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It is Called Risk for a Reason

By Ehsan Honary - Tuesday, January 1, 2008
:: 21 Comments :: Article Rating :: Tactic, Strategy, Beginners
 

You have battled your way through the game. It wasn’t easy and you are glad that you have survived. You really want to win. You have now come to a really decisive point. You have an advantage and you don’t want to blow it up.

End-games in Risk are quite tricky. There is only one winner and when you get to a certain stage, a single mistake or a missed opportunity means you will lose the game and leave the trophy for someone else.

Consider the dilemma you may face in the following game where you are playing as Red. You have eliminated a player who was dominant in North America and have cashed in his cards. You have a choice to place armies on the map and carry on with your march. But you want to pause and think for a second. What are your options? How can you make sure that you will win by choosing the best move possible? You don’t want to leave it to chance. You want that trophy really badly!

Total Diplomacy Risk Map: WhoToEliminate_1
Risk Map: WhoToEliminate_1 --- Open Copy in Risk Map Editor

The game is played with escalating cards 4,6,8,10,… You have received 22 armies that you can place on the map.

Brown, Black and Green all have 4 cards and are likely to have a set. So if you don’t take Brown or Green out, they will come back to cause all sorts of trouble. You think this is a perfect opportunity. You can do a chain; eliminate one player, cash his cards, move on to the next player and so on.

So you decide to start with Brown. You invade South America, remove Brown and cash his cards as planned. Perfect! You think the plan is going really well. That gives you another 24 armies. So you distribute them on the map in strategic places preparing your empire for an attack on Green. You start attacking Africa. However, your luck runs out and you lose many armies in the process. In another front, you attack Alaska and that turns out just as bad. You cannot believe it! Suddenly you realise that this is not going as well as you hoped for and you stop before it’s too late. This is the how the map looks like now.

Total Diplomacy Risk Map: WhoToEliminate_2
Risk Map: WhoToEliminate_2 --- Open Copy in Risk Map Editor

You realise that you can no longer take Green out. Bummer! He has 4 cards. This is a big problem. The game’s turn order is set to simultaneous. It means that after your turn, Green or Black can play whoever plays first. You simply don’t know who is going to do that. If Black is going to play first and has a set of cards, then he will obviously go for Green to get his cards. Even though you have 5 cards now and will cash them in the next turn, you are not quite sure if you can manage to defend yourself. Of course if Green plays first and if he has cards to cash, he is most likely going to reinforce himself and even attack you. Both cases are bad news for you. Not only this will lengthen the game, but it will put you and Green in a potential conflict to the benefit of Black. You don’t want to believe that you lost because of bad luck. You want to know what you could have done so that, irrespective of luck, you would have ended up in a better position.

Should you have attacked Green instead of Brown? Should you have not attacked any of them and just reinforced? This would have meant that someone else could have cashed and eliminated a weaker player and effectively make a chain potentially attacking you in the process as well.

As it turned out, Black cashed in his cards, eliminated Green, got a lot more armies, invaded Red and eventually won the game.

You lost the game, but you feel you could have had it if it wasn’t because of bad luck. But since you don’t want to blame luck, you wonder what could you have done to end up as the winner or at least recover from bad luck. Of course, sometimes you are just not meant to win the game, but then again, why not?

What do you think? Is it possible to turn the it around, even if you had bad luck? Is dice that critical? Should Napoleon or Hitler blame the cold Russian winters for their failure, or was it that they didn’t account for it properly in their strategies?





 

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Comments

Sam By Sam @ Wednesday, January 2, 2008 12:02 AM
Ideally, you shouldnt have placed armies near Alaska. Either way I think it's bad luck

Europa By Europa @ Wednesday, January 2, 2008 6:53 PM
Too bad we can't post the map in this section! Anyway, I think that the intial strategy of placing the extra 22 armies in Western Europe and going through South America that way was a bad idea from the start. I would have placed the extra armies in Eastern US and gone through South America the other way, ending in North Africa. As I march through, I wouldn't leave any armies behind at all (save the mandatory one per territory). I would end up (presumably) with more armies in North Africa to work with. Now, I have 24 additional armies to place and I stand a much better chance at eliminating Green that way. If your objective is to eliminate players and start a chain, then you can't leave armies behind. Focus on your objective. I don't think in this example the player lost because of bad luck, he lost because the plan was faulty in its design.

