far more common for me to lose much more than the 'worst case scenario' would predict, even compared to a 'base case scenario' of underwhelming odds, such as the 6v13, and I'd love to know why.

Maybe we're looking at this dice thing all wrong. We're human so we tend to think the whole world revolves around us. We like to believe we come to this site to play a simple game of world domination. We find the game strangely addictive. We like to complain when we lose that the dice were against us. The dice are merely an annoyance to us.

But what if... this site is really run by a race of superintelligent dice. I mean, come on... has anyone actually met "lack?" There I said it, it's out in the open now. The game is merely a ruse to attract credulous humans to participate in a vast social experiment, designed and conducted by these dice. This CC project is studying how humans react to chance. Each game is really an experiment. The most important results are the human's reactions expressed in game chat and the forums. The games are just the medium in which the subjects are sustained until their usefullness to the project is at an end.

The dice are probably watching your game right now. "How many sixes can we let the defender roll, before the player becomes suspicious?" one dice says to the other, both dressed in their immaculate white lab coats. "Maybe once more. We don't want to push this subject anymore, he's becoming agitated and he might leave before we can complete the study. Let him win the next attack. There, there, that seemed to calm him down. Ratchet up the defender's sixes again and we'll see how long it takes for him to make another complaint..."

[Stopper]

I just had a 16v7.

Worst case scenario should be that I lose 7, best case that I lose 5.

I lost 12.

If I find that statistician, I'm going to slap him.

Maybe I haven't been reading closely enough, but surely the worst case scenario in a 16 x 7 battle is that you lose 15? So, losing 12 isn't all that bad.

[silvanthalas]

Maybe I haven't been reading closely enough, but surely the worst case scenario in a 16 x 7 battle is that you lose 15? So, losing 12 isn't all that bad.

Ideal scenarios, not actual, "man am I always getting raped" scenarios.

[ABSOLUTE_MASTER]

This CC project is studying how humans react to chance. Each game is really an experiment. The most important results are the human's reactions expressed in game chat and the forums. The games are just the medium in which the subjects are sustained until their usefullness to the project is at an end.

OMG, I'll be more careful in the game chat from now on...

[Asclepio]

But what if... this site is really run by a race of superintelligent dice. I mean, come on... has anyone actually met "lack?" There I said it, it's out in the open now. The game is merely a ruse to attract credulous humans to participate in a vast social experiment, designed and conducted by these dice. This CC project is studying how humans react to chance. Each game is really an experiment. The most important results are the human's reactions expressed in game chat and the forums. The games are just the medium in which the subjects are sustained until their usefullness to the project is at an end.

The dice are probably watching your game right now. "How many sixes can we let the defender roll, before the player becomes suspicious?" one dice says to the other, both dressed in their immaculate white lab coats. "Maybe once more. We don't want to push this subject anymore, he's becoming agitated and he might leave before we can complete the study. Let him win the next attack. There, there, that seemed to calm him down. Ratchet up the defender's sixes again and we'll see how long it takes for him to make another complaint..."

Very nice tahitiwahini!! Do you love SF scenaries? I think yes, so keep doing a great imagination job.

[cricket]

i keep losing to the defenders. even if roll 15 sixes, the defenders roll 20 sixes

[AAFitz]

But what if... this site is really run by a race of superintelligent dice. I mean, come on... has anyone actually met "lack?" There I said it, it's out in the open now. The game is merely a ruse to attract credulous humans to participate in a vast social experiment, designed and conducted by these dice. This CC project is studying how humans react to chance. Each game is really an experiment. The most important results are the human's reactions expressed in game chat and the forums. The games are just the medium in which the subjects are sustained until their usefullness to the project is at an end.

The dice are probably watching your game right now. "How many sixes can we let the defender roll, before the player becomes suspicious?" one dice says to the other, both dressed in their immaculate white lab coats. "Maybe once more. We don't want to push this subject anymore, he's becoming agitated and he might leave before we can complete the study. Let him win the next attack. There, there, that seemed to calm him down. Ratchet up the defender's sixes again and we'll see how long it takes for him to make another complaint..."

Very nice tahitiwahini!! Do you love SF scenaries? I think yes, so keep doing a great imagination job.

i lost a team game against blitz and usojacket early on....we had the game sealed up...but then we lost 40 armies and we killed maybe 3 or 4....not exxagerating....i thought for sure since they were higher ranked, it was set up to favor them...even pmed them....

but now that ive played enough, i realize some go your way and others dont....thats why i post on dice matters....ive been there....seen ridiculous things happen, but still know it all averages out..it just might not happen inside of a game, or even a group of games

[AAFitz]

i keep losing to the defenders. even if roll 15 sixes, the defenders roll 20 sixes

i do wish you told me that before i signed up for 3 games with you

[pancakemix]

Those guys' jobs are to play risk! I envy them.

