Simulation Verification of Kelly Formula

Simulation Verification of Kelly Formula

Scene: a bet, you and the banker. You give 1 yuan, the dealer out 0.96 yuan. The number of bets can be doubled.

Based on the results of each of the dice of the single-pair decision-winning.

The winner is given a stake of $1.96.

Questions: how to bet to do, the least risk, the most profitable?

Answer: Kelly formula.

The role of Kelly formula: According to odds and win rate, you can draw the ratio of each money bet

Two forms of the formula:

　　　Formula: (expected rate of return)/(odds)
Formula: (profit probability × profit amount-loss probability x Losses)/(profit/losses)

　　　　Kelly's formula was originally established at T-Bell Laboratory physicist John Larry Kelly According to a colleague Claude Aire Shannon on the long distance telephone line of the institute. Kelly explains how Shannon's information theory applies to a gambler who has insider information to gamble on a horse. Gamblers want to decide the best bet amount, and his inside message does not need perfect (no noise), can let him have a useful advantage. Kelly's formula was subsequently applied to 21 points and the stock market by another Shannon colleague, Edward Sop.

The following uses the Kelly formula to simulate the game:

0. List the results of the Kelly formula in different winning percentages

Odds	0.96	0.96	0.96	0.96
Winning	0.5	0.6	0.7	0.75
Capital ratio	-0.02	0.183	0.388	0.49

1. Winning 0.5

From the above table, there is no play!!

The result of Kelly formula calculation is the mathematical expectation of profitability, it is not difficult to draw such a conclusion: all the profit rate of the mathematical expectations for the negative bet, absolutely can not participate!!

We see: Even if your winning percentage accounted for half (0.5), but because the odds are only 0.96, not 1 (that is, 1:1, meaning 1 lose 1), so your expectations are negative!!!

The odds are so low, is there any play in this game?

Only one way to improve the winning ratio!

2. Winning 0.6

Winning 0.6, which is 10 in 6

Consider three possible cases: 1) Four even loss and six even 2) deficit and Phase 3) six even in the four even deficit

3. Winning 0.7

Winning 0.7, which is 10 in 7

Consider three possible cases: 1) Three even loss and seven even 2) deficit and Phase 3) Seven even in the middle of a loss

4. Winning 0.75

Winning 0.75, which is 12 in 9

Consider three possible cases: 1) Three even loss and nine even 2) deficit and Phase 3) Nine even in the middle of a loss

5. Winning 0.75, do not use Kelly formula

Without using the Kelly formula, money management is confusing.

Like you have 1000,

Half of the first time: 500, not in.

The second time also cast 500, when you met a very bad situation, not yet.

You're out of position! You're out!

Of course, you would say, that I fill the position. That is a question beyond the topic of this article.

But one thing is certain: no matter how many times you fill a position, the result is the same.

Perhaps you will say, my luck is not so back, not the first two innings lose. I seriously agree with this!

But in the long run, there will always be bad luck to find you: four or five consecutive periods, take away your previous good luck gains, even doubled away.

Only Kelly formula can avoid this situation!!!

6. Conclusion

This article points out: Kelly formula to draw the ratio of funds is the ratio of each of your existing funds, not the initial capital ratio

It is not difficult to find that in the case of mathematical expectations, the use of Kelly formula for money management, can be stable profit.

Under the same winning percentage, no profit can be guaranteed without the use of the Kelly formula for money management.

I think one of the main reasons is: insufficient funds, out of position!

Simulation Verification of Kelly Formula