It is true that you leave behind 7 armies in Western Europe, but truth be told, if you are trying to eliminate a player, it is best that you you pick a point of entry and exit and be sure that your exit point allows you to continue to attack. By ending your attack on Brown in Central America, any armies you end up with there you can't use. By going the other way and not dropping off armies along the way, you stand a better chance to have more armies for the fight later on. Also, the armies in Western Europe could come into play if your attack on Brown goes badly.

Once you eliminate Brown, you now have lots of armies in Europe already to begin your assault on Green. Use them and know that you have Western Europe to fortify with once your turn is done. You can bring armies from that territory to whereever you need defense if you can't ultimately eliminate your opponents.

Have a built in contingency like this is crucial to the plan. Your "Plan B" must also not hinder your primary objective. Risk is about concentrating your resources and completing objectives. That is why it is called RISK. By leaving little puddles of armies in your path, you are trying to hedge your bets, but in so doing, you actually make it much more difficult to achieve your goal.

Ehsan Honary By Ehsan Honary @ Saturday, January 5, 2008 7:14 AM
Sam, Placement in Alaska was important because of removing Black and also preparing for attack on Green from Kamchatka.

Grant, I was wondering if the attack on South America itself was something to reconsider. You seem to agree. A better distribution of armies could have helped. Anticipation is probably the key. Once Brown was eliminated there were lots of armies on the map and eliminating Green felt like an easy task. It was critical at that point (the point where you have lots of armies) to think of Plan B if suddenly your luck ran out and you where left with a small number of armies incapable of completing the goal.

As you suggest, having a Plan B would have been ideal. However the question is what is that Plan B? Suppose you distributed your armies correctly and that you decided to invade Green and remove him only to realise in mid campaign that you won't be able to make it. In this game, you are a victim of your own success, because Black will come to get you.

So going back one step, you have removed Brown, have lots of armies to place, but need to plan for a situation where you may not be able to eliminate Green. What would you do? You don't know if your luck will run out, but you need to be prepared for it. The question is suppose your luck ran out (irrespective of an ideal distribution of armies), what would have been your Plan B?

turk451 By turk451 @ Thursday, January 24, 2008 6:04 PM
The whole strategy of going after Brown in the first place was flawed. If you look at the layout of Brown vs. Green, Green is weaker. Green has fewer overall armies, and they are more dispersed. Going after Brown first was a big gamble that happened to work out. The two concentrations of 7 and 9 armies could have annihilated the 27 armies (5 + 22) placed on Eastern US with a few lucky defensive rolls. The better play would have been to start with Green with a placement like 20 on Ukraine, 1 on Southern Europe, and 1 on Western Europe. Then Western Europe attacks south one position into West Africa. Using the Southern Europe Army, attack Africa, with the backup in Western Africa. The key is to take Africa with these two armies. If things go well, then the Southern Europe army takes all of Africa, and there will be a glob of guys sitting in W. Africa for the chain attack on Brown. Then with the army of 28 on Ukraine, roll through Green in Asia. Stop to take out Black's one guy in Siberia, and also expend these forces in destroying the 4 armies black has in Alaska. With a total of 14 armies spread out so much, it would require very bad luck indeed not to accomplish this mission. So, let us assume that Green is then eliminated. With Green's cards, trade in and put all 24 armies on Eastern US, for a total army size of 29. Along with any leftover forces on W. Africa, that should be more than enough to destroy Brown, even with the two strongholds of 7 and 9 armies. So, again with cards, if you can trade in, buffer all forces bordering Black's stronghold in Australia. This is the trickiest situation of all. With Black's massive armies there, the key is containment. I would create a wall in Asia along Ural, Afghanistan, and Middle East, and some kind of blockade in Kamchatka as well. The key here will be holding onto continents. You need to rely on holding territories and continents to combat the large troop buildup of Black. The fact that he may be able to trade in cards only adds to the problem. But, with a little luck, any attack by Black can be countered appropriately with the massive territorial holdings resulting from elimination of Green and Brown, and the card army influx.

