Brain-training tasks related to trading in one way or another. Theorist, game theory, etc.

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Betting system with non-negative expectation


Let there be two mutually exclusive events A and B with corresponding probabilities: p(A) = 1 - p(B).

Rules of the game: if a player bets on an event and this event falls out, his winnings are equal to the bet. If the event does not fall, his loss equals his bet.

Our player bets using the following system:

The first or any other odd bet is always on event A. All odd bets are always equal in size, e.g. 1 ruble.

The second or any other odd bet:

- If the previous odd bet is won, the next even bet is doubled and placed on event A
- If the previous odd bet is lost, the next odd bet is quadrupled and bet on event B

Prove that the given betting system has mathematical expectation more or equal 0 for any given probability p(A) = 0 ... 1.
 
Are you kidding me?
 
sanyooooook:
Are you kidding me?

No, I'm not. Checked: no mines.

 

There are mines, on the right side;)

Files:
sx_1.mq4  2 kb
 
Integer:

There are mines, on the right edge;)

There are no mines in my problem. You made a mistake in the TOR: you need if the odd bet is won, then the even bet is placed on event A. And in your code all odd bets are placed on A, and all even bets on B, which is inconsistent with the TOR.


But the code is not a mathematical proof, it is a PSGCP check. That is, if the code is consistent with the TOR and the probability 0.5 for any event with a large number of cycles is negative, then the PRGS can be thrown out to the trash.
 

There!

Files:
sx2.mq4  2 kb
 
Integer:

There!


Everything seems to be according to the ToR.

Have the mines been found?

 
Reshetov:

Everything seems to be according to the ToR.

Mines detected?


All on the plus side.)

 

in deficit frequently, up to -300 roubles. .... the loss even in roubles is large:)

 
sever30:

is often in deficit, up to -300 roubles. .... the loss even in roubles is large:)


And no one said that the betting system is risk-free. It is win-win according to MO, i.e. at p(A) != 0.5 the profit will tend to grow. But the variance can produce drawdowns.
 

Interesting question: Is it possible to maintain profits on the current position, with a reversal/false reversal and possible turbulence, with an amplitude of two times the current profit in pips, while remaining in the market and maintaining the ability to increase profits on the exit

Any techniques from locking, to volume manipulation

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