Baccarat Shannon's Demon - making money out of thin air

Claude Shannon the father of information theory proposed an idea to make money out of thin air by exploiting randomness or "noise".

He is the inventor of Shannon Entropy, a measure of surprise, and the inventor of the binary digit that we call a bit as well as advancing computing and communications, data compression, the list goes on. The man was a genius.

Shannon also broke new ground with cutting edge scientific investment theory (and it's still cutting edge to this day) as well as gambling; both Shannon and Edward Thorpe collaborated together.

Shannon’s Demon is a simple idea. Let us assume you have two "assets", A and B be they stocks, bets, horses, whatever, the outcomes are random, unpredictable and could be decided by a coin flip, card flip, roulette wheel or dice. The expected return is mathematically zero, and in most cases negative due to commissions, vig, tax and so on.

Most investment focuses on looking for the signal in the noise, divining mystical patterns from the the leaves. Sounds familiar huh? Like bet selection and other voodoo people focus on.

Shannon proposed forgetting about the signal and instead making money from the unpredictable noise, basically making money out of thin air.

Being the first person to mathematically and scientifically define what a signal, noise and information actually is and which underpins all communications theory and systems, he knew what he was talking about.

Lets for arguments sake call the two "assets" A and B and the outcome is decided by flipping a fair coin, so 50/50 probability. It's not necessary to even know the probability but it helps when managing risk and will do for this example.

Shannon suggests that you should invest 50% of your balance in each of the assets A and B and after each decision, “re-balance to 50%”, that is we split the balance evenly to bet/invest on A and B in the next round.

So we are betting on the two games A and B decided by independent coin flips where we stand to get a return r with probability 50/50.

The return r means we may only risk r% of the entire allocation to avoid a quick risk of ruin. It may be 2% of the allocation on an even chance bet.

We will therefore have the following possible outcomes

The balance after round 1 for each game is either (1 + 0.5r) or (1−0.5r) with equal probability.

But, notice as the returns of two simultaneous games can net to zero, a new neutral state
has been added to the player’s space of outcomes. Our net gain or loss playing both games with our capital split between A and B will be +r, 0, -r.

After one round of playing the two games simultaneously, we obtain less extreme
outcomes, but we leave our win-loss ratio unchanged (with a 25% probability for
winning and losing, respectively, and a 50% probability of a neutral outcome). After
two rounds of two simultaneous games, our probability of being down has been
reduced to 43.75%, and we have a probability of 25% of breaking even, and 56.25% of being ahead while the expected value is still zero.

In the long term, the volatility reduction
translates into growth extracted from random noise.

The "assets" A and B can be both losing games, the only thing that matters is the games are independent and not correlated. If they are both random games of chance then by definition they will be uncorrelated.

For the die hard mathematicians there are a number of papers, a good one is
VOLATILITY HARVESTING: EXTRACTING
RETURN FROM RANDOMNESS by J. h. Witte

You will find many papers on volatilty harvesting and volatilty pumping as it is known in the literature, it's suddenly being recognised and researched due to lower trading costs and spreads than existed in Shannons time.

There is a fascinating book and historical account that covers this and more called Fortunes Formula by William Poundstone.

I hope this provokes some healthy discussion and moves the collective thinking into a new direction for attacking the game.

If one has sufficient bankroll to acces non-negotiable/dead chip programs with generous rebates, the margins are getting low enough that Shanons Demon may make returns from randomness a mathematical certainty.