Ehsan Honary By Ehsan Honary @ Thursday, January 24, 2008 8:09 PM
Thanks Eugene Turk for your inputs. Certainly going for Brown is a valid option. But you need to follow the options the same way as the current exercise. Green and Brown have almost the same number of armies (Brown has only one more army than Green). So as far as probability goes, they are the same. The only difference is that more armies are available in Europe that can be used to eliminate Green. But remember, the problem is not removing Green or even Brown. With the cashed armies both can be removed and since both have 4 cards, you will get the same amount of armies after elimination that you can place on the map.

Now here is the problem: what if you start to attack the second player (in your case, Brown) with the left over armies and found that you are consistently losing armies. Just simple bad luck. This is the same as what happened in the game described in the article when Brown was eliminated and suddenly the luck ran out. What if you realized you can’t take Brown out.

So now you are spread all over the world. Black is ready to explode and so is Brown when he cashes his own cards. You know you can’t remove Brown. But Black can and if he gets a chance he most probably will. If you want to clock Brown from Black, then Brown will simply invade you and you will become weak. Black may also attack you, as he sees you everywhere and suddenly you become the weakest player. So again you are back to the same dilemma. It seems that if you have bad luck in this game, you can’t recover. The questions is would you have been able to follow a “safe” strategy so that even if you had bad luck at this point, the game wouldn’t go in one direction quickly and somehow you can extend it enough to survive and gain more power when you get luckier next time.

What do you think?

turk451 By turk451 @ Monday, February 25, 2008 12:37 PM
You raise some good points here, but my answer was a direct response to the question framed: "How can you make sure that you will win by choosing the best move possible?" with the additional data: "Brown, Black and Green all have 4 cards and are likely to have a set."

So, as with all Risk games, the key to winning is to take advantage of opportunities when they present themselves. The game scenario put forth is actually a very grim one for Red due to the defensive play of Black which has led to his or her troop accumulations in Asia. As you mention, the odds are that Green and Brown can trade in a set of cards and get 24+ armies on their turns. Either one of these would prove to be much much more difficult to eliminate next turn than this turn. Now is thus the time to strike. The correct play is certainly to take both of them out if possible this turn, because it will be impossible to take out Black this turn. The only reason for waiting at this point, and allowing either Green or Brown to trade in a set of cards would be if one of them was acting as a buffer between Red and Black, however this is not the case. Europe is but a hop and a skip away from Asia here, and due to the unpredictable nature of human motivations, it isn't even guaranteed that Green or Brown won't attack you even though Black is clearly the biggest threat at this point in time.

That being the case, the only way I see for Red to create the best possible scenario to win this game is to try to take out both Brown and Green right now while they have a large number of cards and only have to worry about Black. Your point that bad luck was encountered vs. green is unfortunate, but there is really nothing to be done there. The best strategy in this situation was to attack green, then brown, and hope for the best. If either task failed, then the game was almost certainly lost. It doesn't mean that there wasn't a very good chance of winning with that strategy, probably the best chance given the circumstances. While sometimes in Risk there is the chance to make a play with an excellent fallback plan built-in, sometimes it is just impossible to do so. The reason why it was impossible to make a plan with a great fallback position here is because brown, green, and black all have cards. Brown and green can be taken out by black on his or her turn if black trades in cards before them. This would clearly make black the overwhelming favorite to win. Alternately, if green or brown trades in, the strategy will likely be to go for the player who has not cashed in of that pair. Neither of these scenarios is good for red. Consequently, red should attack green (which is 100% certainly the weaker of brown and green*). If elimination is accomplished, then the next step must be to try to take out brown. If that step is successful, then this game is still not decided, but at least it will be competitive with the large territorial holdings red should now hold. If it is not successful, then the game is almost surely lost, but the correct play will still have been made.

It is definitely possible to make the best play and still lose.

One additional comment I have is that in the scenario as presented, Red stopped attacking due to bad rolls. This is not acceptable in this situation. Due to the possibility of what eventually happened (Black plays first and eliminates Green), Red needs to follow through and use whatever resources he has to continue attacking and try to eliminate green. With the additional troops from trading in, Red can set up the best defense he can imagine and try to withstand the one-turn onslaught of Black. With any luck, due to the card influxes from Brown and Green, Red will get the next big trade in and counterattack to reverse the damage Black will certainly cause on his turn.

