Let's assume you have a bankroll of 100 bitcoin.
Lets up our base bet to 7 satoshi. That makes bet #30 cost 37.58xxx bitcoin. What the hell are the odds of losing a 50/50 bet 30 times?
Let’s do the math. You roll and the chance to lose is 50% (Given house edge your odds are slightly worse than what I am about to illustrate).
So one loss is .5 (50%). Losing a second time is only a 25% chance (.5 * .5 = .25), a 1 in 4 chance (to find that, divide 1 by the decimal, .25). Losing a 3rd time in a row is 1 in 8... .5 * .5 * .5 = .125. So to figure out the odds for losing 30x in a row:
.5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 = .000000000931, which is, as a percentage (multiply by 100 to get the percentage) .0000000931% chance. And to see that in more easy to understand numbers, the chance of missing a 50/50 bet 30 times in a row is a 1 in 1,073,741,824 chance. One in a billion. One in a BILLION chance of losing 30 times in a row. The price you pay for those odds is winning 7 satoshi on a bet. As I write this, 7 satoshi is valued at 1.58 thousandths of a US penny. So you would need to win 632 times to earn a penny. And you are risking 75 bitcoin, $17,000, to do so (your total losses if you miss 30 rolls in a row).
So, you start betting. Each time you bet, if you win, you net 7 satoshi. If you lose, you keep doubling until you win, and you win 7 satoshi. Keep in mind you're risking 75 bitcoin if you lose. But, what are the chances, it's 1 in a BILLION odds, right?
So you win and win and win, and a few hours later, you're up... what? 9 cents?
You have 75 bitcoin on the line, impossible to lose at 1 in a billion odds. And if you HAVE 75 bitcoin to risk, I'm going to assume you'd like to get more than a few pennies for your time. So let’s say your goal is 5 bitcoin. About 15% of your risk. So let’s run some numbers... you're not getting 7 satoshi per BET, you're getting it per WIN, so it's not 5 divided by .00000007. It's actually somewhere about double that, given the losses that 'waste' bets. The actual math behind that, I'll get into in a moment. But for now, suffice it to say that 10,000 bets nets you about .000335 bitcoin. So to get one whole bitcoin, that would take about 29,771,000 rolls. 29,771,000 / 2 * 7 satoshi = 1.041 bitcoin.
So, therefore, to earn 5 bitcoin, you'd need to make 148,855,000 rolls.
Of those 144.9 million rolls, you have about 74.45 million "cycles". A cycle is you drop the die, and you either win, or you roll until you do win. And that's simple to show: 74.45 million times 7 satoshi is 5.20975 Bitcoin, our target winnings. Make sense? Each individual ROLL does not have a 1 in a billion shot of missing 30 times - that's impossible, a single roll cannot miss 30 times. A cycle of rolls can, a single roll series as an attempt to win can. So we're going to use the number of "wins" or cycles.
1 in a billion odds. What are the chances? When you attempt 74.45 million cycles, or wins, the odds of hitting that 1 in a billion are 1 in 14.42 odds. How? You divide your 74.45 million rolls into your 1 in a billion odds. It comes out to 14.42something. You roll bets for over a week, risking 75 bitcoin to win 5, and reduce your 1 in a billion odds to
1 in 15 roughly. That is one hell of a time commitment to risk 75 bitcoin to win just 5!
What if we wanted to say screw wasting so much time and bets. Pull up the betting screen. Put in 75 BTC for a bet, and set the % chance to win to 93.412%. Your winnings would be 5.209125 BTC, DAMN close to the 5.20975 we were hoping to win. So we hit roll, and we either win, or lose.
What are the chances of winning at 93.412%? Well that’s simple. 100% - 93.412% = 6.588% we have a 93.412% chance to win 5, and a 6.588% chance to lose 75 bitcoin.
Let’s turn 6.588% into a decimal... we divide by 100. That’s .06588. Anyone want to take a guess as to what 1 divided by .06588 is?
1 / .06588 is 15.17.
Wait. What? If I bet 75 bitcoin at 93.412% odds (1 in 15ish) I can win 5.2 bitcoin - or I can bet 7 satoshi, martingale, doubling, risking a possible loss of 75 bitcoin at a 1 in 14.42 odds? Isn't that funny how math works out?
Your odds are actually better to make the single roll.
With such amounts of Bitcoins it's much better to invest in casino bankroll. 75 BTCs ~ $150.000,00. Possible to make good percentages of profit every week, maybe 0.3%-1% (most common), what means $450-$1500. No martingale, no effort making thousands or millions of bets to earn 7 satoshis per bet... The risk you take by playing on long term doesn't worth the return you can receive.