Sorry this may be a newbie question, but I'm not a quant or statician. I've read that you need to have an edge in the markets so over time you will end up on top, similar to how casinos end up winning over the long run. But I've also read that the trade you place now is independent of the past trades you have made. For example, let's take roulette. Since casinos have the edge, it's better to place the majority of your money on the first spin because the outcome is more random. Statistically speaking, the longer you play, the more you'll lose, correct? And every spin is independent of the one before regardless of it being a winner or loser. My newbie question is, how come you can't treat every spin you make like it was your first spin? Since its the spin is statistically independent of one another. I understand the concept of casinos having an edge a little, but this question has been bugging me. Thanks guys for all your help.
OK, try to explain..... say roulette: (only 1 zero, 36 numbers) If you place a straight-up bet you will end with 36 chips (your bet + 35 payout) The table however has 37 numbers (36 + 0) which gives the casino the statistical edge on every spin. (2.7%) If you apply this to playing red / black, you will find the same. So in the long run, the casino's edge will increase (1.027^n) On your first spin you have the best (less negative) edge, but still a disadvantage to the house (casino)
When I was young I spent many hours trying to come up with an system for craps. I did not believe the quants. This went on for quite awhile. Along the way I learned a lot about probabilities and finally understood that you cannot add up minuses and come up with a plus. You might try to design a system for roulette. This is a good exercise.
If the mathematical expection (ME) or the edge is negative, don't bet. If need to bet, bet it all in one trade. You will at least have some chance of winning. However, if you let the number of trades go to "infinite", your chance of winning is zero. By the same token, if the ME is positive, let the number of trades go to infinite to ensure a win. Divide up the portfolio into many small trades and, hopefully, trade on different markets and instruments that are not correlated. You are now the casino. When you go to casino, you are gambling with the house. However, the house is not gambling with you. The house is doing business knowing that, with a positive ME and a large number of small bets, the house is ensured a win.
Which is why almost all casinos have a limit on the size of the bet- they want many small, average sized bets that they are sure to win on.
The casino's edge at roulette will increase the longer you play? You mean, like, that little white ball knows how many time it's been used against any and all players who've come to the table? That's a pretty impressive piece of carved bone. I think that the casino's "edge" on the first spin of the wheel, and the edge on the one billionth spin is exactly the same, and entirely independent of every other spin.
And, doesn't that mean, that for every dollar bet, in the long run, your win/loss will more closely approximate expected value? So, while you may have a higher variance in outcomes on the first spin, that variance cuts both ways, you could win 35 chips, or lose 1. Odds are, at the end of 36 one-chip bets, you will be a net 2.71% of your aggregate bet loser. I just don't want the poster mislead. If he wants to bet his life savings on one securities trade, then more power to him. But, if he loses, he needs to realize that he will lose it all.
Quote from kjkent1: And, doesn't that mean, that for every dollar bet, in the long run, your win/loss will more closely approximate expected value? No, the only thing that the law of large numbers tells you is that the variance around this theoretical mean is proportional to the variance of one outcome divided by the square root of the number of outcomes. The more you try, the lesser the variance. So, while you may have a higher variance in outcomes on the first spin, that variance cuts both ways, you could win 35 chips, or lose 1. Odds are, at the end of 36 one-chip bets, you will be a net 2.71% of your aggregate bet loser. Again, the mean is always the only value you'll never see ;-) Here the game is a game of large variance (+3500% or -100%). Kelly optimal bet would tell the casino not to risk more than 0.7% of its capital on any spin. If the casino is undercapitalized, it won't be able to accept very large bets. The same applies for you. You can reduce your variance, but you can't obtain a positive expectation. I just don't want the poster mislead. If he wants to bet his life savings on one securities trade, then more power to him. But, if he loses, he needs to realize that he will lose it all. I have a single piece of advice for people like that : don't trade...