The Omnivangelist

camisuke 10 July 2008 essays/articles, strategy, videogames One Comment

In the first two installments of the General Video Game Strategy we discussed the limitations and nature of the challenges and difficulty presented to the player in video games, and some techniques in exploiting these limitations. In this third installment, we will look at how to some more abstract philosophical approaches to decision making and strategy.

Making decisions in life can be difficult. We need some rules of thumb. I have two in fact (both rules of thumb, and thumbs).

The first rule of thumb is actually from a legendary poker champion Puggy Pearson. Puggy said,

“There ain’t only three things to gambling. Knowing the 60/40 end of a proposition, money management, and knowing yourself.”

And if you translate that into investing, knowing the 60/40 end of a proposition means knowing when you have some competitive advantage over somebody else. And you don’t bet, you don’t gamble, you don’t invest, unless you have some competitive advantage.

Second, money management means well, okay, if I’ve got a competitive advantage, how much do I invest? Do I invest 10 percent? 20 percent? 50 percent? Three percent? So knowing the proper money-management strategy, the proper amount of money to invest is the second thing.

And then knowing yourself, that means knowing how you react to stress, how you react to adverse outcomes, how you react when things go well. Do you get giddy and overconfident when things are going well? Do you get morose and difficult when things go badly? Do you make bad decisions at both extremes? Just understanding your own psychology, what your weaknesses and strengths may be, as it comes down to evaluating decisions when the markets are at extremes.

Bill Miller, in an interview detailed his rule of thumb of how much to risk in any wager:

The rough formula, in a grossly oversimplified form just for the purposes of discussion, is:

2p - 1

where p is the probability [converted from percentage to decimal form]. So, to make it easy, if you were 100% certain that a particular investment would pay off at your expected rate, then 2 times that p is 2.0, minus 1, yields 1. That means 100% of your bankroll should go into that investment.

Now if you were only 60% sure, then it would be two times .60, which is 1.20, minus 1, equals .20. So 20% of your bankroll should go into that proposition. It also shows that if you have less than a 50/50 proposition, you shouldn’t bet at all. Which again, makes perfect sense.

Well, what [the Kelly] equation says is the same thing Puggy Pearson says, which is you have to know the 60/40 end of the proposition. You have to be confident that you have an edge, that you have some positive probability of an expected positive gain, before you commit any amount of money. And if you can’t identify that edge, you probably don’t have it. And if you can’t identify it, you probably shouldn’t commit the capital to it. (CNN Money)

This rule of thumb or decision making won’t help you necessarily in every game, but it can help you in games like poker, or games that require strategy like Culdcept Saga (XBOX 360). One global rule of thumb this equation does tell us is, when the odds are 50/50, you do not engage the enemy. Only engage the enemy when you have an advantage. You may have heard something like this from a ninja movie. Ninjas flee when they do not have the advantage and return when they do.

Another rule of thumb I use for decision making and evaluating probability is from Warren Buffett. Buffett believes a deal is in his favour when,

Probability of success x money rewarded > Probability of failure x money lost (wagered)

(Note: Probability of failure = (1 - probability of success)

So as an example, if you have a 50% chance of turning $100,000 into $120,000, but if you lose the wager you lose 30k$, would you risk it?

0.5 x 20k$ >? 0.5 x 30k$

10k$ >? 15k$

Answer: No Way. 10k$ is not greater than 15k$. The odds aren’t in your favour. This equation appears to mimic the same one presented by Miller above. Millers will tell you exactly what you should wager however, where this one will simply tell you yes or no. But this equation is easier to remember and calculate on the fly sometimes.

This rule of thumb can also help you to know how to position yourself when wagering anything of quantity in any game. Applied creatively, it could be used to calculate whether paying 300 Gold pieces is worth the extra 10 points of defense that that chain mail armour in the weapons smith shop will provide you.

Another area I’d like to discuss in general gaming theory is human emotions. I recently drew some conclusions on this issue while reading a paper on economics: Prospect Theory: An analysis of Decision Under Risk.

The paper deals with human decisions with regards to options regarding money, particularly decisions where respondents had to choose between two outcomes, one being certain, and another with a finite probability.

The paper was a landmark in the understanding of human behavior because it
pointed out the tawdry little lie at the heart of classical economic models about human behaviour, namely that people weigh risks with perfect information and then make rational decisions. What Khaneman and Tversky showed is that people make two kinds of
decisions with respect to risk and reward, and that neither decision is
rational.

One the reward side, investors tend to overweight certain
outcomes, choosing lower returns with higher probabilities over higher
returns with lower probabilities. Or, in layman’s terms, most investors
prefer the appearance of certain, predictable, single-digit returns from
blue chip stocks or bonds than the higher but lower probability returns
from say, small cap stocks or emerging market bonds.

That investors would over-weight outcomes that are considered certain
isn’t that surprising. It suggests that capital preservation is
psychologically (and financially) more important to investors, than
capital growth.

What’s really shocking from Kahneman and Tversky’s paper is how investors
approach losses. And the conclusion is inescapable: investors seek it. Or,
as the paper puts it, “This analysis suggests that a person who has not
made peace with his losses is likely to accept gambles that would be
unacceptable to him otherwise. The well known observation that the
tendency to bet on long shots increases in the course of the betting day
provides some support for the hypothesis that a failure to adapt to losses
or to attain an expected gain induces risk seeking.

The study concludes that humans are very poor investment machines(from investing money to investing in game strategy). Humans invariably choose investments with low returns that have a high probability of success over investments with a high rate of return with moderate probability of success (People are conservative when they have something to lose). Basically, individuals were tending away from the favourable outcomes of the equations presented above.

The study also showed however, that when individuals had already lost money, they were willing to risk money on investments with low probability of success that had high returns (People engage in risky behaviour after suffering a loss). It showed that human emotions tend toward safety and precaution when money is in hand, and risky behaviour when money was out of hand.

The ultimate conclusion is that humans tend to be poor investors both in good circumstances and bad circumstances - a computer program would be a better investor.

This ties into what Puggy said about “knowing yourself” and your emotions.

Not only can you apply these techniques to yourself to help you make better decisions in situations in video games with certain odds, but you can leverage the irrationality of other players when competing in versus mode gameplay.

For example, I was recently battling in Wartech with a friend, and we commented on our strategy for a best of 3 set of battles. His strategy was to not use his special skills (boss mode) in the fight until late in the battle, in the later rounds. That way he’d have the advantage as I tended to use my boss attacks in rounds 1 and 2. My strategy however was to win the first 2 rounds of competition if possible. I know that when I have a 2-0 advantage (or even a 1-0 advantage) the opponent will be at a loss, and the above theory suggests that the player will tend toward more risk taking in his/her gameplay in order to recover the match. I can therefore take advantage of this risk-taking behaviour to my advantage.

This type of psychology won’t work against an AI opponent. In fact, you are usually at a disadvantage psychologically in all video games. At least be aware of this and put yourself in check when you notice yourself falling victim to this theory. Of course, in the end humans beat AI in video games because AI cannot adapt; but in terms of emotions computers have an advantage - they always correctly weigh the odds and make the optimal decision.

Bill Miller on Investing and Risk: http://money.cnn.com/2007/07/17/pf/miller_interview_full.moneymag/index.htm

Kahneman, Daniel. Tversky, Amos. Prospect Theory: An analysis of Decision Under Risk. Econometrica, March, 1979.