Golden profit percentage innumeracy corrections

After doing more thinking about the golden profit percentage, I realized I'd made some real bloomers in the post where I introduced this concept. At first I was going to try correcting the mistakes there, but soon realized I needed to devote a new post to the corrections, since they're fairly lengthy.

First, let's define five terms:

1. session ratio: this is the number of your winning sessions divided by the number of your losing sessions

2. golden ratio: this is when your session ratio is greater than or equal to 2

3. tgotl: this stands for total gain over total loss; it's the sum of all the money you've won in winning sessions divided by the sum of all the money you've lost in losing sessions

4. profit percentage: this is the percentage of all the money you've wagered which you've made back in profit

5. golden profit percentage: this is when your profit percentage is greater than or equal to some magic number; I don't yet know what this magic number is

There were three glaring examples of innumeracy on my part:

1. there's no numerical relationship between the golden ratio and the golden profit percentage

2. there's no numerical relationship between tgotl and the golden profit percentage

3. even given the faulty assumption that such relationships existed, the golden profit percentage I came up with was wrong

Let me address each of these examples of innumeracy in turn:

1. it's certainly possible to hit the golden ratio but be losing money hand over fist. If you only win a tiny amount every time you win, but lose a very large amount every time you lose, over time you'll steadily be losing money, and not realizing any profit. If there's no profit, by definition your profit percentage is 0. If your profit percentage is 0, it's certainly not golden.

2. you can have the same tgotl in vastly different circumstances. tgotl only cares about the ratio of your gains to your losses; it doesn't take into account the amount you've wagered. However, the amount you've wagered is of paramount importance in the calculation of your profit percentage. Thus there can be no numerical relationship between tgotl and profit percentage; thus there can be no numerical relationship between tgotl and the golden profit percentage.

3. when I came up with a golden profit percentage of 100, that was way too high. I was not taking the money wagered in losing sessions into consideration. Also, I was assuming that the money wagered in winning sessions was the starting stack amount. Finally, I was assuming that the profit earned in winning sessions was the starting stack amount. So many faulty assumptions! And yet, even assuming all these assumptions were correct, I still came up with the wrong number! Here's the mental formula which led to the percentage of 100:

profit / amount_wagered * 100 = (2 * starting_stack_amount) / (2 * starting_stack_amount) * 100 =
1 * 100 = 100

Here's the "correct" formula:

profit / amount_wagered * 100 = (2 * starting_stack_amount) / (3 * starting_stack_amount) * 100 =
(2 / 3) * 100 = 66.66

I got the denominator wrong, as you can see. Here's an explanation of the formula:

Since I'm in golden ratio territory, we only need three representative sessions to calculate my profit percentage. One session is a loss, and the other two are wins. The amount wagered for each of the three sessions is the starting stack amount. Therefore the total amount wagered is three times the starting stack amount. The losing session has no profit. The two winning sessions each have a profit equal to the starting stack amount. Therefore the total profit for the three sessions is two times the starting stack amount.

What I now need to do now is calculate my actual profit percentage, and then pick a magic number out of a hat for the golden profit percentage. Funnily enough, 66.66 seems like a pretty good choice! Once I've done the calculation, I'll report back (in a future post).