Eclipse Board Game Strategy: Eridani Dreadnaughts

I’ve recently fallen in love with the Eclipse board game. Well, really, I should say that I’ve fallen in love with a board game entitled, Eclipse: New Dawn for the Galaxy. The reason I have to be so specific is that if you go to amazon and type in Eclipse Board Game, you will quickly discover that there are two separate Eclipse board games. One is the one pictured to the right.

While the other is a board game version of the sparkly vampire genre. That game I’m less crazy about.

Part of the strategy for the non-sparkly vampire Eclipse game is to chose your which race you want to play. The race that is recognized as the hardest to play are the Eridani. They start the game with two fewer influence disks than the other races and therefore are severely restricted in the number of actions they can take. This is why they are the most disliked of all the alien races.

I devised a strategy for them that seems to work reasonably well. It involves taking the middle in as little as three turns using as few moves as possible. Possessing the middle gives you a tremendous amount of resources and costs precious few of your already scarce influence disks. Once there you can hopefully hold the middle as well as use it to start moving against your more vulnerable neighbors.

The Eridani suffer not only from a lack of influence disks, but also disks, their problem is compounded by a lack of minerals. The middle tile does have a mineral spot as well as another advanced mining spot. I have finished entire games having these be my only populated mineral resources on the board. Those games are never pretty, but holding the middle can still pull you through some games.

The scarcity of resources means if you ever suffer significant loses in a fleet on fleet battle then it’s very difficult to recover. Therefore, Eridani players should be particularly careful not to engage opposing fleets unless they are a solid favorite. It also means that you need to carefully shepherd your starting interceptor. You poor resource production means you have to squeeze the most life out of your starting interceptor you possibly can.

So if we’re gonna take the middle on turn 3, we need to have some idea of how to build toward that. Fortunately, there are a few programs on the internet that will allow us to simulate Eclipse combats and give us a probability of success. First we need to understand that the Eridani love Dreadnoughts. Dreadnoughts are the only ship design where the Eridani get any bonuses (the one built in power). They are also the most survivable ship to build, and the Eridani’s restricted influence disks means they can’t move mass number of smaller ships efficiently.

So if the most likely initial battle fleet the Eridani can build is comprised of their starting interceptor and a dreadnought, then let’s see the best course of action to take with that fleet.
Continue reading Eclipse Board Game Strategy: Eridani Dreadnaughts

A Rough Draft for a Gamma World Character Sheet

I was really unhappy with the character sheet included in the new Gamma World game. The new Gamma World is clearly attempting to dummy down a RPG into something that is more akin to a board game, and I support that. However, in their effort to make the game seem easy, they made a character sheet that just doesn’t have room for enough information on it. So I threw this one together. It’s a rough draft right now, because I don’t have time to clean it up until I get back in town from Texas for Christmas. Oh yea, and I’m getting married on New Year’s Eve as well.

Anyway, if anyone’s interesting in evaluation this rough draft character sheet and providing me with any suggestions, feel free to leave comments.

Here’s the sheet.

The Probability of 4d6, Drop the Lowest, Reroll 1s

No sooner had I figured out that math behind 4d6, drop the lowest, then it seems I was confronted with the gamer practice of rolling 4 six sided dice, re-rolling any 1s, and then dropping the lowest score. One gamer decided just to take my 4d6 math and convert it to 4d5 math figuring that re-rolling 1s meant perpetually re-rolling 1s. Of course, as I asked in the thread, if you’re going to re-roll a 1 every time you get it, why on Earth are you rolling a six sided die to begin with. The dice bag of most D&D/Pathfinder players tends to have more dice than they know what to do with. Wouldn’t it make more sense to just roll four 5 sided dice (which really means you roll a 10 sided die and divide it by two, rounding up) and then add 1 to each die’s result. Doing so would give the same results as 4d6 with a perpetual re-roll and would not involve the seemingly tedious step of re-rolling anything.

