A useful mathematical formula, taken from work on probability theory applied to gambling is the Kelly Optimisation Model. Investing is not the same as gambling, you make your own odds by doing research and exploiting the very inefficient market, however money management is helpful in both fields.
Warren Buffett, the famous American stock market investor who has amassed a fortune of many billions knows all about putting maximum money into high probability events. Peter Lynch also believes in this, and refers to the practice of buying big in the best stocks as "backing up the truck"
Without going into probability analysis, this might be a good place to introduce Kelly's formula. J.L. Kelly was a mathematician who studied the works of other mathematicians working on abstract problems in probability theory, Kelly realised that this work could have practical benefits at the blackjack table. It relates the maximum bet size that a gambler should make given the odds of success, this formula is most commonly used by professional gamblers.
The formula is 2p - 1 = x
Where p is the probability of success, x is the portion of your bankroll (or portfolio) that should be allocated to this bet. If an event has a 40% chance of paying off, don't bet. If a bet has a 55% chance of winning, only put in 10% of your money. If the chance of winning is 95%, invest 90% of your money.
A Kelly bet is the most aggressive bet you should ever take. Bets larger than Kelly are inefficient money management and will cause you to lose your money. The Kelly bet size does not ensure the highest probability of making a gain, it ensures the highest profitability for a set of games, or trades. It is also known as "tear your hair out" trading, as in practice they are actually quite big bets for many games and your equity curve will be extremely volatile.
As an alternative, if you are unsure about the probabilities you can adopt a more conservative stance, and that is to use a half Kelly bet. Gamblers use this all the time, and while it may hurt returns a bit if you have in fact gotten the probabilities right, the returns are parabolic and hence you aren't severely penalised. A Half kelly bet is simply to bet half the amount that the Kelly model suggests. Your chances of success are higher with a half-Kelly bet, but your profits will be lower. You won't become a zillionnaire as quickly, but your chances of getting there will be much greater.
Keep Kelly's formula in mind before you "back up the truck" on another speculative mining share. Apart from the use of this formula in money management, you should never look at investment as a gamble. Investing risk is directly related to the amount of work you do. A person that does regular research will have many high probability events to invest in over a lifetime. The gambling element only kicks in for people that are too lazy to do research.
Yup, so have fun calibrating your own odds and exploiting the pari-mutel system.(this line is written by me.haha.)
Parimutuel
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