found a nice site: gambler’s ruin at wolfram

bottom line: terminal wealth in a fair game is ZERO for one of two players–which we already knew.

I’m a really terrible perfectionist. I’m basically a flake.

what characterizes the real perfectionists (and some other geniuses, successful people, etc.) is a fanatical precision. they get it right.

you can see this in wc3 players too. for instance, TH000 might be a futurist, but his play is messy (although getting better now). clean and crisp is what we desire. sky and moon in their heydays are the best examples.

even now you still see top humans mess up creeping… and people make fun of us for practicing against computers :x

Wiki link: Kelly criterion

In probability theory, the Kelly criterion, or Kelly strategy or Kelly formula, or Kelly bet, is a formula used to determine the optimal size of a series of bets.

f* = (bp – q) / b

where

f* is the fraction of the current bankroll to wager;
b is the net odds received on the wager (that is, odds are usually quoted as “b to 1″)
p is the probability of winning;
q is the probability of losing, which is 1 − p.

You might recognize the numerator , bp – q, as expected return for one ‘unit’. The ‘Kelly return’ for one bet is f* times (bp – q).

We see that according to the Kelly criterion, for bets giving the same expected return, we should prefer the one that gives the highest probability of winning–which we already knew.

See reasons to bet less than Kelly in the article. Also we should find out how things change if bets are correlated.

it’s acceptable to watch TH000 replays now, but still not for the general strategy. you can glean a bit of unit usage and tactical stuff from him and I guess army splitting falls under the strategic category.

do you know what it takes? do you have what it takes? you’re going to be competing with people who are more talented than you, smarter than you, ready to play 5+ hours a day. they’ve been waiting for this game for years, this is their dream. still up for it? either/or, you’ll regret both.

if you’re going to do it, you’ll need a plan. are you going to be the one who masses 10 hours a day? then you better play smart. let other people get a head start and find the strategies and then use what you learned from wc3. copy what’s winning, don’t waste time doing the same losing thing over and over. pay attention to details for a methodical improvement.