Wednesday, June 8, 2011

Solved: Trouble with Assassin's Creed and NVIDIA and Windows 7

I just built a Windows 7 system and Assassin's Creed was crashing regularly.

The solution is to run the DX9 version, even if yours is a DX10 system. The screen will still flash occasionally as the NVIDIA drivers encounter a problem, and your system will run astonishingly hot, but it will recover from its brief blackouts in DX9 -- it doesn't recover in DX10.

Wednesday, April 20, 2011

Have you played Fall From Heaven Yet?

I will write more on this later, but if you are a fan of Civ IV and have not played the Fall From Heaven mod, you should. It turns a scientific, logical positivist game into a fantasy world with angels, demons, and magic.

Saturday, January 29, 2011

What Are The Odds of Rolling a Six?

I've been playing the new Third Reich with its new combat system, which uses Bucket of Dice (BoD) instead of odds / Combat Results Tables (CRTs) to resolve battles. In CRT system, you add up the attacking factors and defending factors and divide attackers by defenders to get a ratio. You then roll once on a table. This is fast and useful, but it delivers extreme results too often.

In the BoD system, you roll one die per combat factor, and each roll of "6" is generally a hit. So knowing the odds of rolling sixes is important.

The odds are not simple.

Many of us simply multiply the odds of rolling six on one die (1/6) by the number of dice to get the odds of actually rolling a six. This system seems intuitively to be right, but careful thought will show that it is not: if you roll six dice, you are not guaranteed to roll a six.

Simplify the problem: what are the odds of rolling a 6 on two dice? Intuitively, you might guess the odds are 1:3. You'd be wrong.

Simplify it further: what are the odds of getting "heads" at least once on two coin flips? It's certainly not 1/2 + 1/2 = 1. The matrix of possibilities of two coin flips are:

HH HT TH TT

There are four possible outcomes of two coin flips and only one of them does not have "heads" at least once.

The odds of getting "heads" at least once on two coin flips is 3:4 or 75 percent. No matter how many coins you flip, it is possible, though very unlikely, that you'll never get "heads" at least once.

The matrix of possibilities for two dice

While there are only 4 possible results from flipping a coin twice (2 x 2 =4), there are 6 x 6 =36 possible results of rolling two dice.

If you roll a six on the first die, there are six possible outcomes for the second. However, if you roll a six on the second die, there are only five unique possibilities for the first die, because we have already covered the possibility of rolling a six on both dice. The odds of rolling at least one six on two dice are 11/36, slightly less than 1/3 (and there's a 1/36 chance of rolling two sixes).

The matrix of other results contains all the numbers between 1 and 5. It is, in fact, 5 x 5 = 25 possible results (1 and 1-5, 2 and 1-5, 3 and 1-5, 4 and 1-5, and 5 and 1-5 = 5 x 5). 25 + 11 = 36, so our math checks out. The odds of _not_ rolling at least one six on two dice is 25/36, slightly over 2/3.

What are the odds of rolling one six on three dice? Now we're dealing with 6 x 6 x 6 = 216 possible outcomes. It's easier to calculate the odds of not rolling at least one six. Those odds are 5 x 5 x 5 / 6 x 6 x 6 = 125 / 216. That means that the odds of rolling at least one six on three dice are 89 / 216 or about 41 percent.

If you visualize the matrix of possibilities as a 6 x 6 square, with columns 1-6 across the top and rows 1-6 across the sides, you'll see that the outcomes containing a six are in the 6 row and 6 column. There are six possibilities in each, but rolling a 12 (two sixes) is a duplicate, so there are 11 possibilities. To confirm the truth of this visualization, imagine the 5 x 5 grid made up of the 1-5 rows and 1-5 columns that contain no sixes. That's 5 x 5 = 25 out of 36, as described above.

What are the odds of most people's favorite attacks, trying for one six on six dice or two sixes on twelve dice?

The odds of not rolling one six on six dice are 5 ^ 6 / 6 ^ 6 = 15,625 / 46,656 = very close to one-third. This is counter-intuitive if you're calculating odds through addition. If you are doing it that way, you'll think you need six combat factors to be guaranteed to get one hit. As I show here, it's not true. There's about a 1/3 chance of failure.

Nine factors give you a better guarantee of at least one hit: 5 ^ 9 / 6 ^ 9 = 1,913,125 / 10,077,698. There's still a 1/5 chance of failure (actually 18.98 percent, which is very slightly less than 1/5).

But I need two or three hits

Calculating the odds of getting two or three hits is much tougher. We're no longer rolling two dice, so the matrix would be a six-dimensional or nine-dimensional. So let's start with the odds or rolling two hits on three dice.

