Grab a coffee or tea and enjoy this read ☕️. If trading and thinking about games and strategies is something you like, you will love this!

A few weeks ago I found an interesting game idea, more or less relevant to trading and risk management in general.

Imagine we have 11 cards. You mix them up and pick one from the stak. If you get a yellow one, your balance is increased by 2x. If you get the blue one, the Devil Card, your balance will be multiplied by 1/2048. So basically a Margin Call. 💥 We start with $1M capital.

In the Devil's Card Game, the ONLY thing under our control is when we walk away.

Our hope is: we'll get to double our $1M a few times, and then walk away safely before the "devil" appears.

In the beginning, there are 11 cards on deck: 10 "double" cards and 1 "devil" card.

So, the chances of drawing a "double" are 10/11 = ~90.9%. Those are pretty good odds.

But as we draw more and more doubles, the odds of the next card being a double go down.

For example, suppose we draw 6 doubles.

Now, there are 5 remaining cards on deck: 4 "doubles" and 1 "devil".

The probability of drawing a "double" now is only 4/5 = 80%.

Still pretty good odds, but not as high as when we started the game.

One thing is clear:

If we ever draw the "devil", we know for sure that all *remaining* cards on deck are doubles -- as there's only 1 "devil".

So, *after* drawing the "devil", we should NOT walk away. We should stay for the full 11 draws, which will leave us with $500K.

So, that's our worst case: we walk away with $500K.

What's the best case? That's if we draw 10 straight doubles. Then, we'll take home $1M * (2^10) = $1.024B.

(After 10 straight doubles, we know for sure that the last remaining card is the "devil". So, we won't draw it.)

Lets have a look at the outcomes depending on the amount of good cards received before the "devil" card appears:

## Extending the Rules: We Decide the Bet Size!

Now, let's go a step closer to the real trading. Let's change the rules. Now we are able to decide our bet size on each card draw.

Then, there is an optimization trick called "__Backwards induction__". Fancy stuff for nerds. Here is a short summary:

With every new card, the probability to get the "devil" increases. Thus, we decrease the bet size.

In order to win the devil card game and to **end it no matter what with $170M outcome**, we start the first bet with 83% of our capital. The second bet with 81.84% etc

## Making Money 📈

Let's use this logic to make money with Forex. In order to come close to the "devil game" I select a strategy, which has a high win rate and a rather large loss (SL much larger than TP).

Using constant lot size, it would look like this:

the chart above shows a strategy, which has been optimized (__read about safe optimization__) to have high win rate. So it has many wins but from time to time there is a larger loss. I guess, you saw already quite a few of this kind around. We can also see that there is a time, where multiple devils (losses) vom quite close to each other. These are the moments, which kill the account if opeople apply martingale strategies.

Let's see how we can make good money from this strategy.

Similar to the solution to the Devils Game, we define following settings:

The max position size is 11x0.01=

**0.11 lots**- which is quite fair for a $1000 account I think.We decrease the positions by 10% after each win. Meaning that the first is

**0.11**, the second is 0.11*0.9=**0.10**, etc

## Conclusion

This is the mega-booster for all strategies, where you win often but sometimes a high drawdown may appear. I guess you know a few of them. So thank you, researchers who invented Backwards Induction for trading! 🙂 (Baum, a former IBM scientist and CTO of Renaissance Technologies).

The backwards induction for risk management is part of the not yet released __BFG 9000 EA__. I can't tell how excited I am about its release! 🚀 To see it in action soon __subscribe__ to the newsletter or to the __BFG9000 Telegram group__

Very interesting. Need re read it again.