There are no real tricks by which you can earn more money by gambling but there are few tricks by using which you can minimize your losses in the gambling. Don't try to win big money in one go for example if you have $ 1000 dollar then don't play with all money in a single session. You can have multiple games or sessions by splitting these $1000 into $200 small games. These increases your winning chances and at least you can recover whatever you are spending.
There is logic in splitting the chances in multiple games instead of one big shot, it is a mathematical relation.
Yeah I remember covering this a couple years back with doog. It's actually pretty logical that reducing bet size reduces potential losses in terms of probability.
Yes.
And you're the first person who responded in such an open manner.
Everyone else just tells me I'm wrong.
The trick is to split up your bet (the amount you were going to risk in a single bet) into a series of amounts which sum to a the same, and which form a sequence such that you can bet the smallest amount, and if it wins, you make the same as if you bet the whole amount at 49.5% (so you'll be betting with a smaller chance, and higher payout multiplier). And if it loses, you want betting the 2nd amount to cover the first loss and make the same net profit. Etc.
If you can find such a sequence (and you always can, though it can involve some hairy math depending on the length of the sequence you're looking for) then the amount you expect to risk is less than your whole amount (since there's a non-zero chance that you will win before the last bet, and stop at that point), and so the amount you expect to lose, being 1% of the amount you risk, is less than when you make the single bet.
Here's a very simple example:
you have 1 BTC and want to double it.
* you could bet it all at 49.5%, and succeed in doubling up with probability 0.495
* or you could bet 0.41421356 BTC at 28.99642866% with payout multiplier 3.41421356x, and if you lose, bet the rest at the same chance. If you win either bet, you double up, else you lose. Your chance of doubling up is 0.4958492857 - a little higher than the 0.495 you have with the single bet.
Cool, huh?
That's breaking the single bet up into a sequence of length 2.
If you break it up into more, smaller bets, then the probability of success increases further.
The more steps, the closer to 0.5 your probability of success gets.
You'll be limited by real-life barriers, like the
invisibility indivisibility of the satoshi, and the limit of 4 decimal places on the chance at JD. But in theory you can get arbitrarily close to 0.5. I think.
And some quick maths (plus graphing)
I cannot believe I'm saying this but I think you might be right.
I went ahead and played around with a case where the player starts at 1 wants to move to 2 by making two bets (of any size between 0-1 inclusive). Hence I went to go graph the function to see if it was true and I got this:
https://www.desmos.com/calculator/obkfifgbnlWhere y = probability of succeeding
and d = the value of the first initial bet
Notice how at both d = 0 and d= 1 the probability is 0.495 as expected (as you are either betting nothing then 1 or 1 then nothing and both are equivalent cases). And in between you get a probability higher than the 0.495 offered for the single bet.
I've tried a few set values for cases where you split your value up to more than two and you do get a better result. I can only theorise that this is because as your bet size approaches 0 with the number of bets approaching infinity your expectation approaches 1.
However, what I do not understand at the present is why this is so. I almost fell out of my chair when the numbers came out (I checked like 6 times), as it's inferring that you can get better than what the house 'technically' offers. The problem with this is that your expectation is better than just flat betting and logically that doesn't make sense. Both should have the same expectation.
I'm going to mull it over.
I haven't given it a lot of thought beyond this - doog explained it quite elegantly.
When you bet your whole bankroll in a single bet, you expect to lose 1% of it.
When you split it up and bet the pieces in order from smallest to biggest, and stop when any bet wins you often don't end up betting the whole bankroll, and so you expect to lose 1% of less than the whole bankroll.
By splitting it up you reduce the amount you expect to bet, and so you reduce the amount you expect to lose.
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