* My note here is just to say that dispersal always makes a player weaker if that player has left many instances of 1 army on countries. If I hold 10 countries with 1 army on each, then that will be significantly easier to destroy than one country with 10 armies on it if you assume that the attacker is always going to use 3 attacking armies. This is because the best possible scenario for an attacker is 3 vs 1. This can only occur if the defender has 1 army on a country. Otherwise, it is always beneficial to defend with the maximum of 2 armies. In any scenario with a large army vs. a large defending army, there is a much larger chance of something really unlucky occurring for the attaching army resulting in huge losses and an inability to continue attacking. Thus, with green's largest accumulations of troops being 2 and 5, I would always try to take out green first in this scenario.

Ehsan Honary By Ehsan Honary @ Thursday, February 28, 2008 3:56 PM
Eugene Turk, I see that our discussion is getting more intense :-) I appreciate your response.

Let’s say that I pretty much agree with what you say. I understand what you mean by Green is weaker, since your argument is certainly true. I also agree with the fact that no matter how good your strategy is, you may sometimes lose. This is in fact the main theme of the article. I am trying to explore a number of solutions that could have been employed as a fall back so that despite the bad luck, Red would have survived.

Naturally as you put it well: “While sometimes in Risk there is the chance to make a play with an excellent fallback plan built-in, sometimes it is just impossible to do so. The reason why it was impossible to make a plan with a great fallback position here is because brown, green, and black all have cards.”

That pretty much sums it up. Opponents were too risky to deal with and they should have been eliminated as soon as possible. It’s the inherent feature of Risk that cards bring instability towards the end of the game (which actually makes it quite entertaining).

There was only one thing in your comments that I thought needs more expansion. I still think that Red was right to stop attacking Green once Red realized Green wasn’t going to be eliminated. The reason is that if you know your opponent is going to eliminate a player you were trying to remove, then why should you make his life any easier? Let him spend his armies before he gets his hands on the cards. Of course if you are not sure you can eliminate someone, then you need to evaluate the risk. If not feasible, I don’t see why you should go for it. If you go for it, you may end of stretching yourself too much and weakening yourself in the process.

Eliminating a player usually makes sense when you can get the cards and cash them to protect yourself from backlash. Otherwise if you go all the way, and just leave three territories for the opponent to take, you have spent all the armies, and are now a sitting duck; ready to be taken out in the chain when your opponent starts invading one player after another.

turk451 By turk451 @ Saturday, March 1, 2008 6:23 PM
Thanks Ehsan for your comments.

To clarify my point about Red stopping attacking, I am just looking at the final game state presented. What I see is 3 armies sitting in Brazil, and 4 in North Africa. This implies to me that a conservative choice was made to stop attacking and leave three armies behind in Brazil after taking North Africa. If the free troop movement had been used instead to create an army of 6 in North Africa, those 6 armies could (and I would argue should) have eliminated green from Africa entirely. The remaining troops green has in Asia can be eliminated through the armies in Kamchatka, Ukraine, and Southern Europe. Because green has 4 cards, after eliminating him it will almost surely be necessary to trade in cards per the rules I have used recently, so red will get 24+ armies to fortify and attempt to withstand black's onslaught. Yes, from one perspective it is silly to try and do another player's work for him or her, but in this case, to fail in the task of eliminating green is to hand the game to black. Yes, it will be risky with armies of merely 3 (Egypt) and 6 (N. Africa) to attempt to take out 4 solitary countries in Africa with 1 army on them each, but it is a Risk that might pay off with a victory in the case presented. There are no alternate paths to victory here than a gamble and a prayer.

But in general I absolutely agree that letting players weaken themselves through conflict which does not result in the elimination of a player is beneficial to those not participating in the conflict. However, as the three players in question each have 4 cards, I'm sticking with my original intuition here.

Thanks again for the comments and great site. I'll have to pick up your book.

Ehsan Honary By Ehsan Honary @ Saturday, March 1, 2008 7:28 PM
Yes, you are quite right Eugene Turk about the risk taking. That's exactly how Red felt when he stopped attacking that there is no hope to kill Green.

