Quote from: hosseinimr93 on May 04, 2021, 04:23:40 PM

Quote from: icopress on May 04, 2021, 02:59:59 PM

Secondly, I believe that I did not take into account one of the important variables, given that in addition to the 47% chance there is also the value "HI" "Lo" and the fact that I did not use an auto rate.

Since the game is provably fair and numbers are determined 100% random, it doesn't really matter if you bet on HI or LO.

Quote from: icopress on May 04, 2021, 02:59:59 PM

I have no other explanation, because with the usual 47% chance there cannot be 10-15 losses in a row.

100 losses in a row is even possible.

By using the doubling strategy (it's also called as martingale strategy), you don't really increase your chance.

Let's say I have 1 BTC and I want to convert it to 2 BTC with HI-LO game.
If I put the whole 1 BTC in a single bet, I will have 47.5% chance of winning.

What if I put 1 mBTC instead of the whole 1 BTC? If I lose, I will double the bet amount. If I win, I will return to 1 mBTC.
Will I increase my chance?

No.
For converting the initial 1 BTC to 2 BTC, using this method, I need to win 1000 bets.
As my total balance is 1000 times my base bet, I can lose the bets up to 10 times in a row.

Let's calculate how much is the probability of winning the bets 1000 times without hitting 10 losses in a row.

(1 - 0.525¹⁰)¹⁰⁰⁰ = 0.203 = 20.3%

As calculated above, the chance has decreased to 20.3% from 47.5%

What if I set the base bet amount to 0.001 mBTC instead of 1 mBTC?
In this way, I can lose the bets up to 20 times in a row.

If I do this, I will decrease my chance even more.

(1 - 0.525²⁰)^1000000 = 0.079 = 7.9%

Someone may say that I don't want to double my initial balance. I will stop the game, when I make 10% profit.

Again it's not a good idea to use martingale strategy.
If I bet the whole balance and set the multiplier to 1.1, I will have more chance of winning.

You've explained it well, I only disagree with your last sentence. I think the chance of winning is absolutely the same either with martingale or betting with 1.1x multiplier. With this particular multiplier you have 10%+ chances of losing your whole balance right away, with the very first bet, even on a site with the smallest house edge.