Final Four

 ...and I was worried when my bracket didn't have any number 1 seeds going to the final four.

UCONN at the moment has the best chance of the teams left, and I'm not just saying that because of how the seeds worked out.  The dice chose UCONN.  Which means they have always had the best chance of winning the tourney.

The dice also choose to form impossible shapes

In all seriousness, I've been thinking that maybe this whole method is not actually as good as I want it to be.  The NCAA is really bad at choosing seeds.  I mean, sure you can get some information out of the seeds, but really the seeding makes some teams just have an easier path towards the end of the tournament.  Given the assumption that a three seed (like UCONN) is just as good as a one seed (i.e. each has a 50/50 chance in winning...which is an assumption I made), the only thing that makes a difference is the path that the teams take to get to the championship.  UCONN is going to be facing better teams earlier than, say, Ohio State did.

 Furthermore, the sheer number of possible outcomes makes it so that it is nigh impossible to get a bracket which is good (on the other hand, the sheer number of people making brackets makes it so that somebody is going to have a good bracket *wink*).  Think about it this way...instead of playing basketball, each team decided to flip a coin to determine the winner.  The model should be pretty clear...each team is going to have a 50/50 chance in winning.  Given that there are five rounds of play, the probability that you pick the correct winning team is (1/2)^6, or 1/64.  The problem here is that all of these probabilities are being multiplied together.

Warhammer fans should be familiar with this decay; a space marine squad rapid firing into another space marine squad has 2/3 chances to hit, 1/2 chances to wound, and then 1/3 chance for the opponent's armor to fail.  These aren't awful odds for this situation, but when you multiply it all out, you're only expecting 1/9 shot to wound.  That means that on average, from 20 shots, you're killing 2 marines a turn.  Not exactly stellar odds, but because three things need to happen for you to kill a marine, you're multiplying all these numbers together which are less than one, and they get small quickly*.  So no matter what the odds are for a 1 seed to win the championship, the probability is very slim that it will happen because of the layers of events which need to happen in succession.  Oh, and unlike Warhammer, you only get one shot at this one.

U Newbie!!  I kill you!!...Or...maybe not....

Now the interesting question becomes...can you do better than the average bloke will with a bracket rolled with dice?


*Side note: this is why things like Fortune, Feel No Pain, Ghosthelms vs Perils attacks, etc. are so freaking good....they add more dice which need to be rolled to kill your guys.  This is also why power weapons and other armor-ignoring weapons are so fantastically good...they subtract the number of dice which need to be rolled to kill other guys.

Taco Bell

They are now serving shrimp.  I have spent the last six hours carefully analyzing the probability that this will not give the eater some sort of disease.  Drum roll please:

<.01%.  I base this on the fact that I am throwing up in my mouth right now.  The picture is obviously infecting my brain.

That is all.

Perudo

Basically the game liar's dice from Pirates of the Caribbean.  Except you aren't giving this man your soul when you lose:

Do you fear dice?

My friends hate it when I play this game.  Because I think too much, and it's a drinking game.  But the whole concept of the game is fascinating.  There's a total of 5 dice per player (so with 5 players, you start with 25), only 5 of which you know.  You have to guess with strictly increasing bets how many dice there are with a certain number or a one.  Therefore a bet of three threes means that you think that under all the cups, there are at least either three threes, three ones, or a pleasant combination of the two.  An average roll at the beginning of the game will net you about 8 each of two's and one's, three's and one's, four's and one's, etc.  But the whole idea is to use your dice in order to give yourself an advantage: there's a lot more chance for your five dice to roll abnormally than the other 20 to roll abnormally.

The betting system is thus: each subsequent bet must either increase the number of dice with a certain number OR increase the number on the dice but keep the same number of dice.  So if I say there are four threes, then a legal bet would be either five threes or four fours.  However, 2 threes is right out.

And he shall snuff it....

 After each bet, the next player can call bullshit, bologna, liar, scurvy dog, or some other appropriate (or inappropriate) phrase.  If he does not, then he must make a bet.  If bullshit is called, all dice are revealed.  The loser removes one of his/her die, and the game continues.

Ones are special.  The initial bet must halve the number of dice bet previously (rounding up).  After ones are started, there are two separate betting tracks, one for ones and one for everything else.  They do not affect each other.

Now the trick of the game, after playing several times, is to force an opponent to make a bet which is just completely awful and ludicrous.  This means that if I am holding five of one side in my cup, I'm betting high just so the betting doesn't make it all the way back to me.  It should go without saying that the more dice you have, the better advantage you have.

 The second trick is to recognize when someone has you beat and you need to analyze your options.  Picture this: there are three dice left.  Two fours are bet by your opponent.  You're looking at a three in your cup.  There are a couple bets you might consider.

1.  Bullshit.  Think about your opponent.  The probability that they have two fours (or two ones, or some combination) under their cup is 1/9.  This is not as simple as it seems.  The probability of rolling "doubles" is 17/36, or just under 1/2.  Does your opponent seem like the lying type?  If so you're in luck.  Does he seem like the play it safe type?  Well then maybe you want to choose another option.

2. Three fours.  You're only putting your opponent into a pickle if he actually *has* two fours.  I hope you're a good liar if you choose this one.

3. Three threes.  You already know there's one.  So of the two unknowns, both have to be threes.  1/9 probability of winning.

4.  One one.  Either there's a one on his first die or a one on the second.  1/6+1/6.  1/3.

Here, bullshit might be your best option, depending on who you're playing.  A lot of times when I'm starting out rounds with 10 or fewer dice I just spout out "One [insert random number here]."  Second best option is clearly one one.

Now the challenge here is to be able to do this in your head.  While drinking.  Do it.

Make your friends some of these so they are placated while you think.

March Madness

I have a strange fascination with statistics and probability.  As such, rather than completely filling out a bracket randomly, or just going by seed, I decided that the best option was to roll dice.  I figure that a good goal will be to get 50% of the games correct.  This might be a project for next year where I do several hundred brackets to find an average winning percentage and a standard deviation.

In short, I've created a chart.  If the seed of the opponents are within 2 (a 3 seed vs a 5 seed, etc), then each has a half of a chance of winning.  Between 3 and 5 seeds apart, the lower seed will win on a 7+ roll of two dice (best two of three).  6-8 is 6+ (best two of three), 9-10 is 5+ (BTOT), 11-12 is 4+ (BTOT), 13-14 is 3+ (BTOT).  There is zero probability for a 16 seed to beat a 1 seed.

So I rolled up a bracket.  UCONN should win.  So sayeth the dice gods.  If I were less lazy I'd find the probabilities for you and make a nice graph to post to find probabilities of seeds winning games.

In other news, I will never get tired of CSI Miami's one liners.

OMG!

OMG I have a Blog!