Probability & The Bet (My Answer)

Here is my answer, there are no right or wrong answers. My answer is steered towards how I would make this intelligent bet with Mr Market(The Stranger).

1) A stranger walked up to me and say that he has a fair coin in his hand. Which means that the probability of flipping the coin to get either heads or tails is 50%. The stranger said that he will flip the coin 20 times and wants me to guess what is the result of the 20th flip. There were no tricks involved during flipping, no foul play seen.

After the 19th flip, the result was 19 heads and 0 tail. He asked me to guess the result of the next flip. What is the probability of getting either heads or tails on the 20th flip?

What is your answer and your reasoning?

Mr Market walked up to me and said that he has a fair coin. Imagine the process of flipping up to the 19th flip. After 5 flips, 5 Heads. I thought to myself, the odds of 5 Heads in a row is around 3%(0.5^5) since there is an equal chance of getting heads or tails. After 10 flips, 10 Heads(something must be wrong, my alertness increases). After the 19th flip, 19 Heads and 0 Tail(he must be kidding me!). Either this coin is biased(Mr Market lied to me that this coin is fair) or the odds of this probability happening is very rare! We live in not a perfect world, people lie, cheat, steal etc. The market is a brutal place.

My opinion would be that this coin is biased, more weight is placed at the side of tails so it always lands on tails and show heads on top. Since it is a biased coin, 99%(what if Mr Market do magic trick?) the next flip would be Heads.

Let us go back to purely numbers and data that this is indeed a fair coin(Mr Market is not lying). The flip is independent and probability is non-accumulative or you can say that there is no conditional probability attached. The next flip either heads or tails is 50%, is correct. Doesn't matter if it is 10 Heads in a row or 1 Billion heads in a row.

If you said that the probability of Tails occurring at the 20th flip is very high(eg. >50%). You are wrong. Past data of the flip cannot predict accurately the outcome of the next flip. It just shows you that a rare event just happened, which is consecutive 19 Heads in a row.

If you think carefully, there are a lot of lessons that we could apply in the market.

2) The bet. The stranger said that if you want to bet, every $1 bet will give returns of 200%. If you lose, you lose all. Your R/R is 1:2. How many % of capital would you bet on this 20th flip to get optimal R/R returns, based on your probability answer given above?

I would use Kelly's formula(odds/edge) to bet. It is used to determine the optimal size of a series of bet when the odds are in your favor, in the long run. You are right no matter which case you choose because you do not know whether Mr Market is lying or not. Assuming 10k capital.

Case 1(not lying): 50% Head, 50% Tails, R/R 1:2

Your Odds:
(0.5 x 2) + (0.5 x -1) = 0.5

Odds/Edge:
0.5 / 2(divide by max win) = 25%

Bet 2.5K either heads or tails is the same.

Case 2(lying): 99% Head, 1% Tails, R/R 1:2

(0.99 x 2) + (0.01 x -1) = 1.97

1.97 / 2 = 98.5%

Bet 9.85K on heads.

However if I were to bet, I don't want to put 9.85k. I'm a conservative guy and don't want to risk almost all the money(call me a turtle gambler).

I bet on Heads by combining both scenarios adjusting probability to 100%:

(0.25 x 2) + (0.25 x -1) + (0.495 x 2) + (0.005 x -1) = 1.235

1.235 / 2 = 61.75%

Since I'm a turtle gambler and a value investor, with a 50% margin of safety, I would bet 3K(30%) of capital on Heads.

Kelly's formula also shows you how much confidence you have in the bet. In this case, my confidence level is 61.75%. If you think that the coin is fair, your confidence level would be 25%. In the stock market, most would bet if their confidence level is more than 70-80%. So if you said that you don't want to bet, you are right too. Like I said, there are no right or wrong answers, only bet with money that you can afford to lose.

Probability & The Bet

Came up with this very lame question because I'm very bored haha... Posted it in Huatopedia forums and decided to post this Quiz/Question for my readers too! Hopefully we can learn from each other. If you could spend some time to think this through, you will learn something in the process. Good Luck!

1) A stranger walked up to me and say that he have a fair coin in his hand. Which means that the probability of flipping the coin to get either heads or tails is 50%. The stranger said that he will flip the coin 20 times and wants me to guess what is the result of the 20th flip. There were no tricks involved during flipping, no foul play seen.

After the 19th flip, the result was 19 heads and 0 tail. He asked me to guess the result of the next flip. What is the probability of getting either heads or tails on the 20th flip?

What is your answer and your reasoning?

2) The bet. The stranger said that if you want to bet, every $1 bet will give returns of 200%. If you lose, you lose all. Your R/R is 1:2. How many % of capital would you bet on this 20th flip to get optimal R/R returns, based on your probability answer given above?

Ps: R/R is Risk/Reward.

I will give my opinion in the next posting. =D

Edit: Spotted the mistake. The rest are correct. $1 bet will reward you $2, so total you will have $3. Sorry for the mistake.

Update about myself

This week has been a hectic week. School work is starting to pile up with lots of materials to read. There have been some problems in school, which I feel is insignificant and not worth mentioning.