Naturally, since Red went on to lose anyway, it might have been a good gamble to try to eliminate Green if he could suddenly get lucky. At least that way he would have a chance. Otherwise he would have lost anyway. That makes sense and I agree with you. The name "Risk" is the best explanation.

And of course it would be my pleasure if you read the book and of course would look forward to hear your views. Thanks

C-dawg By C-dawg @ Tuesday, July 15, 2008 6:48 PM
To start off, red's offensive attack is horrible and where is there not even the slightest defense in North America???

The key question is how do you win in this condition -- which is pretty shabby by the way. I would never guard Greenland with only 3 nor Ukraine with 8 and southern with only 7. Whoever is playing this game is pretty bad might I add.

So, first of all, I agree with both Samuel chin and Grant Blackburn that you don't even want to touch Alaska and don't even think about attacking from Western Europe. That is just a total waste of army and you isolate yourself from reinforcements. Useless!!! Secondly, I would put all 22 in eastern United States and totally anihalate the brown. Thirdly, this is the tricky part, you want to do both of these things at once: encroach the grey and finish off the red at the same time. Fourthly, after spending all your soldiers to waste green, you must then attack grey from china onwards to siam and into Australia to have a chance. With a little luck and vigilence, you will thin down his troops and be able to play the cat-and-mouse game of who has more territories, and from those territories you would gain my armies that way. That to me, is the objective and the only solution to winning this goal. Otherwise, in all other senarios, Grey wins, by default, due to his defensive front he has on Australia. Unless you take the fight to grey, and fight on his turf, you are gonna play what-if games.

Now in the case you think you are smarter than the inevitable, and believe you don't have to finish off brown. Let's say green is next, then they will finish the brown and start attacking red in North America. In that case, red still loses due to lose of land. Now, in the case grey goes next, he would still attack and finish green. Get 24 armies, and finish brown next and get 26 armies. Then all grey has to do is smash his way through the Ukraine or southern europe since red is already starting to fall. So, overall, due to red's gullibility or perhaps horrible stategies, probably has 0% to 20% chance of winning. Though if his initial moves were listed, I would say he has no chance. That being sad, grey wins 80% of the time.

Dookie By Dookie @ Thursday, September 18, 2008 10:35 PM
I think you have misled everyone here to miss one possible decision. Conitnue the attack on Green. You stated that "You realise that you can no longer take Green out. Bummer! He has 4 cards. " I believe you do not have to stop attacking.

From the second board layout, Red has the following units to attack with:

4 - North Africa
3 - Egypt
8 - Southern Europe
8 - Ukraine
8 - Kamchatka

While it may not work (due to the unknown of bad die rolls, the original reason given to stop attacking now), it is mathematically probable that Red will eliminate Green on this turn and get the 4 cards (and the armies to go with it).

You start with North Africa and roll against, Congo, South Africa and Madagascar. If you make it this far, you have added to your ability to withstand Black's coming onslaught.

Then you use Egypt to attack East Africa.

If you are not able to get all of the way to Madagascar with the North Africans, then you must fall to the use of Southern Europe to take all of the rest of Africa via the Middle East.

Once you have completed the take over of Africa and the Middle East from Green (with either of the above scenarios), you now focus on taking out the rest of Green from Ukraine and Kamchatka.

With 8 armies in each place, you start with Ukraine and work your way through the following countries: Afganistan, Ural, Siberia, Yakutsk, and Irkutsk. You end your Ukrainian invasion once you get to this point or before, if you run out of troops.

From Kamchatcka you mop up the rest: Japan first, then Mongolia and then any others that Ukraine troops could not take.

You have now eliminated Green and receive the 4 cards and the armies.

Your example did not count the number of cards in your hand after the elimination of the "dominant player". However, you did state that you had 5 cards in your hand at the decision point. The rules state that you must turn in cards when you have 5 or more cards in your hand. So I must assume that you had 4 and would be getting one at the end of your turn giving you 5, if you chose to not attack Green.

When eliminating the "dominant player" you recieved enough cards to get you to 5 or more cards. For this example I will assume that you had 6 cards at that point (with Brown, Green and Black still playing and having 4 cards).

