The Risk Calculator allows you to determine the likelihood of success of a series of attacks in a game of Risk. I created it to allow you to gripe about either how unlucky you were last game or how crazy lucky your opponent was. I only expect it to be used for post-game analysis - it wouldn't really be fair to use it in the middle of a game.
You: "Man! I can't believe you took Australia from me with just 12 armies! That was so freaking lucky!"
Conceited Jerk: "Nah, the attacker has the advantage. You didn't have a strong enough defence."
lame, pre-Risk Calculator You: "I did too!"
cool, post-Risk Calculator You: "Actually, the chance of that attack succeeding are less than 12%! 62.9% of the time you don't even capture Indonesia!"
Okay, maybe not cool. But at least you now have a solid basis for your feeling of injustice.
To use the calculator, first populate the board with units of various territories to reflect the situation you want to analyze. Each territory has one or more little squares on it that represents the number of units there and the power that controls them (yellow, gray, red, blue, or purple).
To remove units, click on the white wedge. You can remove units one at a time or by threes. When you remove the last unit from a territory, it is empty and had no associated faction.
There are two types of modifiers: modifiers that affect the attacker's dice, and modifiers that affect the defender's dice. Attack modifiers go in the top half of the circle and defence modifiers go in the bottom half. Note that modifiers never raise a roll above a 6 nor lower it below a 1.
To assign a modifier, click on the semicircle with the modifier you want to assign. To unassign it, click on an empty semicircle.
Attacker modifiers:
•+++: plus one to all attacker dice (e.g. 2, 3, 5 → 3, 4, 6)
•*-: minus one to the lower defender die (e.g. 3, 5 → 2, 5)
•+*: plus one to the higher defender die (e.g. 3, 5 → 3, 6)
•++: plus one to both defender dice (e.g. 3, 5 → 4, 6)
Note that some Risk rules apply here:
•you can't attack a territory that is already controlled by you (this is responsible for the weirdness of Risk that your own territories can be a bigger impediment to expansion than your opponent's territories)
•you can't attack a territory that is already part of the attack path
You can define an attack path that could not possibly succeed because you don't have enough units to get that far. In that case you'll see that completely gray circles beside the territories that can't be reached.
Note that you can have only one attack path on the board at a time. If you want to start an attack from a different territory, click on the target circle at the start of your current attack path and you will be given the option to discard the current attack. Once that attack is discared you can start a new one from a different territory.
•the green wedge represents the probability that your attack will both reach and conquer the associated territory
•the red wedge represents the probability that your attack will reach the territory but will fail there
•the grey wedge represents the probability that your does not reach the territory - because the attack already failed earlier, or because there are not enough troops left in the previous territory to advance an attack against this territory
Pictured here is the Gray's campaign to capture North America, starting from Alaska. You can see that the outer edges of the pie charts are almost entirely green as the attack moves from Alaska to the Northwest Territories and Alberta. This makes sense - it's very unlikely that an army of ten units could not capture two singleton territories (How unlikely? It only happens .2% of the time!). Ontario is the first territory where you start to see failures - in fact the attack is rebuffed in Ontario 17% of the time. Even when the attack succeeds in Ontario, the attacker usually takes significant losses (2.44 units, on average). After that things start going downhill for the attacker. The size of the green wedges falls below 50% in the Eastern U.S. and it is very small by the time it gets to Greenland, the last territory needed to capture North America. There is only an 8.3% chance that the campaign to capture all of North America will succeed. This is not too surprising: Gray is trying to capture 7 territories and destroy 10 defenders with only 9 armies, and has to leave one unit behind on each captured territory. Gray can only afford to lose two units - and that only happens 8.3% of the time.
The smaller wedges within the red and green wedges give you information about how many defending/attacking units are left after a loss or a win, with their associated probabilities. There is, for example, a 10.7% chance that the attack which started in Alaska will conquer Ontario with 7 units left (if you set this up in the Risk Calculator, you can hover over the wedge to see the precise probability). That represents a perfect result for the attacker, since they started with 10 units and had to leave 4 behind en route to Ontario (one unit in Alaska, another in Northwest Territories, and another in Alberta).