[yowzer14]

I just had a 16v7.

Worst case scenario should be that I lose 7, best case that I lose 5.

I lost 12.

If I find that statistician, I'm going to slap him.

Statistically speaking you probably won't find the statistician.

[AAFitz]

I just had a 16v7.

Worst case scenario should be that I lose 7, best case that I lose 5.

I lost 12.

If I find that statistician, I'm going to slap him.

Statistically speaking you probably won't find the statistician.

what are the odds for each search engine of finding him?

[Robinette]

Okay, I just have to add something here since this is all about Improving Your Odds. I think we can all agree that the attacker has an ever so slight advantage over the defender in the Long-run, and therefore has no noticable advantage during a particular move or even during a particular game.

So for me I have found that the best way to improve the odds is to maniupulate the system to gain an extra card. This, combined with sound strategy skills, will result in a statistical advantage over the long run. This does not ensure a win by any means, but it does just what this thread is all about... IT IMPROVES THE ODDS.

It's a bit complicated to explain without a whiteboard, but if you REALLY want to know how I've improved the odds for myself, then keep reading.

First off, it doesn't work with flat rate, and it doesn't work with team games. Here 's why... it is all about the Cyclomatic Code Complexity within this site. The simple part to explain is that on this site the code complexity is defined by control flow, and obviously there are different ways of measuring complexity (e.g. data complexity, module complexity, algorithmic complexity, call-to, call-by, etc.), and although these other methods are effective in the right context, it seems to be generally accepted that control flow is one of the most useful measurements of complexity, and high complexity scores have been shown to be a strong indicator of low reliability and frequent errors. That's simple enough, but it's what we do with it that's so cool... This measure provides a single ordinal number that can be compared to the complexity of other games. Because of static software metrics intended to be independent of language and language format, Cyclomatic Code Complexity becomes a measure of the number of linearly-independent paths through a program module and is calculated by counting the number of decision points found in the code. Stay with me people... I use a Lutz Roeders Reflector which basically allows the user to point his Reflector tool at any Common Langauge Runtime (CLR) assembly, and it will then de-compile this creating an entirely reflected treeview with all the objects from the source assembly shown, with code. Yes with code. Great stuff. Basically you can use this tool to see how any valid CLR (assuming it has not been obfuscated) assembly works. Anyway the up shot of it, is that we get a boolean to say that the current file is valid or not, that is all we care about at the moment. So if the file requested is not a valid CLR type an error message is shown, and nothing else is done. However, if the input file is a valid CLR file, it is then checked to see if the file is a "System" assembly, and if it is... eureka! I get an extra card. Ok so thats pretty much all there is to it.

A while back I started to modifiy this to work with flat rate, but I don't think it would really be worth all the effort. So if you really want this for flat rate, let me explain how far I got and you could work on finishing it. You would have to revisit the treeview with ONLY valid namespaces and ONLY valid classes created. We would also have to find the NameSpaces object which contains the list of strings (for namspaces) and for each string of ucClass objects (for the classes). The list of ucClass objects are created by this and are then ready and waiting to be placed on a suitable code. But as yet we dont know what classes the user needs, it could be all of them, or it could be 1 of them or even none of them. It depends on what the user selects from the treeview on the mainform (frmMain.cs). And that's where I got stuck. So I looked and I looked for an answer. The only thing simliar at all, was GDI+ and in order to do something like this, a destination target needs to be created at the full string size, and then the viewable (onscreen) fragments are printed to individual page framements and saved into the destination image at the correct x/y co-ordinates. In order to do this the application has to programatically perform scrolling to get the next page fragment code to merge with the destination code. I managed to get this to work, but it was a complete nightmare, and there were definetly bugs everywhere, which resulted in losing more cards that I gained! So if there is anyone reading this that is totally rad and knarly at GDI+, and knows how to save the entire contents of a scrollable control to an exisiting code, please feel free to let me know. As for the above code, it is code that I am kind of 1/2 proud of, but would rather wasn't there. Do you know what I mean? After all, sometimes you just get completley stuck with trying to patch all these code fragments together, to form the final destination code.

So for these reasons, it only works properly with 6 player std escalating games. And why I mostly play 6 player std escalating games.

And why I always seem to have 1 more card than you.

[tahitiwahini]

Okay, I just have to add something here...

...

So for these reasons, it only works properly with 6 player std escalating games. And why I mostly play 6 player std escalating games.

And why I always seem to have 1 more card than you.

Any explanation that long has just got to be true.