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

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Some people think that these probabilities change, once a string of TTTT has occurred. This is the Gambler's Fallacy.

The probability to get an H after a HHHH string is the same probability as the probability to get an H after a TTTT string. The coin does not have a memory, or otherwise put, the coin tosses are non-correlated or stochastically independent.

Last edited by Fat Tails; April 1st, 2011 at 08:05 PM.

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This thread reminds me of a remark made to me by a trading mentor. I had personal knowledge of his trading success, and he used several different indicators including a form of linear regression.

At the time he was trading a 5 minute SP chart, with no over night data. So using a 10 period linear regression indicator it was obvious if there was a big gap the indicator was very wrong the first 10 bars.

I wrote him and explained how the indicator was wrong and shouldn't be used in the first 10 bars if there was a gap. I'll never forget his answer.

It was, "If I understand all you do about this indicator, I might not use it to help me make money, but I don't understand what you are talking about, so I use it, and it does help me make money." This is a real trader talking.

So to me while the discussion about the advanced math and gaming theory is interesting, to me, wanting to improve my trading, it is really irrelevant.

Pete

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If what everyone said is true then for the past 3 years I have been the theoretical and statistical anomaly that keeps statisticians up at night… And I am ok with that.

I actually have more to say, however it is pizza and movie night with the family.

And just for the record I am not giving up or giving back the 135 dollars I won 3 months ago at the Grand Victoria casino using the before mentioned technique, no matter what the theory says!

Again, no one is disputing the probability of a given singular event, we're discussing STRINGs of events. The probability of strings is a different consideration.

You can calculate the probability of a string of events. That is the concept at work here.

The law or large numbers says that the probability of a 4 series sample is just as much H-T-H-T as it is H-H-T-T,

but where the theory falls short is when you DON'T have an infinite sampling. When you have a finite sampling, you observe strings of events. It's those strings that allow a progressive strategy to be beneficial.

The idea is to take advantage of enough events that strings are relevant, but not enough that they become irrelevant (if that makes sense).

I fully concede that this strategy becomes more prolific with card games, because the prob of a win in blackjack increases with every loss...thus they are not mutually exclusive.

The theory becomes particularly relevant in examining probabilities that aren't even. A 70% win ratio for instance will yield a significant number of positive strings. If you utilize a progressive strategy along positive strings, the yield is MORE. It's simple math.

However, as I've pointed out in other threads, in order for the theory to be effective, you need to have a fairly resolute/continuous instrument. Futures contracts for example, are relatively discrete. A CL contract with it's marginal reserve will NOT allow you to "rollover" profit amounts like stocks. (i.e. you can't increase your "wager" with a futures contract like you can with stocks....because of the marginal reserve).

The other part is that the strategy must incorporate a similar profit/loss ratio. If you're strategy incorporates a 50/50 ratio, and you're anything above 50%, then string theory and progressive wagering INCREASES your rake.

For example, in a 100 trade sampling, at 70%, you'd expect the string distribution to look something like this....

Losing Series:

1 - 18
2 - 3
3 - 2

That means that you have an 18/23 (78%) probability of a winning trade after a losing trade. Losing series progressive strategies aren't as effective, because you have to have additional capital in reserve in order to take advantage (i.e. you'd have been better off simply risking your reserve over all trades).

However, as I said, with stocks, where you can rollover your profits more resolutely, winning string progressive strategies will help.

A 4 string winning series for example, will yield .25, .3125, .3906, .488 and .22 (for the last loss) for a total of 1.66 units of profit. That same series when only using the same starting positionsize will end up making 1.5 units (for 4 wins followed by a loss). It simply helps to ensure that you have increasing profits without risking ALL of your past profits on every subsequent trade. The phenomenon is even MORE pronounced when you use 100/100 ratios.

Furthermore, a progressive strategy for wins (and a reduction to the original positionsize for losers) helps to ensure that losing strings are minimized.

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For the fair coin example, strings or the number of prior samples is irrelevent as the outcome is not serially dependent on history. Its a straight forward binomial tree.

In cards, that is different. Each card drawn changes the probabilities moving forward. If an ace is drawn, there are no longer four aces in the deck.

In slots, that is different. I'm no expert on gaming regs but the slots are required by law to return x over n runs.

So the string thing only works if the future outcome in contingent on prior outcomes.

Progressive betting on the future outcomes is then a seperate issue.

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What is the probability of rolling a pair of dice 154 times continuously at a craps table, without throwing a seven?

The answer is roughly 1 in 1.56 trillion, and on May 23, Patricia Demauro, a New Jersey grandmother, beat those odds at Atlantic City's Borgata Hotel Casino and Spa. Demauro's 154-roll lucky streak, which lasted four hours and 18 minutes, broke the world records for the longest craps roll and the most successive dice rolls without "sevening out."

I'm just a simple man trading a simple plan.

My daddy always said, "Every day above ground is a good day!"

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Either events are correlated. In this case you can use strings to define conditional probabilities and execute progressive betting strategies can be used. They betting strategies will not become irrelevant with a high number of samples.

Or the events are independent, as is the case with throwing dice. In this case progressive betting is entirely useless.

This is the whole point. If the outcome of the event n (loss) has an impact on the outcome of the event (n+1), progressive betting makes sense. For black jack there is a negative correlation, as a loss increases the probability to win. Note that statistical analysis has been done on the ES, to find out, whether an up move is more likely to be followed by another up move (positive) correlation or a down move (negative correlation). The correlations that were found for ES were so small and unstable that they did not allow to compensate for transaction cost.

Again, no. The point is not, whether a probability is even or uneven, but how much that probability is affected by positive or negative auto-correlation.

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There is an even bigger problem with all this stuff, and that is the fact that the markets are moved, not by all this stuff, but by people who react to stuff with emotions.

Look at how markets react around reports, or some news crisis. On many occasions, the markets take off in one direction and then immediately come back. Then there is gunning for stops. What experienced trader isn't aware of this.

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You say there is gunning for stops. Yes, of course it is. This is the truth of trading. Now, if you are gunning for stops, all you need to find out, where these stops are located. Once they have been triggered the market is free to reverse.

I even believe that this stop triggering is part of the hygiene of a reversal. How can the market reverse from short to long, if the new longs have not be stopped out? Trading is a zero-sum game, where you simply exploit the behavior of other traders, so you need to have an idea of what they are doing and how to trap them.

Emotions are creating feedbacks. This changes the market movement from random to trending (positive correlation) or counter trending (negative correlation). Once the market is not random any more, it becomes tradeable. Progressive betting can be introduced, if the correlation is known.

Chart attached: Assumed Stops detected by indicator

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