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Subject: Magic Realm Probability for Beginners - I rss

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Steve McKnight
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1. Introduction

Part of the reason why Magic Realm is such a puzzle to so many beginning players is that the probabilities behind the game are a mystery. They wander through the Realm, unclear where they have a good chance of accomplishing a goal and where their chances are impossibly remote. The popularity of Robin Warren's RealmSpeak computer realization of Magic Realm exacerbates the problem; one of the problems of computer games is that while you know what happens, you may have no idea why, or if it is likely to happen again.

This is unfortunate, because the probabilities in Magic Realm can be calculated, or at least estimated closely, and knowing what your chances are of getting a particular result opens up Magic Realm for what it is: a great risk/reward game. Die rolls play a huge role in Magic Realm, and without taking chances it is nearly impossible to gain any Victory Points. On the other hand, there are many encounters in the game which can be fatal, and a character who blithely ignores risks has a short life expectancy in the Realm.

The purpose of this article is to let players put some numbers on their risks so they can improve their decision-making and fully enter into the strategic depth of the game. I will assume that the reader has no training in probability. Those who have a nodding acquaintance with probability and statistics will find much of this familiar, but may find it useful to have the results reviewed and tabulated.

2. Die Rolling

Magic Realm is the only game I am aware of where most character die rolls are made with two dice and the higher of the two dice is used to find the result on a table. A 5 on one die and a 2 on the other is interpreted as a "5" result, for example. This creates an unusual non-uniform probability distribution (like the normal roll two-dice-and-add where the most probable result is "7" with "2" and "12" equally unlikely), but with the interesting twist that low numbers are harder to get and nearly always more desirable. Some special advantages or items can give a character the ability to roll only one die which makes it easier to roll low, but it is often unclear how much better this is - our intuition is often not a good guide for this unfamiliar system.

To put numbers on these chances, we invoke the fundamental theorem of probability: the probability of any outcome is proportional to the number of equally likely events that result in that outcome. So, if we consider that the roll of each die (the red die and the white die) are equally likely to come up with any number from 1 to 6, there are 36 equally likely outcomes of rolling two dice as shown in the table in Table 1 below. On the top row we show the result of the white die and in the left-hand column we show the result of the red die. The results in the table are indicating both dice in the following format: (white die roll, red die roll). Assuming the dice are fair, all of the 36 results in the table (six white die possibilities time six red die possibilities = 36 total results) are equally probable.


Table 1: An illustration of all possible results of rolling a red die and a white die simultaneously.


3. The Hide Table

If a character rolls on the Hide Table, any result except a 6 will result in him hiding successfully. Since only the highest number counts on each roll of the dice, all the results with a 6 on the red die in the bottom row and all the results with a 6 on the white die in the right-hand column give a game result of 6. The rolls that result in a 6 are high-lighted in blue on the following chart (Table 2).


Table 2: The results of rolling two dice that give a 6 on the higher die ("No effect" on the Hide Table) are highlighted in blue.


By simple counting, we see that there are 11 chances of getting a result of 6 on the highest die, and 25 (=36-11) chances of getting a result other than 6. Thus the chances of rolling a 6 result with one roll on the Hide Table (and not hiding) are 11/36=0.3056 =30.6%. So there is nearly one chance in three of failing to hide on a single roll on the Hide Table - much too great a chance to take if failing to hide would result in your character's death!

In the second part of this tutorial we will look at how recording multiple Hide Phases increases your chances of hiding successfully. But first we will look at the probabilities of some other common rolls.

4. The Locate Table

In Magic Realm you need to discover a treasure site by using a Search Phase to roll on the Locate Table before you can roll on the Loot Table to take any treasure - which often entails a long and frustrating search requiring many Search Phases. If you are in a clearing with one or more treasure sites, you need a "Discover chits" result on the Locate Table to find the treasure site so that you can begin looting. "Discover chits" requires either a 4 on the Locate Table, or a 1, which gives a "Choice" result. The rolls which result in either 4 or 1 are highlighted in blue in Table 3 below.


Table 3: The die roll results that give either a 4 or a 1 on the higher die (required to discover a treasure site) are highlighted in blue.


