6 ms·
Note that you need to be able to infinitely divide your stake for this to work out for you all the time. For example, if the deck has 26 red cards on top, you'
by pcthrowaway 2y ago
Note that you need to be able to infinitely divide your stake for this to work out for you all the time.
For example, if the deck has 26 red cards on top, you'd end up dwindling your initial $1.00 stake to 0.000000134 before riding it back up to 9.08
- jmount 2y agoVery good point. I did some experiments and the system is very sensitive to any sort of quantization or rounding of bets. You get the expected value about the right place, but the variance goes up quickly. So in addition to your important case, things are a bit dicey in general.
- boothby 2y agoIf 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.
- fragmede 2y agoIs the lesson: choose to be born to wealthy parents?
- darkerside 2y agoOr is it to choose appropriate betting amounts based on your capacity for risk
- Onavo 2y agoIEEE-754 isn't precise enough for my capacity :( I too need rich parents.
- laidoffamazon 2y agoI guess it then does follow that having rich parents does expand your capacity for risk!
- darkerside 2y agoThis is a truism
- User23 2y agoThe lesson I'm taking away is "learn math and how to use it."
- barrenko 2y agoLearn math and discover poignantly all the situations where it is effectively useless.
- paulluuk 2y agoApplying 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.
- Etheryte 2y agoOr is it to choose appropriate betting amounts based on your parents?
- croes 2y agoIt’s easier to make money if you already habe money
- mannykannot 2y agoIt would really help if your parents know someone who can and will take the other side in this game.
- renewiltord 2y agoA 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”.
- Rastonbury 2y agoPractically 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
- cbsks 2y agoMy 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.
- deleted 2y ago[deleted]
- boothby 2y agoNearest 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.
- xelxebar 2y agoAre 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.
- cbsks 2y agoI 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)
- xelxebar 2y agoFor anyone interested, here's a more pedagogical breakdown of the code: ⊢cards←52↑26⍴1 ⍝ We encode a red-black sequence in a bitfield 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⊢rem←⌽⍳≢cards ⍝ Remaining card count after corresponding play 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 ⊢sgn←¯1+2×cards ⍝ Contribution to re-black delta 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ⊢del←+⍀sgn ⍝ Delta between count of red vs. black cards 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 ⊢rat←0⍪¯1↓del÷rem ⍝ Our ratio is r-b delta as fraction of remaining cards after play 0 0.01960784314 0.04 0.0612244898 0.08333333333 0.1063829787 0.1304347826 0.1555555556 0.1818181818 0.2093023256 0.2380952381 0.2682926829 0.3 0.3333333333 0.3684210526 0.4054054054 0.4444444444 0.4857142857 0.5294117647 0.5757575758 0.625 0.6774193548 0.7333333333 0.7931034483 0.8571428571 0.9259259259 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ⊢pay←1-sgn×rat ⍝ Payout ratio: sgn×rat is negative on win and positive on loss 1 0.9803921569 0.96 0.9387755102 0.9166666667 0.8936170213 0.8695652174 0.8444444444 0.8181818182 0.7906976744 0.7619047619 0.7317073171 0.7 0.6666666667 0.6315789474 0.5945945946 0.5555555556 0.5142857143 0.4705882353 0.4242424242 0.375 0.3225806452 0.2666666667 0.2068965517 0.1428571429 0.07407407407 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ⊢tot←×⍀pay ⍝ Total stake is product scan over individual payout ratios 1 0.9803921569 0.9411764706 0.8835534214 0.8099239696 0.7237618452 0.6293581262 0.5314579733 0.4348292508 0.3438184774 0.2619569352 0.1916758062 0.1341730644 0.08944870957 0.05649392183 0.03359098055 0.01866165586 0.009597423014 0.00451643436 0.001916063062 0.0007185236481 0.000231781822 0.00006180848586 0.00001278796259 0.000001826851799 1.353223555E¯7 2.706447109E¯7 5.412894219E¯7 0.000001082578844 0.000002165157688 0.000004330315375 0.00000866063075 0.0000173212615 0.000034642523 0.000069285046 0.000138570092 0.000277140184 0.000554280368 0.001108560736 0.002217121472 0.004434242944 0.008868485888 0.01773697178 0.03547394355 0.0709478871 0.1418957742 0.2837915484 0.5675830968 1.135166194 2.270332387 4.540664775 9.081329549 ⊢min←⌊⌿rat ⍝ Minimum stake 1.353223554704754E¯7 ⊢start←⌈÷min ⍝ Minimum starting amount is ceil of inverse min stake 7389762 ⊢fin←⊃⌽tot ⍝ Final stake is last element of totals 9.081329549 ⌊fin×start ⍝ Gross winnings are floor of start times final stake ratio 67108864
- lawlessone 2y agoThis sounds similar to the Martingale system. https://en.wikipedia.org/wiki/Martingale_(betting_system) https://en.wikipedia.org/wiki/Martingale_(betting_system)
- deleted 2y ago[deleted]
- TeMPOraL 2y agoWhen 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.
