Kelly Can't Fail

If you start out with a $1e12 stake, you're able to avoid catastrophic rounding errors even in the worst case. There's probably a life lesson here.

Is the lesson: choose to be born to wealthy parents?

Or is it to choose appropriate betting amounts based on your capacity for risk

IEEE-754 isn't precise enough for my capacity :( I too need rich parents.

I guess it then does follow that having rich parents does expand your capacity for risk!

My simulation shows that with a 52 card deck, if you round the bet to the nearest $.01 you will need to start with $35,522.08 to win a total of $293,601.28.

If you start with $35,522.07 or less, you will lose it all after 26 incorrect cards.

The lesson I'm taking away is "learn math and how to use it."

Nearest rounding does seem like a mistake here. Rounding down is quite safe: rather than lose it all, you end up with at least 2^26 pennies.

Learn math and discover poignantly all the situations where it is effectively useless.

It’s easier to make money if you already habe money

Applying math to a more practical betting situation, like poker, is a lot harder. You'd have to be able to calculate your exact odds of winning given only a small amount of information, without a calculator and without it taking so long that the other players notice, and then also factor in the odds that the other players are bluffing and the advantages that you might have from (not) bluffing.

Or is it to choose appropriate betting amounts based on your parents?

It would really help if your parents know someone who can and will take the other side in this game.

A popular view is that having wealthy parents gives one a great advantage. Another popular view is that working extraordinarily hard for money is a waste of one’s life even if one gets the money. But the two are only consistent if one believes that one’s own life is the optimization target. If I live a life of misery so that my children live a life of prosperity that would strike me as a phenomenal result.

So another reading is “choose to give your children wealthy parents”.

This is a truism

This sounds similar to the Martingale system.

https://en.wikipedia.org/wiki/Martingale_(betting_system)

Practically if you live life fearing a 26 red cards event something like e-15, you'd never leave the house and leave your money under your bed

Are you sure about those numbers? I get that the smallest fraction of original stake we hit is around 1.35E-7:

          ⊢min←⌊⌿ratio←×⍀{1-d×0⍪¯1↓(+⍀d←¯1+2×⍵)÷⌽⍳≢⍵}52↑26⍴1
    1.353223554704754E¯7

In which case we need to start with $73,897.62

          ⌈÷min
    7389762

For a total payout of $671,088.64

          ⌊(⌈÷min)×⊃⌽ratio
    67108864

Thanks for getting me to actually check this!

Note: above code is Dyalog APL.

I cannot decipher the runes you write, but your magic looks to be more powerful than mine so you are probably right. (i.e., my Python script may have errors; it was pretty hacked together)

When Poland first introduced the capital gains tax in 2002, banks were quick to notice the tax law still generally required tax amounts to be rounded to nearest full złoty when accrued, so they started offering financial products with daily capitalization, which were effectively exempt from the new capital gains tax, as for most customers, the daily gain would be low enough that the tax on it always rounded down to zero. This only got corrected 10 years later.

I find it fascinating that we could have a whole class of financial products hinging on something seemingly so trivial as a rounding strategy.