How advanced mathematics and gaming theory can help you as a trader

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This applet simulates a gambler who repeatedly bets $10, until he either loses by going broke, or wins by doubling his initial fortune (Init).

The applet accepts the following keyboard inputs. (You may need to "click" on the applet first.)

Use the numbers '0' through '9' to set the animation speed level higher or lower.

Use 'r' to restart the simulation, or 'z' to zero the Win/Loss counts.

Use '>' and '<' to increase/decrease the win probability of each bet. (Possible values include 0.492929 [the probability of winning at craps] and 0.473684 [the probability of winning at roulette] plus various other values like 0.333333, 0.4, 0.45, 0.49, 0.495, 0.499, 0.4999, and 0.5.)

Use '+' and '-' to increase/decrease the initial fortune by $10 (and restart). Or, use 'T' or 'H' or 'G' or 'F' to set the initial fortune to $10 or $100 or $1000 or $5000, respectively.

Use 'A' to jump to $10 ahead of bankruptcy, or 'B' to jump to $10 behind victory.

The following 2 users say Thank You to jungian for this post:

"The primary thing required to obtain what you want from life, is simply the will to pursue it, and the faith to believe it is possible." - Author Unknown

"The ability to maintain discipline and stick to the rules is the hallmark of the experienced successful trader" - Curtis Faith

The following 2 users say Thank You to PositiveDeviant for this post:

Maybe this those have some merit to a degree. I live about 30 min. from Oklahoma so this last weekend me and the wife decide to take a small drive over to Oklahoma to check out the Wyns Casino. I don't know how to play any cards game such as blackjack or texas hold em. Slot machines are a waste in my opinion so my game of choice was roulette. My game plan was to watch all the numbers that had come up recently so I wrote down the #'s that had come up more than once . Then what I did I wrote numbers that had not come up at all. Then Ipaired numbers together. All this while the wheel kept on spinning and new numbers would come up. When I had up to six pairs of numbers I was ready to begin. I placed my wagers up to 5 chips covering pairs of #s that had been hot and the ones that were cold. At first I won three wagers at once and was like this works but then a string of losses came up that almost took me out. Just when I was about to lose all my money I had strings of wins again that put me where I started. In a span of three hours I played with the same money I began while I saw people come and lose everything. My plan was simple but changing constantly oh and I had no alcohol in me either. At the end of the night I ended up flat...which is better than losing. So my probabilties on that night were at 50/50

If you play roulette, you have a negative expectancy. Your probabilities were less than 50/50. You simply did not play long enough to lose all your money.

In roulette there is no such thing as hot or cold numbers. Consecutive wheels runs are independent from each other, so the result of any run does not depend on the previous run.

Writing down numbers is a futile endeavor, as the outcome of the current run does not depend on previous runs. For further information check the "Gambler's Fallacy".

I don't know I played for about 3 hours straight with the same money. I have done this technique before in vegas and it worked for me their as well until I started drinking....lol. Im not saying that your going to beat the system but in my experience your odds at winning do get better.

I've heard that Craps is the only percentage based casino game where you can alter the odds in your favor.

It stems from having physical control over the die while throwing them. Gamblers have practiced rolling with a specific number on each die facing upwards and another facing either right or left.

Casinos must be wise to the method if it has really worked well for some.

I pasted at the end of this post an Excel analysis of DAG data created based on real time publicly published signals and results from a popular candlestick trading system.

I've calculated the Optimum f bet size using that data.

Let's say one has 100K capital.

The DAG optimum f% under that system when buying is 22.92%, for a bet size of $22,920.

Historically, the largest buy loss is -9.4% and 9.4% of $22,920 optimum f bet size is $2,154, or 2.154% of the assumed 100K equity.

Adjusting the max optimum f% loss of 2.154%/$22,920 = 1%/x makes the bet size $10,640

A 9.4% loss on $10,640 is $1000.16, or 1% of the 100K equity

Note that the max 1% drawdown limitation cut the bet sizing by more than half for both the long and short side signals.

A max drawdown bet size limitation is a real benefit when trading multiple asset classes simultaneously.

Using this kind of limitation and adding systems and instruments can get one closer to what Vince describes in his recent Leveraged Trading Space.

Good luck!

DAG AGRICULTURE DOUBLE LONG ETN KELLY ANALYSISAGA is the 2X inverse but has no volume DYY is another double long commodities ETF

# Trades58#Wins#Losses# BUYS34# Buy Wins26#Buy Losses8Total Buy Gain437Av BUY Gain0.079629015Av BUY Loss-0.034470462Largest Buy Loss-9.400%Long BUY Winning Probability (W)0.764705882Long BUY Win/Loss Ratio ("R")2.310065194Long (BUY) Only Kelly %0.662849832Arithmetic Expected Return1.531226325Optimal f22.92%Opt f x Largest Loss as % of acct value-2%1% Portfolio Loss Opt f x Largest Loss Limit Bet Size10.64%Variance in Holding Period Returns0.008609919Standard Deviation Actual HPR's (no stop)0.092789648Multiplicative Growth Function (sq rt A2-S2)1.528412294TWR15324290.13# SELLS38# SELL WINS23# SELL LOSSES11AV SELL GAIN5.879%AV SELL LOSS-4.294%LARGEST SELL LOSS-15.080%Short (Sell) Winning Proability (W)0.605263158Short (Sell) Win/Loss Ratio ("R"1.369Short(Sell) Only Kelly %31.6955%Arithmetic Expected Return43.40%Optimal f15%Opt f x Maximum loss as % of acct value-2.32%1% Portfolio Loss Opt f x Largest Loss Limit Bet Size6.63%Variance in Holding Period Returns0.005242327Standard Deviation Actual HPR's (no stop)7%Multiplicative Growth Function (sq rt A2-S2)43%TWR6.81462E-13

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(Average Profit * Probability of Winning) (Average Loss * Probability of Losing)
Average Risk amount (or Average Loss)

So your expectancy in your example is always 0.2, regardless of bet size.
Expectancy is a measure of your trading system, it is based on Win Rate and Reward:Risk ratio, nothing else. It has nothing to do with bet size or position size percent.

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