Of course most people aren’t as elegance minded as I am, but I also suspect that most people have the habit of re-rolling 1s once and then taking the result whatever it is. My friend Taylor had just asked me a couple of weeks ago how to figure the math on a six sided die with a single re-roll of 1s. That math is actually quite simple. When you roll a six sided die, the chance of getting any particular result is 1 out of six, or .1666 repeating. Now when you roll a one, it creates a new probability event and you re-roll. So for the die to end up on a one would require you to roll a 1 twice in a row. So the odds are 1/6 times 1/6 or 1 in 36, .02777 repeating. Of course, the chances of you rolling a 1 and then rolling any number are the same .02777, so all you need to do is add that amount to the other scores. Thusly, the probability of getting any particular result on a single six sided die with a single re-roll of 1s is:

Result          Probability
1 1/36 or .02777
2 7/36 or .19444
3 7/36 or .19444
4 7/36 or .19444
5 7/36 or .19444
6 7/36 or .19444

Simple enough. But what about the problem of 4d6, single re-roll 1s, and drop the low result? We know for last time that there are 1296 possible combinations of four six sided dice. When we single reroll a 1 result, we still end up with 1296 possible combinations, we’ve simply weighted some more heavily than others. In the problem with a single re-roll of a six sided die, a 1 is still a possible result, it’s just much less likely than any other possible result. Similarly, I figure in the 4d6 problem that there are still 1296 possible results, but we just need to weight them differently. It’s still possible to get a result of (1,1,1,1) on four six sided dice, it’s just much less likely than (6,6,6,6), but how much less likely?

Well, we can see from the six sided die result that getting a result of a six is 7 out of 36, whereas a 1 is only 1 out of 36. If we compare the two probabilities by dividing the chances of the 1 result by the chances of the 6 result, we get 1/36 divided by 7/36, which simplifies to 1 in 7, or .14286. That is, you are the comparative probability of getting a 1, rather than a six (or any other score) is .14286. So if we take an array or results and we weight all the results with 1s by .14286, we should get the results of the array weighted so that 1s are far less likely.

Let’s take a look at a single six sided die’s results to check our work. A six sided die has an equal probability of generating a 1,2,3,4,5, or 6. Each has a probability of 1 in 6. If we multiply the 1 result by 1 in 7 (or .14296) then, we get the following table.

Result Weighted ProbabilityRe-Weighted Probability

1 1/42 1/36 2 1/6 7/36 3 1/6 7/36 4 1/6 7/36 5 1/6 7/36 6 1/6 7/36

The problem here is that the probabilities do not add up to 1 anymore like they are supposed to, but we can re weight them by adding up everything and dividing each probability by the sum. If we add up all the probabilities above, we get 5/6 + 1/42, or 35/42 + 1/42 = 36/42 or .857. If we now divide each probability by the sum of 36/42, we get the re-weighted probability in the column in the table above. Voila! The re-weighted probability is exactly equal to the original probability we calculated in the first table.

What this means is that we can take any array of six sided die results, multiply each result that has a 1 by 1/7 for each 1 it has, re weight the results, and we will get the precise probability of getting each result with a single re roll of ones. If you’re curious, I can show how any exact probability was calculated. Most people don’t care, so I’m leaving that off. Here are each of the following commonly used stat generation methods in D&D/Pathfinder: 2d6+6, 4d6 drop the low, 4d6 with a single re-roll of 1s and drop the low, 3d6+2, and new method I’m proposing which is just 4d5 keep all. I graphed the probabilities of each against their respective scores and got the following graph:

A chart of each of the popular Pathfinder / D&D Stat Generation Methods

Here’s the data that went into generating this graph.

Number2d6+63d64d6, DL4d6, DL, R14d54d4+2

3 .00463 .0007716 5.96eE-07
4 .0139 .003086 1.67eE-05 .0016
5 .0278 .007716 .000192 .0064
6 .0463 .0162 .00262 .016 .003906
7 .0694 .0293 .00873 .032 .01563
8 .0278 .0972 .0478 .0199 .056 .03906
9 .0556 .115 .0702 .0391 .0832 .07813
10 .0833 .125 .0941 .0674 .1088 .1211
11 .111 .125 .114 .0983 .128 .1563
12 .139 .116 .129 .126 .136 .1719
13 .167 .0972 .133 .150 .128 .1563
14 .139 .0694 .123 .155 .1088 .1211
15 .111 .0463 .101 .138 .0832 .07813
16 .083 .0278 .073 .105 .056 .03906
17 .0556 .0139 .0417 .0626 .032 .1563
18 .028 .00463 .0162 .0252.016.003906
19 .0064
20 .0016

The Mathematics Behind 4d6 Drop the Lowest

Unlike most other roleplaying games, Dungeons and Dragons and recently spun off Pathfinder RPG allow for multiple ways to generate your characters starting characteristics. A point-buy system has become the most popular way by most players because it will result in each player having a starting character that is roughly of the same power level. This is a concern for a lot of gaming groups because the games they play are dominated by combat (which chews up quite a bit of game session time per encounter) and players tend to feel resentful if one player is significantly outshining the other players in terms of body count. In more social games, I think disparity in character power levels doesn’t mean as much. If we are roleplaying out Bilbo Baggins’s birthday party does the difference in power level between Gandolph and Samwise Gamgee really matter all that much?