You turn in 3 cards, leaving you with 3 cards. When you eliminate Brown, you gain their 4 cards, giving you 7 cards. You again turn in 3 cards, leaving you with 4 cards (this is the point of my assumption from your comments in the example). When you eliminate Green, you will receive another 4 cards, giving you 8 cards. You will turn 3 more in, leaving you with 5 cards. You must, again, turn in a set of cards. This gives you two sets of armies (26 and 28 or 54 total). This makes the decision easy, as you should have enough armies available to eliminate or severely lower the total number of armies Black continues to have on the Board. Most likely Black will be eliminated before the end of this turn, but if not, your shear number of territories will make it almost impossible to come back.

If however, I was incorrect in my assumption of the number of cards in your hand after the elimination of Brown and you only had 3.

When you eliminate Green, you will receive another 4 cards, giving you 7 cards. You will turn 3 more in, leaving you with 4 cards.

Before deciding what course of action you will take next (defense against the coming Black invasion or attack to lower their ability to infiltrate your complete control of 4 of the 6 continents), you know that you will be receiving another card, giving you 5 cards again. You will definitely be getting another set of armies at the beginning of your next turn, whether or not Black can turn in on their's. If they can't, then it is game over.

Taking the example further, if you play defensively, choosing to not attack Black, you already have some troops in the choke points on some of your continents (3 in Greenland, 3 in Brazil) and you should have some left over from taking over Green. This will give you a base to distribute your armies in enough places to put the onus on Black to decide which continent(s) can they keep Red from profiting from on their next turn.

Black will be recieving a minimum of 3 armies for still being in the game, but being under the 12 country limit to getting more armies, and 2 for holding Australia for a total of 5. If they turn in cards, this will give them and additional 28 armies (since you cashed in with Green to get 26 in defense).

This is a large number, but, as stated above, you will be receiving 30 for your cards, plus a large number of territory armies for holding most of the board, plus any surviving continents (potential of 5, 5, 2, and 3 or 15 total more armies).

The other option is to take the 26 armies from the elimination of Green and "RISK" attacking China (11) and Siam (10) and then the "undefended" Indonesia (1). This would eliminate more than half of Blacks current armies, stop them from getting the Australia Bonus, and give them little choice on what to do with the additional armies garnered from turning in cards.

Again, you know that you will be getting 30 armies from turning in cards next turn, plus your normal turn replenishment of armies.

I understand and agree that there were better choices in the beginning of your explanation as to who and how to distribute armies to end Brown's existence in the game, however, I think that it is still possible to continue the turn and also eliminate Green from the game. Giving you the upper hand for the rest of the game.

Just my two cents (that's 1950 cents, which adjusted for inflation, should get you to about $2.50).

Interesting strategy question, thanks for putting it out there.

Ehsan Honary By Ehsan Honary @ Friday, September 19, 2008 9:18 AM
Thanks Andrew for your comments.

I agree with your calculations that once Green is eliminated, the cards can be cashed in and Black can be controlled or even eliminated in the same turn. I think that's pretty much agreed on.

The problem Red faces now is to either go for Green or not. Although you explain how Red can move forward to eliminate Green, I simply don't see that chance. The weakest point is Africa. How can Red in North Africa get Congo and South Africa with only 4 armies? It's a shot in the dark.

There are really only two possibilities at this point. Red will eliminate Green by sheer luck and will go on to eliminate Black and win, or, Red will stop and hope that the next player to play is Green. In that case, Green will become strong enough not to be eliminated and Red will take his chances from there.

So in essence, the only reason Red is hesitating to take the gamble and go for it is the hope for a Green turn next. If not, you are quite right. Red is almost dead anyway, might as well try his luck now. If he succeeds, all the best, if not then he was dead anyway.

Cheers.

Dookie By Dookie @ Friday, September 19, 2008 1:36 PM
Agreed this is the turning point for Red. Go for it or chance a big loss by not going for it.

However, Red can use 4 in North Africa to attack as many as possible in Africa. There are 8 in Southern Europe that can move to: Middle East, East Africa, Madagascar, South Africa, Congo....basically backwards from North Africa's ideal target list. Whatever North Africa fails to take, Southern Europe will need to complete the task.

