Statistics and Probability (part 4)

Probability and Statistics (Part 4)

By Madison Nef

Random Walks 

To take a random walk is to do things based off of random occurrences- but to put it in a way everyone can understand, a random walk (literally speaking) would be taking a coin and starting at point zero. Let’s say that for every time you flip a head, you have to go one block North and for every tail you flip, you have to go a block South. THIS is a random walk- typically. However, a simple graph with points on it can turn a random walk into just about anything- monetary, distance, even measurements.

 What is the probability of returning to the point of origin?

When you take a random walk, there is a chance that all 100 times you flip that you will just walk back and forth in one set direction. MOST times you do inevitably return to the point of origin, but it is possible not to.

 Starting at 1 and going back to 0 (the origin point) has a probability of 50%. However, if you make negative progress and go to 2 instead of 0, the probability of getting 2 tails in a row is a probability of 1… even though it is possible you WON'T return to 1. This is known in statistics as “the infinity problem”.

 What's the probability of going 100 blocks away in one direction when flipping a coin?

There is SOME non-zero probability of getting 100 heads in a row, but a more likely way is to get 100 blocks away in one direction by alternating back and forth through blocks by flipping the coin for an infinite amount of times. Since you are flipping for infinity, there are an infinite number of chances for rare occurrences such as flipping 100 heads in a row, OR infinitely returning to your starting point (zero).

 Gambler's Ruin

You start off in a casino with $2,000. You're betting, and each bet is a $200 bet. It has completely fair odds.  Flip a coin- if it lands on heads, you gain $200 more. If it lands on tails, you lose $200. Since it's a fair game, you have equal odds of winning and losing and going back and forth. However, with this probability… you will always go broke eventually. The point is to see how far you can go before you go broke; and that is the gambler's ruin. Remember, this is set in a FAIR casino where the casino doesn't get a cut of the money.

If even Gambler’s Ruin, which takes place in a FAIR casino has you going broke… how can you expect to make any profit from an UNFAIR casino in real life? Yes, every once in awhile someone gets lucky and wins… but often times, that same “lucky” person then overstays their welcome and attempts to bet again and loses everything. Life lesson to be learned from this lecture? DON’T GAMBLE. It’s stupid, addictive, and a waste of time. The odds are truly against you, no matter where you go; so just don’t bother.

The only thing gambling is good for is showing how dumbed down society has become and how statistics and probability come into play in real life circumstances… and that is all.