I have been monitoring the markets more and reading economic data extensively to get a general feel of the market, this has caused me to have insufficient sleep for the past 1 month. Made a few good buys and sells which I will not reveal now. Wait for end of the year to see my new portfolio allocation. :)

I have realised that there are so many things to do in life and I need to refocus. All these experiences costs money and the 2.5K salary that I'm going to bring home in the future is not going to get me anywhere. Anyway, I'm not in this profession for the money. I need to find ways to earn more, so that I can afford to spend more. I reiterate the word "afford" again, a prudent investor needs to spend within his means.

The compounding effect of money is simply too powerful to ignore. Having a capital of 100k and compounding it at 20% per year can be easily an average person's annual salary. If I can compound it 20% consistently for 5 years, I would have easily 248K. To the average person, it is a significant amount. To the one who has made it, it is just merely numbers.

I have stopped trading forex on paper months ago because there is not enough time to monitor while I'm in school. However I still believe that over time, I will be profitable. If anyone wants to pick up trading, forex is the way to go. Tough, brutal, challenging and it takes lots of discipline to control emotions. I don't like the idea of having rollover fees if I were to keep my trade the next day. Pitting your skills against the market is tough enough and yet as a retail trader, one has to pit their skills against the brokerage too. There are many wide swings and false breakouts to lookout for.

I need to refocus on what is important to me. Over the years, I've narrowed down and filtered out those that are not and kept those that are very important to me. I'm glad that time has made me realise this.

My focus now would be school work, trading/investments and the occasional drinks with my best pals. Life just keeps getting better. :D

Anyway

Was at a hospital attachment and found this meaningful quote. Found online that it is a quote from Mother Theresa edited from Kent Keith's quote. Pardon my lousy photo taking skills, I will upload it anyway. =D

Forex 16/03/09 to 20/03/09

Japan bank holiday today and currencies didn't move much, decided to close for the week. It is always better to under-trade than over-trade. Two of the trades did not move how I imagined it to be, the price action was acting weird, so I closed out the positions. The other trade was a big bang, holding it for 3 days.

Total No. of Trades = 3
Accuracy = 2/3= 66.7%
Win-Loss ($) = 44.12-0.06= 44.06
Average Win ($) = 22.06
Average Loss ($) = 0.06
Max Win($) = 43.62
Max Loss($) = 0.06
Pips = 442
Capital left(Using $500 fake money, $) = 483.87

Thinking back, computing performance is much easier with just a few trades. Why make my life so difficult trading so many positions? =D

Walking in the dark and found light

The past 2 weeks of trading forex was an eye opener. I was walking in the dark and now found light again. Here are some of the lessons.

1) There is no perfect system, if you are looking for the "holy grail", there is none. You might find answers when you look into the mirror.

2) Price action is king, indicators are just guides, does not mean that they are not useful. Train your naked eye to look at price actions, you dont need a trend line to tell you where the trend is.

3) Patience, patience, patience- Yes! A trader needs lots of patience, he needs to wait for the big move, the signal, when most factors/probabilities are with him.

4) Trading doesnt mean more activity. When it gets too exciting, you are walking on the wrong path. It should be boring and dull. Trading more is actually bad.

5) Anything less than H4 chart is just noise. Know how to differentiate between signals and noise.

6) Let your profits ride, cut your losses fast. Money management is crucial, you can lose 7 out of 10 times and still make money.

7) Look out for sharks in support/resistance levels, round numbers like 100 or 500, psychological levels like Dow 7000 level. Sharks will trigger your stop loss at these levels, making false break outs or break downs. When they have cleared the amateurs out, they will continue on their buying or selling where there is less competition.

8) Be the predator and not the prey.

9) Keep a ear of news on the ground. When looking at retracements, is it a normal reaction or an abnormal one?

10) Do not trade when crucial news is going to be released. Wait for the release and see how it goes before you take the position.

Forex 02/03/09 - 06/03/09 (Still walking in the dark like last week)

Total No. of Trades = 20
Accuracy = 5/20= 25%
Win-Loss ($) = 2.61/45.62= -43.01
Average Win ($) = 0.52
Average Loss ($) = 3.04
Max Win($) = 1.4
Max Loss($) = 13.82
Pips = -351

Here is where I found enlightenment. Learning how to fish with dream's help. Many thanks.
http://triple-screentrading.blogspot.com/

And here, Feb2865 the pro trader. http://www.forexfactory.com/showthread.php?t=54528

Forex 09/03/09 - 13/03/09 (After I learnt the lessons from above. Still need to cut down on the number of trades)
Total No. of Trades = 14
Accuracy = 9/14= 64.3%
Win-Loss ($) = 17.86-12.04= 5.82
Average Win ($) = 1.98
Average Loss ($) = 2.41
Max Win($) = 8.85
Max Loss($) = 4.40
Pips = 74
Capital left(Using $500 fake money, $) = 439.81

Forex 23/02/08 to 27/02/08

The week was very volatile. Some of the currency pairs were trading at weekly or monthly resistance and support lines. This is one thing which I must take note and incorporate into the system. Another issue that breeds the lousy performance is my risk management skill. Many times I was in 50-100 pips profits and then it turned it's back on me. I need to take profits when I can and maybe trade 2 lots and cash out on one and let it run.

Here are the week's result.

Total No. of Trades = 121
Accuracy = 43/121=35.5%
Win/Loss ($) = 135.92/158.92= 0.86
Average Win ($) = 3.16
Average Loss ($) = 2.04
Max Win($) = 15.27
Max Loss($) = 5.2
Pips = -259
Gains/Losses ($) = -23
Capital left(Using $500 fake money, $) = 477