Quote from: Chris314 on January 14, 2018, 08:02:07 PM

Quote from: Don Pedro Dinero on January 14, 2018, 06:43:51 PM

Quote from: TheQuin on January 14, 2018, 11:36:51 AM

many players actually increase the house edge by using strategies like the martingale.

Could you expand on this?

I would be curious too to know why a martingale strategy increases house edge.

Because you go back to base bet after each win you end up increasing your average loss in proportion to your win. You can only ever win the base bet amount but often risk much larger amounts. There are ways to gamble that make winning less likely but none that can give a better expectation than the house edge.

I just spent ages on Google trying to find a decent mathematical example of this and without finding my old maths teacher I can't remember exactly how to demonstrate it myself. This roulette example is the best I could find:

https://en.wikipedia.org/wiki/Martingale_(betting_system)

Quote

In this example, the probability of losing the entire bankroll and being unable to continue the martingale is equal to the probability of 6 consecutive losses: (10/19)6 = 2.1256%. The probability of winning is equal to 1 minus the probability of losing 6 times: 1 − (10/19)6 = 97.8744%.

The expected amount won is (1 × 0.978744) = 0.978744.
The expected amount lost is (63 × 0.021256)= 1.339118.
Thus, the total expected value for each application of the betting system is (0.978744 − 1.339118) = −0.360374 .

Quote from: Chris314 on January 14, 2018, 05:53:05 PM

So you just play from time to time for fun with a reasonable bet compared to your balance, and thus manage not to lose too much satoshis there. That's it?
I've tried to use bonus they gave, but always ended up losing all, including the amount they took from my balance.

Pretty much, if you have a balance of 0.05 and try to win 0.0005 in a few dice bets you have a fair chance of coming out a winner. If you try to get 0.0005 up to 0.05 then most times you'll end up busting.
They changed the hi-lo bonus requirements a while back. The "The maximum wagering requirements that you can fulfil in a single bet cannot exceed 10% of the original amount of your bonus account." makes it much harder to come out on top now. But the reward points quickly add up especially on the weekend when it is 4 or 5 points for every 500 satoshis wagered. So you end up with getting past the 100,000 minimum quite quickly with a few big bets.

Edit:

I found a book extract that unfortunately doesn't give the full maths but the table is worth a look.

The house edges compared for various betting systems, note how martingale dramatically increases across the table with more rolls.