Agreed that this is their weakest point. With 4 armies vs. 1 there is about a 97% chance that the defender is defeated. Then a 91% chance on a 3 vs 1. This gets them to South Africa. Then Southern Europe only needs to take out Middle East, East Africa, and Madagascar starting with 8 armies. Should be a walk in the park.

Obviously, everyone that has played RISK with any frequency has seen the 8 vs 1 turn ugly for the defender (the video you posted makes fun of that, hilarious). However, the probabilities of it not working are close to zero (within a few percentage points).

The reward is winning the game, the "RISK" is losing, which just about everyone has decided that Red will lose if they do not complete the elimination of Green.

So the choice is obvious. Kill Green.

Ehsan Honary By Ehsan Honary @ Friday, September 19, 2008 5:21 PM
Yes, going from Southern Europe makes sense and then South Africa tries to get the rest.

Just a comment on the math though. The chances to win are far less than what you mentioned. To attack with a 4 army against the one army, you have 65% chance to win. Then you need to move 3 armies forward. Now you can only attack with two dice which gives you a mere 57% chance to win.

For South Europe to take three countries, it has similar chances with a maximum of 65% each time.

In practice, I would say it is extremely risky as all you need to do is the inability to get the last territory of Green and then you are out.

I haven't calculated the probability but say you have approx 60% chance of winning against Green. You need to compare this with the chances of Green playing first which is unknown or if considered fair 50%. In this case you have a marginal chance of winning.

It will be great if someone calculates the true probability of the attack against Green. In other words, given the map, what are the chances of eliminating Green given the rules of Risk? Anyone up for challenge?

j409603 By j409603 @ Friday, June 25, 2010 11:15 AM
I simulated the above position, following the routes suggested by Dookie. Over a million trials, Red won in Africa 83% of the time and in Asia 76.7% of the time. The overall probability for Red eliminating Green is 63.6%, so Red should certainly continue attacking at this point.

Ehsan Honary By Ehsan Honary @ Friday, June 25, 2010 1:26 PM
j409603, thanks for the calculations. It seems that the probability of 63% is approximately similar to the original guess.. This is not a comfortable margin in my book. I see that you recommend the attack, but would you really do so knowing that there is 40% chance that you will lose instantly with no way to recover?

j409603 By j409603 @ Tuesday, June 29, 2010 8:17 PM
Personally I would, but I would in no way make myself out to be an expert Risk tactician, just an average player. I'll happily take the last half a sentence of my post back, which was largely based on the comments above. It seemed to be agreed that the chances of winning if Black plays next are virtually zero, so as long as the chance of beating Green is greater than 50%, it's worth attacking. Also, my feeling is that, other things being roughly equal, I'd rather have my fate in my own hands than rely on another player.

I've never played this simultaneous version of Risk, but is it possible that, since Black was in a strong position and Green was not, Black is the one more likely to be ready and waiting and keen to play next?

Ehsan Honary By Ehsan Honary @ Tuesday, June 29, 2010 8:42 PM
I understand what you mean, specially about wanting to be in control of the game rather than relying on someone else.

As for simultaneous games, it is indeed possible that a player literally waits for the next turn to play first, however considering that the games can be played internationality, the times zones play a significant part on when players play their turn. So in general it is pretty much random and you may get unlucky.

Of course, if you care a lot about the game, you can always stay up all night so you can make sure that you are first to play :-)

slickandjake By slickandjake @ Wednesday, September 22, 2010 7:09 PM
My first thought regarding stopping the attack on green, before reading the comments, was the same as Dookie. I would have given myself a greater than 50% chance of taking out Green yet on this turn. If I fail to eliminate Green, then you basically have no chance of winning at all. If Green by chance went first and received a card set, there is no guarantee he will attack Black first. I think it is worth the risk. Also, had the armies been placed in a better position, i.e. in Eastern U.S. first, they could have made their way to North Africa for a stronger starting position in Africa, and this is where you will be weakest when you go for Green. If you ran into bad luck in S.A., you will still likely capture it and if the armies in Brazil at that point were less than 7, then you could have taken Africa with the armies in western and southern Europe, trying to use the western Europe armies to take as much as possible to allow the southern Europe armies to have to go no further than East Africa to complete the continent takeover. Then you have some armies in Africa that can still be used towards the Middle East and Asia. The key here is to maximize all of your army strength in every territory you have.