The matrix of possibilities is a cube with 216 entries (6 x 6 x 6). There are three sets of six outcomes containing two sixes, with a duplicate at the remote possibility (1/216) of rolling three sixes. The odds of rolling two hits on three dice are 5 + 5 + 6 = 16/216 or almost 7.5 percent. It is exactly 2 / 27. It is very unlikely.

Math check: the odds of not getting two hits on three dice is 6 x 5 x 5 = 150 possibilities if the first die is a six, 25 possibilities if the second die is a six, and 25 possibilities if the third die is a six.

It is 6 x 5 x 5 + 1 x 5 x 5 + 1 x 5 x 5 = 200 / 216. Math check complete.

So what are the odds of getting two hits on twelve dice?

The odds of not getting two hits on twelve dice are, I think, (6 x 5 ^ 11 + 11 x 5 ^11) / 6 ^ 12 =

(292,968,750 + 48,828,215 * 11) / 6 ^ 12 = (292,968,750 + 537,109,375) / 2,176,782,336

= 830,078,125 / 2,176,782,336 = 38 percent, which is very close to one third, just like the odds of not getting one hit on six dice. I am not certain that my math is exact here, but I am certain that it's close to accurate.

6 x 5 ^ 11 represents the possibilities in which the first die is any number and the subsequent ones have no sixes. The remaining 11 x 5 ^ 11 represent the possibilities that involve a six rolled on any one of the other elevent dice.

What are the odds of rolling three sixes with eighteen dice?

The odds of not getting three hits on eighteen dice, I believe, are made up of

6 x 6 x 5 ^ 16, which are the possibilities of rolling a six on the first two dice

x 16, representing the possibilties that involve rolling sixes on the first die and any of the remaining sixteen dice.

But in fact, we want to use a different mathematical function. We want to calculate the exact number of ways we can roll two sixes on eighteen dice. The number of possibilities are 17 given a six on the first die, 16 given a six on the second die (with a six on the first die already covered) ... the number of possibilties is 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 153.

I think that the odds of not rolling three sixes on eighteen dice is 153 x (6 x 6 x 5 ^ 16) / 6 ^ 18 =

153 x (36 x 25 x 25 x 25 x 25 x 25 x 25 x 25 x 25) / 216 x 216 x 216 x 216 x 216 x 216) =

153 x (5.49316406 × 1012) / 1.01559957 × 1014 = which doesn't help at all, so I'll just plug the numbers above into Google and I get:

a number that does not work, so I take out the "36" and I get

153 x (25 x 25 x 25 x 25 x 25 x 25 x 25 x 25) / 216 x 216 x 216 x 216 x 216 x 216) = 23 percent.

Again, I'm not certain that this is correct, but it will, I think, explain your actual experience with bucket of dice games. You need to know the odds.

Wednesday, October 27, 2010

Mass Effect 2 First Thoughts

Bioware has learned some important lessons from Mass Effect and those lessons make Mass Effect 2 a much better game. While Mass Effect had more role playing player upgrade options than Mass Effect 2, the original game suffered from several key flaws (that few reviews seem to mention).

The biggest of those flaws was at the helm of the ship, the Normandy. You could spend 15 minutes trying to reach a console, locking on to it while too far away and then failing to see it when you were in front of this. You interacted with this console frequently, every time you wanted to go from one planet to another. Now, Bioware allows you to interact with consoles from farther away and the problem has mostly disappeared (you still don't want to get too close to something you'd like to examine, but you should never have to).

The dialog is better, and the software (surprisingly) runs better on my PC, the noob build, which is now underpowered.

Your interactions with planets have changed completely. There's now a mini game for finding elements on planets, instead of just click and you're done, and you walk around planets instead of driving on them in a vehicle that, in Mass Effect 1, was virtually impervious to fire but which could get caught in a ravine, forcing you to reload the game.

The interaction with characters and between them is much, much smoother, and the stories are more believable. It is in the writing and the voice acting that the new game really shines. The old one had some excellent performances from very actors, such as Seth Green as the ship's pilot, but he's even better in Mass Effect 2, where he gets to play some light comedy in addition to serious moments. Mass Effect 2, as the article says, is full of stars.

It is also gorgeous -- without straining my PC -- which makes the game even more enjoyable. Part of the joy of a space romp is visiting strage alien lands that are beautiful. Too many science fiction games take place in dark and narrow spaces or monochromatic wastelands.

Friday, September 17, 2010

Strategy for "Falling Seeds" in Plants vs. Zombies

Plants vs. Zombies is an excellent tower defense game. This strategy guide covers "Falling Seeds", a particularly interesting and replayable mini game.