The pie charts provide a good feel for the outcomes of an attack, but if you want precise answers to questions like, "how many units will I lose on average during this attack?" then you need to look at the result table. To access the result table, click on a pie chart, and the result table will be overlaid atop the board.
•The total row shows the average results across both wins and losses
•the win row shows average results for cases where the campaign has been successful to this point
•the loss row shows average results for cases where the campaign has been unsuccessful to this point. It includes statistics for those cases where the campaign failed in an earlier territory
The columns for the summary information are as follows:
•casualties are the number of units the attackers loses on average
•kills represents the average number of units the defender loses
•diff shows the difference between then number of defenders lost and the number of attackers lost - a positive number means there were more defender losses than attacker losses
•probability is the probability for a particular outcome (win or loss - this will always be '1' for the total row)
Also included are every possible outcome of for the attack into Eastern U. S. from the Western U. S. - there are win and loss rows which correspond to cases where the attack succeeded or failed at this point. Campaigns that did not make it this far are not represented. The columns are defined as follows:
•avail shows how many units are available to deploy following the attack
•leave shows how many units the attacker will leave behind (in the attacked territory for a win, or in the attacking territory for a loss)
•killed shows how many defenders were killed during this outcome
•%chance shows the likelihood of this outcome occuring
•%ile shows the percentile for this outcome - percentiles above 50% means that this is an outcome where the dice have been favoring the attacker, percentiles below 50% describe outcomes where the defender has been getting the luck. If you are seeing loss outcomes with percentiles about 50%, it means that you're attack is losing even in cases where you've been relatively lucky.
There are a couple of options that you can play with for your attack. The defaults are to continue attacking as long as you have any units available (meaning 2 or more units in the attacking territory), and to leave behind only 1 unit per territory. These are the right settings if you want to know your chance of success if you completely commit to the attack - which is what you want to do if you're going for a takeout or the win.
However, if you're thinking more defensively, you might want to change these settings and see what the odds are.
The options in the 'while' box control when you want your attack to be abandoned. The options are:
•2+ attackers: this is an all-out attack. As long as you have at least one unit available to commit to an attack (i.e. two or more units in the attacking territory), then keep attacking. With this setting you will take more losses since there will be losing attacks where you fight 1 on 2 defenders (which only works about 25% of the time).
•3+ attackers: same as 2+ but you give up when you're down to only 3 units or less. You will attack 3 on 1, 3 on 2, 2 on 2, and 2 on 1.
•4+ attackers: same as 2+ but you give us when you're down to 4 units or less. This is a conservative setting - you only attack in 3 on 1 or 3 on 2 situations.
•dice advantage: this is another conservative setting, but a little more nuanced than the 4+ attackers setting. With this setting you only attack if you have more attack dice than the defender. You attack in 3 on 1, 3 on 2, and 2 on 1 situations.
•attack > defence: with this setting, you only attack if there are more units available to attack from the attacking territory than there are in the defending territory. For instance, if you have 5 units in India set to attack 4 units in China, you will not attack with this setting since only 4 Indian units are available, no more than there are in China. You would need 6 units in India for the attack to proceed. This setting makes sense if what you want to do is whittle down an opponent's armies but don't want to take the risk of ending the turn with fewer units than the defender.
•attack >= defence: same as attack > defence but you also attack when you have the same number of attacking units as there are defenders, e.g. if you had 5 units in India against 4 in China, you would attack because it would be 4 against 4.
The 'leave' box controls how many units you leave behind in each territory. For an all-out attack, you want to leave behind as few as possible - 1 per territory, the default setting. However, if you are thinking defensively, you might just want to see how far that attack into Asia will likely get if you leave 2 or 3 units behind in each territory. For instance, in the online Risk variant Major Commander, it's normal to start with 3 units per territory. If you leave less than 3 units behind in an exposed territory, it will likely become somebody's target next turn. Of course, the more units you leave behind per territory, the less far your attack will go. If you bump up the 'leave' setting, then an attack will not be initiated it if might result in capturing a territory but not having enough troops to leave enough behind in both the attacked-from and in the attacked territory. For instance, if you set the leave to '3', only territories with 6 or more troops can attack at all.