Brain-training tasks related to trading in one way or another. Theorist, game theory, etc. - page 11

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How to mathematically estimate/compare (which is better) the profitability of the two transaction options.

X - Spread in pips

Z - size of win in pips

Z - size of loss in pips

Y - probability of winning

-------------------------------------------------------

With the actual other trade with different indicators. Probably need some sort of formula...

 
TVA_11:

How to mathematically estimate/compare (which is better) the profitability of the two transaction options.

X - Spread in pips

Z - size of win in pips

Z - size of loss in pips

Y - probability of winning

-------------------------------------------------------

With the actual other trade with different indicators. Probably need some kind of formula...

MO = (Z - X) * Y - (Zo + X) * (1 - Y). Which deal has a higher MO, and that one is more profitable.
 

Here's the thing.

Suppose we play eagle/dash.

We lose 2 and win 3. For the sake of simplicity, let's discard the spread.

3*0.5-2*0.5 = 0.5

Now we face the task what percentage of equity should be invested to maximize its growth.

Again, this is pure mathematics... how to calculate it I do not remember. Let's assume 25% - gives the maximum.

Next, we need to determine the average percentage capital growth per trade - this growth rate of %/growth / N - (transactions) will be the evaluation of the strategy.

How do you calculate it?

**************************************************************

Here's an example let it be MO=1 coin, not 0.5.

And the chance of winning is 1%. I'm sure the capital gain rate will be minimal.

 
TVA_11:

Here's the thing.

Suppose we play eagle/dash.

We lose 2 and win 3. For the sake of simplicity, let's discard the spread.

3*0.5-2*0.5 = 0.5

Now we face the task what percentage of equity should be invested to maximize its growth.

Again, this is pure mathematics... how to calculate it I do not remember. Let's assume 25% - gives the maximum.

Next, we need to determine the average percentage capital growth per trade - this growth rate of %/growth / N - (transactions) will be the evaluation of the strategy.

How do you calculate it?

**************************************************************

Here's an example let it be MO=1 coin, not 0.5.

And the chance of winning is 1%. Surely the rate of capital gains will be minimal.

For such purposes, there is the Kelly Jr. formula:

stake = ((b + 1) * p - 1) / b

Where:

stake is the rate as a percentage of the deposit

b - potential win in money / potential loss in money

p - probability of potential winning

 

((3+1)*0.5-1)/2=0.5 - 50%

Is this the correct solution for the Eagle/Reshku problem?

Thank you.

 
TVA_11:

((3+1)*0.5-1)/2=0.5 - 50%

Is this the correct solution for the Eagle/Reshku problem?

Thank you.

b - potential gain in money / potential loss in money = 3 / 2 = 1.5

((1.5 + 1) *0.5 - 1) / 1.5 = 0.16666666666666666666666666666667

 

Made a check in Excel

via solution search

maximum is reached at 28%

100 0,28 28 56
156 0,28 43,68 -43,68
112,32 0,28 31,4496 62,8992
175,2192 0,28 49,06138 -49,0614
126,1578 0,28 35,32419 70,64838
196,8062 0,28 55,10574 -55,1057
141,7005 0,28 39,67613 79,35226
221,0527 0,28 61,89476 -61,8948
159,158 0,28 44,56423 89,12846
248,2864 0,28 69,5202 -69,5202
178,7662 0,28 50,05454 100,1091
278,8753 0,28 78,08509 -78,0851
200,7902 0,28 56,22126 112,4425
313,2328 0,28 87,70517 -87,7052
225,5276 0,28 63,14772 126,2954
351,823 0,28 98,51045 -98,5104
253,3126 0,28 70,92752 141,855
395,1676 0,28 110,6469 -110,647
284,5207 0,28 79,66579 159,3316
443,8523 0,28 124,2786 -124,279
319,5736 0,28 89,48062 178,9612
498,5349 0,28 139,5898 -139,59
358,9451 0,28 100,5046 201,0093
559,9544 0,28 156,7872 -156,787
403,1671 0,28 112,8868 225,7736
628,9408 0,28 176,1034 -176,103

 
TVA_11:

Made a check in Excel

via solution search

maximum is reached at 28%

You've done the wrong check. Kelly is absolutely right. Correct simulation easily demonstrates this. The maximum is achieved at ~12-17%,. It's no use arguing with the classics, that's why they are classics.
 

TVA_11:


Made a check in Excel

via solution search

the maximum is reached at 28%.

You need to learn basic arithmetic first, so that you can use the formula to get the right result. You do not know how to do this yet, but you get into Excel and try to "disprove" an already proven and repeatedly tested and rechecked formula with some inarticulate nonsense.


In Excel, the check is very simple:

Column A is the share, column B is the increase in the deposit after two coin flips. The cursor is at the maximum value of column B. To make it clear how the calculations were performed, the value of cell B17 is shown at the top of the screen.


 

I will reveal the essence of Excel. It's simple and obvious.

100 0,28 28 56
156 0,28 43,68 -43,68
112,32 0,28 31,4496 62,8992
175,2192 0,28 49,06138 -49,0614

Depo*** interest **size **win or

******* of the deposit *** bet **size **win (size)

100*028=28 we won 2 coins. 2*28 = 56

the depo became 156

156*0.28=43.68 we lost 1 coin -43.68

depo became 112,32.

and so on. There is no mistake here.

*****************************************

The question is more about using the Kelly formula correctly.

Are we putting the right values in there?

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