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van tharp's marble game

Discussion in 'Trading' started by Gordon Gekko, Jun 7, 2002.

1. Gordon Gekko

for those that have read van tharp's "trade your way to financial freedom", you may be familiar with a game he discusses:

40 people played the game 100 times
they had a 60% win rate
they started with \$1,000
they could bet as much or as little as they wanted each time
2 of the 40 made money

tharp said if they had bet a constant \$10, they would have ended up with about \$1,200 on average. the optimal bet, 20% of their new equity each time, would produce about \$7,490 on average.

my question is, how is the optimal bet determined? why 20%? why not 21%, 19%, or some other number?

thanks

3. chasinfla

I don't know about Tharp, but Ralph Vince wrote Portfolio Management Formulas, the definitive work on optimal bet size.

He explains the logic, derives the formulas, and provides spreadsheet and BASIC logic.

5. rpc

Chapter nine of "The Mathematics of Gambling" by Edward O. Thorp describes the Kelly system for optimal bet size. The formula is: p - (1 - p). From the above marble game the win rate is 0.6 = p which gives 0.6 - (1 - 0.6) = 0.6 - 0.4 = 0.2

I think that this is only applicable to the marble game where the marble representing the win and the one for a loss are each the same size. Tharp has marble games where he throws in marbles which represent various sizes of wins and losses.

6. mattjclark

I believe optimal betting is reached with this formula

WP- winning percentage (in decimal form)
RW- average return of winning bets
RL - average return of losing bets

Optimal %= (WP - ((1-WP)/(RW/RL))

if the average winning return equaled the average losing return the formula would look like this:

Optimal %= (.60 -((1-.60)/(1/1)) or 20%

if the average winning return equaled 20% and the average losing return equaled 10% the formula would look like this

Optimal %= (.60-((1-.60)/(.20/.10)) or 40%

7. darkhorse

Optimal bet size is dangerous and foolhardy because true risk can never be defined. I trade small enough so that even if some freak event hits me for ten times my planned risk I will be down but not out. The odds of that happening are super low but so what.

Would you play ever play Russian Roulette for a fat payoff?

No?

How about six thousand chambers? That would be about the same risk as dying in a car accident.

But whatever your answer, I doubt you would 'optimal F' the question. The real world requires that low odds are balanced out by gravity of outcome.

8. chasinfla

Well, that IS the downside of optimal F -- that you're always pushing the envelope on size. SO, when the bad day -- that many here seem to think will never come to them -- comes, you feel it. Big.

The idea of f was that if your largest loser wasn't exceeded, you couldn't blow up. And that is in your control.

9. darkhorse

Are you saying that you can quantify your risk 100%, that you can know in advance how big your biggest loser will be?

No way.

If you are only stating that risk control is a qualification of Optimal F, then Optimal F is still useless for trading, like an economic theory that does not match real world conditions.

Risk can be accepted but never truly quantified. We live with undefined risk every day.

10. chasinfla

I'm saying that you can control whether or not you exceed your previous largest loss.

I don't know what you mean by 'optimal f being a quantification of risk.' That's ambiguous. Optimal f is the optimal fixed fraction of your account that you should reivest as derived from a statistical analysis of your trading history. That is all it is.

I don't know about Taleb, but Dr. Niederhoffer continues to trade and to do so profitably.

We determine how much we are willing to lose on a given trade. We can control that the majority of the time.

#10     Jun 7, 2002
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