- deleted 2y ago[deleted]
- kamaal 2y ago>>Note that you need to be able to infinitely divide your stake for this to work out for you all the time. This is what most people discover, you need to play like every toss of the coin(i.e tosses over a very long periods of time). In series, like the whole strategy for it to work as is. You can't miss a toss. If you do you basically are missing out on either series of profitable tosses, or that one toss where you make a good return. If you draw the price vs time chart, like a renko chart you pretty much see a how any chart for any instrument would look. Here is the catch. In the real world stock/crypto/forex trading scenario that means you basically have to take nearly trade. Other wise the strategy doesn't work as good. The deal about tossing coins to conduct this experiment is you don't change the coin during the experiment. You don't skip tosses, you don't change anything at all. While you are trading all this means- You can't change the stock that you are trading(Else you would be missing those phases where the instruments perform well, and will likely keep landing into situations with other instruments where its performing bad), you can't miss trades, and of course you have to keep at these for very long periods of time to work. Needless to say this is not for insanely consistent. Doing this day after day can also be draining on your mental and physical health, where there is money there is stress. You can't do this for long basically.
- auc 2y agoIf you assume coin tosses are independent, it shouldn’t matter if you miss coin tosses.
- kamaal 2y agoCoin tosses are not independent. Unless the premise is coins toss themselves. A person tosses a coin, so tosses are are connected to each other. Ask yourself this question- Would your thumb hurt if you toss a coin 5000 times? If so, would that change the results?
- PaulHoule 2y agoNaturally tossed coins tend to land on the same side they started with 0.51 of the time, see https://www.stat.berkeley.edu/~aldous/157/Papers/diaconis_coinbias.pdf https://www.stat.berkeley.edu/~aldous/157/Papers/diaconis_co...
- tgma 2y agoYup, the dual would be saying Martingale can't fail with infinite money.
- aidenn0 2y agoIt's not because there is a finite amount of money at which this can't fail, which is never the case for martingale. Martingale is actually likely to bankrupt you against a casino that is much more well staked than you even if you have a small advantage.
- ab_goat 2y agoFinally a real world use case for bitcoin!
- amanda99 2y agoBitcoin isn't infinitely divisible, you can't do smaller than one satoshi.
- nyeah 2y agoIt's a good point. I think it affects the realism of the model. When the stake is very low, finding a penny on the street gives an astronomical improvement in the end results. At the high end, it's possible the counterparty might run out of money.
- jmount 2y agoI've added a follow-up note on the case of discrete stakes here: https://win-vector.com/2024/12/21/kelly-betting-with-discrete-stakes/ https://win-vector.com/2024/12/21/kelly-betting-with-discret... . It is known there is a dynamic programming strategy that guarantees a return of $8.08 on a $1 bet. Simple rounding of the Kelly strategy does not achieve this.