Personally I’ve discovered that I tend to enjoy game sessions where characters tend to be subpar and the power levels are asymmetrically dispersed. First off, it’s a bit more real because not everyone brings equivalent skills to the table in life and why should games that imitate life be all that different. Secondly, something about rolling three six-sided dice (which is abbreviated 3d6 in gamer notation) and having those dictate what your characters scores are in the exact order in which you role them disconnects you from your character. If you’re using a point buy system, or even a method of assigning the stats in the order you like, you become invested in your grand design for the character. Having luck determine what your character’s stats are reinforces that you are not designing this character but instead being asked to play a character who is very different from you and, for that matter, very different than you might have preferred.

Some of the most beloved characters have come from subpar stats. Continue reading The Mathematics Behind 4d6 Drop the Lowest

Atom Weaver’s Deck Bashing Challenge

I’ve long been an advocate of trying to make powerful decks from a limited selection of cards. Such “commons” decks thwart the argument that a given CCG is merely the realm of the those who want to invest large amounts of money into it if they can do reasonably well against such decks. This was the reasoning behind my Barbed Wire decks that I made and still sell that mostly use Jyhad card stock.

Another VTES player, perhaps inspired by my Barbed Wire decks, made his own limited card selection challenge: Atom Weaver’s “Deck Bashing Challenge.” This challenge revolves around making as competitive a deck as possible by combining two starter decks of your choosing. While I like the idea, I do have a few reservations about the idea.

For one, starter decks in VTES are much like Magic: the Gathering and are set specific. If one were to find a great combination of starter decks to make an excellent general purpose deck, the starters you were using might be out of stock two years down the road and simply be of little use to the proposed newbie who needed it. Secondly, the starter decks all revolve around a certain strategy; by combining two of them, all you are really going to be able to do is refine that strategy a bit. The starter decks themselves are not toolboxy enough to really serve as the blank slate that I like as a deck constructor. Of course, one could combine two separate starters, but that runs into it’s own problems. Lastly, VTES is a game that has always favored certain strategies such as sneak and bleed or vote and cap. Starter decks, such as the Malkavian or Venture starters from Keepers of Tradition, will be quite competitive whereas working with the other starters from that set means that you will be building a deck that will simply never be as competitive. That’s just the nature of VTES and CCGs in general.

Continue reading Atom Weaver’s Deck Bashing Challenge

The problem with Use Magic Device in Pathfinder

aka Another Reason for a Unified Magic System

I’ve never liked the Arcane/Divine divide in magic in what is now Pathfinder. It worked OK in first first and second edition D&D because there were really only two spell-casting classes, but as third edition D&D attempted to take the classes and make them into certain metrics such as Base Attack Bonus and Reflex Save bonus that are additive, the divide became increasingly wonky. For one, now that we had a skill system that was the same across classes, you had skills for sneaking around. If you multiclassed between different classes, your ability to sneak was related to how many skill points you continued to put into your stealth skills. Thus skills of the traditional Thief class from prior editions of D&D were now nicely delineated and could be treated as discrete parts of a greater whole.

The skill system attempted to do that with magic by giving one Spellcraft skill that related to your ability to determine magic regardless of it’s source, but in so doing they created a wonky element to their magic system because the skill itself was not, in any way, related to the actual working of magic. One could be a completely proficient high level wizard or cleric and not have a single rank in Spellcraft. So it was really just a knowledge skill, but why have one knowledge skill that represents two very different forms of magic when you have other knowledge skills that represent the different between knowledge of local events and knowledge of which crest belongs to the local noble? Continue reading The problem with Use Magic Device in Pathfinder

Opponent Makes an Unbelievable Laydown

An interesting series of hands happened today that culminated in one of my opponents making a laydown I just couldn’t believe. The opponent in this question is another house player named Mary Sue. She doesn’t seem to have a lot of No Limit experience and, in my estimation, she tends to make a lot of bet sizing errors by making her average bet too large.