Again, simple counting give the probability of discovering a treasure site in one roll on the Search Table = 8/36=22.2%, about one chance in five. This relatively low probability is the reason that in multi-player games treasure locations are often transferred by gift or sale from one character to another or discovered by "spying" on another character who is looting a site.

To discover a secret passage requires a roll of 3 ("Passages"), 2 ("Passages and clues"), or 1 ("Choice") on the Locate Table. The rolls that result in a 3, 2, or 1 on the higher of two dice are highlighted in Table 4 below.


Table 4: Die rolls that would result in finding a secret passage or hidden path on the Locate Table or Peer Table, respectively, are highlighted in blue.


There are nine rolls out of 36 possible that give a 1, 2, or 3 on the higher of two dice, so your chances of finding a secret passage in Search Phase roll on the Locate Table is 9/36=25%, one chance in four. (This is also the chance of finding a hidden path in one roll on the Peer Table.)

The probabilities of various results on other tables can be calculated from the data in Table 6 below; they are explicitly listed in Scott DeMers and Vittorio Alinari's "MagicRealmOdds" Excel table which can be found on the Magic Realm Keep site at: http://www.geocities.com/finiasjynx/


5. Rolling One Die

Character special advantages, like the Dwarf's "Cave Knowledge," or items like the Lucky Charm that allow a character to roll only one die, offer a huge advantage in using the tables. To illustrate how this works, consider the Druid who rolls only one die on Hide rolls. There are only six possible results of rolling one die, and only one result (die roll = 6) that would prevent the Druid from hiding, as shown in Table 5 below. The probability of missing a Hide roll is clearly 1/6=16.7%, about half as great as the character who rolls two dice.

[IMG]http://www.thewinternet.com/mcknight/BIMR6/MR_Prob_6 (1 Die)(Tb5).gif[/IMG]
Table 5: Illustrating the probablility of the Druid failing to hide by rolling a 6 on one die.


Similarly the Dwarf in a cave has two chances out of six (33.3%) to roll a 4 or a 1 and locate a treasure site, and three chances out of six (50%) to roll a 3, 2, or 1 to find a secret passage. Compared with a character without a roll-one-die advantage, the Dwarf is about 1.5 times as likely to find a treasure site - and twice as likely to find a hidden passage - with one roll on the Locate Table in the caves.

In summary, the probability of rolling any result when rolling one die or rolling two dice and taking the higher number is given in Table 6 below. The probability of rolling one result OR another result is the sum of the two probabilities. Using this table you can predict the probability of any Magic Realm die roll with one die or two dice. For example, the probability of rolling a 4 or a 1 with two dice is 19.4% + 2.8% = 22.2% as we saw in our discussion above.


Table 6: Probability of getting any one result by rolling one die or by rolling two dice and taking the highest die.


5. The Loot Table

Once you have discovered a treasure site, you can use a Search Phase to roll on the Loot Table to try to draw treasure out of the site. A roll of 1 on the higher of the two dice (1,1) permits you to take the top treasure in the site, a roll of 2 takes the second treasure from the top, a roll of 3 the third treasure from the top, and so forth. So, if there are only three treasures left in a treasure site, you need to roll either a 1, 2, or 3 on the higher of two dice to take a treasure; otherwise you take nothing. The rolls of two dice that give you a 3 or less are exactly the same as the rolls required to find a secret passage or hidden path illustrated in Table 4: 9/36=25%.

The probability of looting a treasure from a site with any number of treasures left can be found from Table 6 by adding the probabilities of all numbers less than the number of treasures remaining, as shown in Table 7 below.


Table 7: Probability of taking a treasure from a treasure site (or an item from a pile of abandoned items) with one roll on the Loot Table as a function of the number of treasures in the site (or items in the pile).
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Dallas Apollo
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This it outstanding! Thank you!! I've just recently started playing (having had my copy of the game in storage for almost 25 years) and have been obsessing over the probabilities of certain rolls. This is exactly what I've been looking for!
 
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Shane Is Board
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I'm using the latest version of Firefox and it shows up just fine for me.
 
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