1) The opening

You will get three seeds before the zombies start coming. Hopefully, they will be shooters. If not, place any lights and magnets farther back than you would usually place them.

If you get lily pads, you can either place them at the back of the water row or forward. Since you know that none of the first wave of zombies will go through the water, if you place a lily pad forward and then get a star, light, or magnet, you can place it on a lily pad.

Which row should you place the shooters in?

There are two top rows (1,2), two water rows (3,4), and two more grass rows (5,6). I like to place shooters in 2 and 5.

Note that you can always see zombies through the fog in row 1, and can often see zombies through the fog in row 6.

If you get a threepeater, place it in 5. If you get a second, place it in 2. If you get two in the opening, you have already covered all six rows with shooters!

2) The first wave

Once the zombies start coming, try to get one shooter in each of 1,2 and 5,6. Initially, if you get an expendable plant, such as a spud bomb, you can place it in a row and consider that row covered by a shooter. I also like placing expendables (and the little puff shrooms) on lily pads as far forward as possible, but at least 3 columns from the end.

If you get spikes, place them on the far right and use their sound to warn you of a zombie attacking that row. If you get spikes later in the round, place them right in front of a nut (this is from the gamefaqs.com strategy guides: http://www.gamefaqs.com/pc/959255-plants-vs-zombies/faqs -- the survival endless guides contain some very creative and powerful strategies).

Besides the spikes, there are only two plants that hit more than one zombie in their row: the watermelon and the big fume shroom. These are very valuable and should be protected. The watermelon can be placed at the back, but the fume shroom has a short range and is best placed 2 spaces behind a barrier or, if necessary, protected by a pumpkin.

Also valuable are the plants that slow down the zombies: the butter and freeze plants. These should be protected. In the early part of a level, they can save you when a zombie gets farther than you'd like.

Also try to place chompers directly behind a barrier (or garlic) or a pumpkin.

Place one shooter in each row before you place a second shooter in any row unless there is a conehead advancing on a valuable plant.

In particularly difficult levels (after you've played the game at least 10 times, they will happen occasionally), you will not get enough shooters to cover even the start of the first wave. If two zombies have progressed far enough down one row, let them get to the end and let them meet your lawn mower.

Once you have placed a large number of lily pads, you desperately want to prevent zombies from reaching the end. Protect the lily pads.

Never place in the back: nuts, single use plants, spikes, marigolds.

Never place far forward: threepeaters, watermelons, and scaredy shrooms.

3) Using garlic

Garlic is a very difficult plant to use correctly. If you ever get two in a row, you can place them adjacent to each other, and the zombies will go back and forth. If you ever have one row poorly defended, or you lose a lawn mower early in the game, you can protect that row with garlic, but then you must take care to place powerful plants in the adjacent row. The row with garlic should have some shooter in it. A freeze or butter plant is preferred.

If you are depending on garlic to protect a row, and you get the garlic early on, you will need to place a second garlic in the same lane after a few waves.

4) Using bombs, chilis, and nukes

If you get these too early, they're useless. Hold them for as long as you can. They are especially valuable in destroying the bungee zombies.

5) Using chompers

The chomp zombies can be used to protect key plants. They will eat a zombie that is attacking the plant in front of them, but then they need time for digestion. If a chomper needs time, an ice shroom can help.

6) Using torchwood

These are the most difficult to place. For best effect, they need to placed forward but they are vulnerable. Chompers and pumpkins can protect them, as can barriers. Note that if you place a split pea to their right, they will protect the plants in the lane against bungees.

Note that torchwood will drive back a very small amount of the fog.

7) Using nuts and pumpkins

These barriers are the key to the survival of your most valuable plants. Early on, you may want to place them in the grass rows, but later on, it's great to also place them in the water rows.

Place them forward so that you can place the following behind them (in order of value): lights, magnets, fume shrooms, stars, and chompers.

Note that if you get another nut of the same type, you can place it directly on top of your existing nut to heal it and make it stop crying.

8) Zombies to fear

The metalheads (football players, pailheads, and screeners) are especially dangerous if you're playing in a level that has no magnets. Otherwise, they (and the jack in the box) are relatively harmless. The metalheads must meet a barrier. Even if you fill a lane with shooters, the football player will get through.

The jack in the box is the most feared zombie. Make sure that by the late first wave, you have enough plants in each row to defeat a jack in the box. Generally, this means 2-3 shooters per row. A jack in the box that explodes can destroy your barrier and completely disrupt your strategy faster than any other zombie (except the bungees, who can do the same).

The newspaper zombie is feared in the early stages of the game, before the barriers are set up. This zombie is particularly likely to get to your short range plants, the puff and fume shrooms. If necessary, place an expendable plant such as a marigold as a barrier.

