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
>>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.
Coin 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?
>>I suppose you left out words here and there as a metaphorical proof of your claim that you can't miss a single toss, didn't you?
You must always practice in real world conditions. Notice in the experiments conducted in programs, you are taking series of tosses as they come, even if they are in thousands in numbers, one after the other, without missing a single one. Unless you can repeat this in a live scenario. This is not a very useful strategy.
Kelly criterion is for people who are planning to take large number of trades over a long period of time, hence the idea is to ensure failures are not fatal(this is what ensures you can play for long). As it turns out if you play for really long, even with a small edge, small wins/profits tend to add to something big.
If you remove all the math behind it, its just this. If you have a small edge to win in a game of bets, find how much you can bet such that you don't lose your capital. If you play this game for long, like really really long, you are likely to make big wins.
You are conflating 2 concepts: a) that the reality converges to what the theory predicts only after a great number of samples; b) that if you skip some events the results will vary.
Now, b) is false. You can change the code to extract 3 random numbers each time, discard the first 2 and only consider the third one, the results won't change.
Instead a) is generally true. In this case, the Kelly strategy is the best strategy to play a great number of repeated games. You could play some games with another strategy and win more money, but you'll find that you can't beat Kelly in the long term, ideally when the repetitions approach infinity.
>>Now, b) is false. You can change the code to extract 3 random numbers each time, discard the first 2 and only consider the third one, the results won't change.
Might be in theory. In practice, this is rarely true.
Take for example in trading. What happens(is about to happen), depends on what just happened. A stock could over bought/over sold, range bound, moving in a specific direction etc. This decides whats about to happen next. Reality is rarely ever random.
Im sure if you study a coin toss for example, you can find similar patterns, for eg- if you have tired thumb, Im pretty sure it effects the height of the toss, effecting results.
>>Instead a) is generally true. In this case, the Kelly strategy is the best strategy to play a great number of repeated games.
Indeed. But do make it a point to repeat exact sequences of events you practiced.
Naturally 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_co...
Linked paper does not state that; it states that tossed coins tend to be caught on the same side they stared with slightly more than half the time. The results explicitly exclude any bouncing (which will happen if a coin lands on a hard surface).
The paper does discuss coins allowed to land on a hard surface; it is clear that this will affect the randomness, but not clear if it increases or decreases randomness, and suggests further research is needed.