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Ever wondered were to put your units to minimize the risk of any of them getting eliminated because of the plague? Ever wondered on how to minimize the risk of having to cough up some ducats to relieve famine? Ever wondered about the mean variable income for your Home Country? Well here are all your answers. In this exclusive review, Jon Ashman has calculated these probabilities for you. He has also added an explanation on how to calculate these risks. As you probably want the hard data first, the explanations are last. I have appended a list of famine and plague probabilities for each province at the end of the article. Here is also a link to a color coded map (highquality version, lowquality version) I have made showing the unknown year probability and the row and column index for each province. Do notice that these tables apply to Classic Machiavelli only. The Machiavelli2 tables are much simpler. "Disaster" percentages have all been rounded off to two decimals and that they do not necessarily sum 100%...
The ProbabilitiesVariable income probabilities Let me begin by drawing your attention to the expected mean incomes for the different countries / cities. All probabilities have been rounded to the nearest whole percentage. Notice also the two columns at the right showing the probability of getting at least 6 ducats or at least 9 ducats. In particular do notice that Venice is 86% certain of getting enough money for two units, just from the variable income roll. Which, as he would need at least two provinces to be able to build, actually means Venice is >100% certain of being able to build/maintain 2 units if he has control of at least 2 build centers.
(The simplest way to calculate the mean above is to sum the values and percentages as this: ((1*17) + (2*17) + (3*33) + (4*33)) / 100 = 282/100 = 2.8.) Venice's income -- an expanded look Consider this: Venice is almost guaranteed to gain 6d from his variable income. If Venice also holds Venice city/province then he is guaranteed enough income to maintainin a Citizens Militia garrison. The most cost effective way to remove that unit would be to convert the garrison to autonomous. This would normally cost 9d but has to be doubled for the citizens militia and doubled again for Venice being a major city. Thus costing 36 ducats to remove! Add to that the fact that the garrison cannot be besieged (remember the special Venice rule that only allows one unit in the province thus hindering sieges) and you realize what a problem you will have to get rid of that pesky unit! Thus if the venetian player should have an alliance going against him, he has a major diplomatic advantage. For that alliance to, for example, be able to make a draw in a DIAS game, Venice must be removed. But if Venice is in control of Venice city, his guaranteed 6d income will give him a major bargaining position. Will any one player in that alliance singly, and very bravely (and possibly terminally), attempt to remove the garrison? If one player spends all his money that will make him very vulnerable to the others. On the other hand would the alliance players share the cost? Would they trust one player enough to give him that amount of money? As you can see this guaranteed 6d income for the Venice player gives him a major advantage, when holding venice city, a very nice bargaining tool. But on the other hand it could also mean that an early game alliance will form against him. An alliance that will just wait around until plague strikes... (As Venice's income is as high as it is, you cannot count on famine to get rid of him.) Hoping for plague in Venice may seem a little optimistic though, as it has a chance of 17.7% to occur in any year. But on the other hand see it this way: the probability of plague striking at least once in a 3 year period is 44%, and for a 5 year period it is whopping 62%. So if you keep the alliance going for a few years, you may not need that bribe ! But then of course, why would any Machiavelli player ever care about DIAS draws ;-) What tip to give to Venice? Well either stockpile enough money to buy off any enemy in the lagoon, as plague strikes before the expenditures and movement phases!, or keep a Citizens Militia Fleet in Venice that supports an ordinary fleet in the Lagoon, as to block or slow the enemies in their attempt to gain the Lagoon. (Or set your hopes to the bouncing game...) But better still: avoid getting there in the first place ;-) Disasters Here is what you want to know. The probability of getting hit by a disaster in an arbitrary year.
As the table is a little complicated I will give a few examples below. Famine example
Plague example
Calculating the ProbabilitiesApologies if it may seem a little too meticulous to begin from the very basics. A probability table for a 2d6 This is basic statistics. As you have two six-sided dice with the faces having a unique value from 1 to 6, you'll get a finite number of combinations.
As you'll get 36 by summing all frequencies, the probability for getting a four is 3/36th's and so on. Notice that a result of 1 with 2d6 is impossible. Disasters if it is known to be a good year If it is a good year the judge software will either roll for a column or a row. As both require a 2d6 roll you'll get this table of results for either a row or a column:
This is the easy one as the probabilities for either a column or a row can be obtained directly from the 2d6 frequency table. Look, for example, up Provence in the famine table (at 4,2) and you'll get the probabilities of 3/36 and 1/36. The backside is of course: how will you know it will be a good year ? So we'll have to proceed in our calculations. Disasters if it is known to be a bad year In this case you'll get both a column and a row and the probabilities table will look like this:
This is a bit harder to explain unless you are proficient with set theory (in which case you would use the formula P(A u B) = P(A) + P(B) - P(A n B)). So I'll try to explain this in a simpler way. Imagine you toss two coins. If at least one head (H) is thrown (regardless of which coin) you'll get a bad year famine. Also think of the first coin as the good year column and of the second coin as the good year row. So you would get a bad year by throwing (T,H), (H,T) and (H,H). This would mean a probability of 3/4 (1/2*1/2 + 1/2*1/2 + 1/2*1/2) for a bad famine. Also consider this: the probability of a bad famine happening is also equal to one minus the probability of famine not happening. The only way of a bad famine not happening is when (T,T) is thrown, so you could also get at 3/4 by 1-1/4. Which by the way is quicker to calculate. So back to the Provence example:
Probability of famine in Provence a good year row is 1/36. To get the probability of NO famine in a bad year you have to multiply the row and column probabilities. That is 35/36 times 33/36, which equals 1155/1296 [(35*33)/(36*36)]. Conversely the probability of a bad famine would be 1-(1155/1296), which equals 141/1296. The backside is of course still: how will you know it will be a bad year ? So we go on. Disasters when the year is unknown Ok, ok. I know you cannot a priori know which year it is. So to really, really be on the safe side you need to consult this table shown at the beginning of this article. That is the table you will use as it answers what the probability is of getting a disaster in any given year. To get at that value you have to begin to calculate the probability of getting a certain disaster result. Which, according to the "year chart", are: No disaster: 3/36 So getting back to the Provence example this would result in a: So to get at the probability of famine in Provence any given
year you would have to add the following: This is the end of my article. I would also like to thank Sergio Lidsell for the idea of looking at the disaster probabilities. This article would not exist if it was not for his initial idea. Additionally I would like to thank him for the time he has spent on making this presentation.
Final noteWell, having learnt all this you are now prepared to go forth and conquer without fear of the unknown, or... Is this all there is to it? Certainly not! There is more that can be gleaned from the results. Take a look at the map I have made, where you quickly can see how your build centers fare and where there are "hot spots" to factor into your tactics. And finally my thanks to Jon Ashman for taking me up on my idea and making this article possible.
Appendix 1: List of probabilities by province and disasterThe values are expressed in percentages.
Appendix 2: approximate yearly frequency of disasters used in the mapI have grouped most values as year+-0.4 as the results pretty much sorted themselves in this pattern. The frequency is expressed as once every n years. This is also a key to the map colours.
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Sergio Lidsell If you wish to e-mail feedback on this article to the author, click on the letter above. |