The bungee zombies can be your most challenging opponent. I find that freeze, bomb, and butter plants do the best to stop them. If you have a large number of stars in a column, they can help fight the bungees.

9) The endgame

Wave four differs from the other waves in that it: a) attacks the water rows more than the grass rows and b) some zombies appear in the water row. Towards the end of wave 3, place more firepower in the water. Also, some of the single use plants will be particularly useful in the end game. If you get a nuke, the end game is over very quickly

Note: You should occasionally look at the bottom right hand corner of the screen. It shows the progress bar. The start of each new wave is marked with a flag.

10) Why "falling seeds"?

My gf pointed out to me that of all the mini games, this one offers the greatest variety precisely because you do not control what plants you get. The fog adds to the variety and uncertainty, but I try very hard to eliminate the fog.

Sunday, June 13, 2010

Bethesda RPGs: Morrowind, Oblivion, Fallout 3

These are the best three RPGs from recent years. Each features a massive interactive world that has a small number of Main Quest quests and a large number of Side Quests. The Main Quest is a linear story that you must follow and the Side Quests are all optional.

Each features a world that is beautiful. But that initial beauty is quickly destroyed by the onset of the enemy. Morrowind gets a blight wind, Oblivion gets hell gates, and in Fallout 3, you step out of the womb and into post-nuclear Washington, D.C.

These games are superb, but they would be even more enjoyable if the world itself stayed beautiful.

Also, the wondering monsters mean that you will be attacked regularly as you wonder through the world. This seems unnecessary. At some point, animals should run away when hurt. Wandering monsters are a concept that dates back to D&D, but they are too frequent and in some cases too brutal in these games. Wandering would be more rewarding with fewer wandering monsters.

Some complain that the treasure system in these games is wrong. The treasure you obtain is entirely dependent on your own level, so once you reach the higher levels, opponents will all have high quality weaponry. Thus, in the magical fantasy settings, even the poorest lowlifes will have the most expensive armor. But I think this is a quibble. It makes for good play balance and for an incentive to level up (I have a friend who's trying to play Oblivion through completely at just level 1).

The worlds are all vast and, if you ignore the main quest, you can play through a virtually untouched Morrowind and Oblivion before embarking on the Main Quest to finish the game. I recommend doing it this way.

The worlds are so vast that I strongly recommend purchasing the book about each world, which will allow you to find the secrets of the world and completely explore it.

You'll do a lot of fighting in these worlds, and the combat system in all three is excellent, complex, and rewards level progression. In the fantasy settings, you can fight with hand weapons, ranged weapons, unarmed (not recommended) or magic. In Fallout 3, you can fight with a variety of guns, with hand weapons (or unarmed, also not recommended), or with passive mines and with grenades. Sniper rifles add to the strategic options, with several areas set up to allow a sneaky sniper to eliminate much of the opposition before entering.

There are stories and hints of stories throughout each game which are not part of the Main Quest. In Fallout 3, the location and position of charred skeletons tells part of the story of postwar America, from the couple dying in bed together spooning to the skeleton in the bathtub with a toaster.

In Fallout 3, several of the stories are more like horror than science fiction (especially the rarely visited Dunwich Building), but there are a wide variety of stories, and many are interesting. There is even a detainment camp convoy in which America once again locks up those of its own citizens whose ancestors hailed from a nation we're at war with.

In Oblivion, the stories are particularly inventive. A sleepwalker may expect the first Fighter's Guild quest to be about fighting rats -- and be suprised to hear from a woman how beatiful and delightful her pet rats are. More humor would add much to this game, and most of the stories are deadly serious.

In Morrowind, there are fewer stories, but much to do and see. I particularly like the fact that, with a small donation at a particular temple and a spell that will return you to that temple, you can spend most of the game flying around. Flying may have made the game a little unstable and was eliminated in Oblivion. It's the one thing in Morrowind that I miss in Oblivion. Also, there are too many of a single species of bird that attacks anyone who flies.

Quests are easy to follow in Oblivion and Fallout 3 (the system in Morrowind needed, and received, a significant upgrade). In-game maps are good but not great, and it helps a lot to have the quest book. The quest book cost about $15 at the time the games were released (and is usually now out of print) and contained several hundred pages of information. The Fallout 3 quest book is hardbound and even longer than previous quest books and contains concept art and design comments.

These are 3 of the best RPGs available. I strongly recommend them.

To view the depth of each, check out its wiki:

Morrowind

Oblivion

Fallout 3

Saturday, May 15, 2010

New Version of Republic of Rome Board Game is Superb

The quality of the game is excellent. It's not cheap, but well worth the price, and much improved over the original AH version.

Question answered?