⭐ Merited by eternalgloom (2)
A big LOL to this one. For the others, long as you have a big bankroll, you can make profit. That's it. Just have an infinitely big bankroll 
Now that I am thinking about it, I wonder if there's a casino with the biggest possible wager that would allow to maximize such a Martingale strategy? I know 999dice has 40 BTC max profit so that's 40 BTC on a x2 martingale which means you could go for a 36-streak martingale on x2 payout, starting at 1 satoshi and 36th bet at 34.36 BTC.
I suppose you could go all day autobet. Chances of hitting a losing streak 36 times in a row is 1 in 34 billion or something because of house edge.
If you can do 100k bets a day = 50,000 satoshi profit average daily.
Chances then become that you bust 1 every 34,360 days, almost 100 years.
So if you only play for 1 year, you have a 1 in 100 chance of busting that. If you get away with this. you make BTC 0.1825
Worth risking 40 BTC?
First of, you need more than 40 BTC in your balance for using this strategy. To beat a losing streak of 36 times in a row with 1 satoshi as initial bet you need to have 2 to the power of 36 sats:
2^36 = 68,719,476,736
So, as you can see, it's 687 BTC which is much more than 40.
Secondly, although no less significantly, is wearing-out of your equipment working 24/7.
Although we can neglect the power consumption because it is $0.5 per day max for a laptop, I think no one would risk 687 BTC in order to earn 50k sats daily.
To prove how much you're going to be risking just to earn a small amount of money in martingaling, let's do the whole math to this:
(since the basebet = 1 satoshi, I didn't include it in the formula. The formula should have been, 1 satoshi x 2^0, 1 satoshi x 2^1, 1 satoshi x 2^2, and so on.)
Bet Number | Formula | Amount (satoshi) |
Bet 1 | 2^0 | 1 |
Bet 2 | 2^1 | 2 |
Bet 3 | 2^2 | 4 |
Bet 4 | 2^3 | 8 |
Bet 5 | 2^4 | 16 |
Bet 6 | 2^5 | 32 |
Bet 7 | 2^6 | 64 |
Bet 8 | 2^7 | 128 |
Bet 9 | 2^8 | 256 |
Bet 10 | 2^9 | 512 |
Bet 11 | 2^10 | 1024 |
Bet 12 | 2^11 | 2048 |
Bet 13 | 2^12 | 4096 |
Bet 14 | 2^13 | 8192 |
Bet 15 | 2^14 | 16384 |
Bet 16 | 2^15 | 32768 |
Bet 17 | 2^16 | 65536 |
Bet 18 | 2^17 | 131072 |
Bet 19 | 2^18 | 262144 |
Bet 20 | 2^19 | 524288 |
Bet 21 | 2^20 | 1048576 |
Bet 22 | 2^21 | 2097152 |
Bet 23 | 2^22 | 4194304 |
Bet 24 | 2^23 | 8388608 |
Bet 25 | 2^24 | 16777216 |
Bet 26 | 2^25 | 33554432 |
Bet 27 | 2^26 | 67108864 |
Bet 28 | 2^27 | 134217728 |
Bet 29 | 2^28 | 268435456 |
Bet 30 | 2^29 | 536870912 |
Bet 31 | 2^30 | 1073741824 |
Bet 32 | 2^31 | 2147483648 |
Bet 33 | 2^32 | 4294967296 |
Bet 34 | 2^33 | 8589934592 |
Bet 35 | 2^34 | 17179869184 |
Bet 36 | 2^35 | 34359738368 |
Bet 37 | 2^36 | 68719476736 |
The total is exactly 137,438,953,471 satoshis (~1,374.39BTC) to recover from 36 loss streak. As I'm typing this, the value of that is $9,438,000. It seems like you can do a lot more with that amount of money and someone who's in possession of that amount of money can surely afford a private mentor or tutor which can teach him where to use the money either invest in business or simply becoming a better spender so he doesn't lose that amount of money over purchases that aren't so practical.
As you can see, we came up with these huge numbers because the growth in your bet in martingale method is exponential. At first, it doesn't seem much. But as the losing streak is increasing, your bet just to earn back your losses and that additional 1 satoshi "profit" is becoming more and more ridiculous. Gambling sites are known to have tremendous number for losing streaks in x2 multiplier and it's the reason why martingale never really worked in the long run.
To put an end to your desire of using the technique martingale, think about this. 50k sats per day is 0.0005BTC per day which is $3.43. Is $9,438,000 worth risking for $3.43 a day?
And since the people who wants to gamble with a "mathematical formula" likes to treat gambling as a business, you're obviously a bad business man.