Here are a few hands we played together to give you some context for our big hand. All hands were played with a big blind of $5 and a small blind of $2. Hand 1: She started with about $150 and I had her covered. I raised it to $12 with AK off suit and she called out of the big blind. Flop comes KQ7 rainbow. She bets $30 into me and I call. Turn comes another spade to give two spades on the board and she goes all in for $100 more with JT of spades. I call and she misses her draw.

Hand #2: She and a couple of other players limp in. I’m on the button and limp with K4 of hearts. Flop comes Jh 10c 6h. Checks to her and she bets $60 into a $20 pot. I fold my hand, but she does get one caller. She puts him all in on the turn for another $100 and wins with a set of sixes.

Hand #3: She has about $600 in front of her and I have her covered. It folds down to her on the button and she raises it to $15. The small blind calls and I raise it to $45 with Ad Ks. Both players call. Flop comes: As 7s 5h. I check to her because I feel she tends to bet too large and will freely commit more chips to the pot than I would in the same round of betting and I want her to continue to make that error. Surprisingly, she bets a rather rational amount of $70 into a pot of $135. The small blind folds and I call.

The turn comes the 10h to make two separate flush draws on the board. I check and she tanks for a good minute. I’m trying to put her on a hand and her general uncertainty tells me she doesn’t have a monster. She bets $100 into a pot of $275, since that will leave her only with a pot sized bet of $350 or so, and since I feel I have the best hand, I put her all in. She thinks and thinks about this for a couple of minutes and then folds, face up, pocket 7s! She said she was sure I had a set of Aces or I wouldn’t have checked the flop with a flush draw out. All I had to say was, “Wow.”

Letter from a Magic: the Gathering Fan

I received this letter today from a 24 year old man in Brazil who is, apparently, a fan of mine. I don’t often get fan mail, so I thought I’d reproduce it here. Note that it is hand written in cursive, and I can’t quite decipher a few words. I also think that English may not be Pedro’s native language, so there are a few grammatical errors, but what the hey. How many fan letters to do you get?

Hello Mr. Preston Poulter,

My name is Pedro. I’m 24 and a big fan of the Magic: the Gathering card game. I enjoy this game so much as I enjoy legendary players like you, man. I don’t know if it’s your correct address. I’ve been trying to find duelist’s addresses I admire to write to them (like you) but it’s so hard to find. The only 1 I found (I guess) is yours.

All of you contributed to build my love for this game and have a happier life playing it with friends and family. I used to build my own personal decks, but I used to copy the strongest duelists decks to make me feel more powerful. With movies and rock-n-roll, Magic is the one thing that’s part of my life and people like you make us, our fans, see you as idols and people that transform the game in serious ways. So I’d like to congratulate you, first because I love your 1996 deck, and, second, because I write to everyone that takes part and contributes for the expansion of this lifestyle everyday, since my brother, the players that are more close to me, until Mr. Richard Garfield, that answered to me twice (always kindly).

And, as a great appreciator of this funny game, I’d wanna ask you something: could you please sign these 06 cards and give them back to me?? I’ve included $3 for it. Because of the work (I’m a safety technician) and the family (I got married in Oct. 2009) I don’t have much time to play now, but when I can, I do it. So, because of it I review my Magic collection of signed cards, a practice that makes me happy to get exclusive cards and, more than this, bring to you, artists of this game, my admiration and attention to thank you for all you do for your fans.

When you can/ have time/ want to answer, my address is: REDACTED

Thanks again, now for opening my letter and reading it. Now my goal is almost finished, only waiting for your answer when you wish.

All the best from your Brazilian fan,

It’s always weird getting these letters from the past. They’re addressed to me, but really, the person they’re written to doesn’t exist any more. He was a 22 year old Graduate Student in Chemistry who’s only real love seemed to be hanging out with his friends (none of whom I talk to anymore) and playing Magic: the Gathering. Still, it always makes me smile to get them and to think back on that time. My life is a lot happier now. Fame is a strange thing and I’ve always considered myself lucky to have found that out by having it in so limited a capacity.