I agree with attacking Brown before Green. Even though Green has 2 less armies, they have 13 territories to conquer versus only 6 for Brown. Conquering Green is more difficult because you are leaving an army behind for each territory you capture, so to me you need effectively more armies to conquer Green initially then you do Brown just for the mere fact of having the one army garrison in so many territories. Also, by capturing Brown, whatever armies remain can be used in the beginning assault on Asia, which is where your two remaining opponents are. If I take out Brown and then took out Green, I would attack Black on the remainder of my turn as long as I could muster 3 dice to roll in attacking. This is because you have a slight statistical advantage in attacking 3 on 2, which will give you an edge in armies over the long-run, as well as reducing Black's flexibility in the counter-attack by forcing him to start with less armies and minimize the length of his counter-attack, perhaps allowing you to hold on to an extra continent for an army bonus next turn.

slickandjake By slickandjake @ Wednesday, September 22, 2010 7:39 PM
Also, plan B. If for some reason you have very bad luck in capturing Africa with what you have left, meaning North Africa fails to capture a territory 4 on 1 and the attack from southern Europe to the Middle East lost 3 armies and left you with 4 in the Middle East, i.e. a mathematical impossibility to capture Africa, then leave your 4 armies in the Middle East. You are no worse off then the current situation because you made a tougher path for black to wipe out Green next turn. True Black will likely still wipe Green out > 99% of the time, but again you are in a slightly better situation by "protecting" some of green's territories.

This also illustrates how the red player made a mistake in his attack. How do you end up with 3 armies in Egypt and 4 in North Africa? Why were these armies split up? I think the planning on the initial attack was very flawed and could have been set up to better maximize your army numbers.

shadowguynick By shadowguynick @ Wednesday, January 2, 2013 2:47 AM
From what I see, and the comments I have read, you have three choices, all with its drawbacks and benefits.

1.)Reinforce your position- This is probably the worst move you can make, since the other two both have cards and will dominate you easily. Only way to win is if you get an EXTREMELY lucky defensive rolls.

2.)Continue attack on green- This is a somewhat viable option, given a little luck you could conquer green. But if you don't there is absolutely no way you can win the game with poor defenses, and an extremely powerful black.

3.)Attempt last minute diplomacy with green- I came up with this option because of the fact that neither green nor red seperated have the might to face black. But maybe together. Let me explore this option in detail...

Green begins his turn. You ask him before he starts deploying if you two could have a talk. You inform him of the dire situation conflicting both you. You suggest the only way to ensure victory for either one of you is to face black together, by encircling him with as many people as possible and trapping him. Taking Siberia is a priority as well. At first first green is wary. He asks how would he be able to win if you broke the deal? And what does he actually gain from this? To sweeten the deal I suggest offering Africa back, along with Australia if they conquer black. If he is still not willing offer Asia as well. Green is happy with this so he accepts.

Now let's see what could happen from here...

Happy Ending 1- Green went with the plan, captured Siberia with ease, and encircled black. Black, caught off guard by the alliance, cashes his cards in and goes to break through, let's say, the Middle East. Green rolls a couple good ones, and black has less troops to attack the rest of Africa with, but still a good amount. As he goes through Africa and gets all the green there he is looks happy. But then he gets to you and has trouble pushing through your defense. Black, a somewhat over-aggressive player, keeps pushing on and ends up losing most his troops, but still getting a decent sized portion of the map including Europe and Africa. He had also tried to take green out and get his cards but he did not have enough troops left over to break through. Now it's your turn. You cash in, retake all your territories(Not including Africa) and attack his weak spot via Middle East. Taking India and Siam, you end your turn leaving his forces in china untouched. Like you promised you pull out of Africa, let green retake it. Green also attacks Black in China with a large army. But due to his peace treaty with you he cannot attack Australia. You then take australia(and black's cards) and fortify Brazil and Europe telling green he's welcome to take the contineants. From there it's just maneovoring and tactics to win.

Sad ending- The plan fails. Black gets a stroke of good luck, and you are too weak to fight back. Green's defense couldn't have been worse, and he falls swiftly. Sorry, but you did try though.

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