HG for no zero?

[ati]

So in theory you are right, but that applies if you have unlimited bankroll and table limits. Otherwise the last bet that your stop loss/bank roll allows, will always be negative and won't converge toward zero.

I know from experience  As I posted a couple days ago, I played at least 200K no zero real money spins with progressions and my losses were kept increasing. I've lost tens of thousands of units.

[Bigbroben]

It applies to any stoploss, table limit or Wingoal.

If you played 200k spins and ended in negative territory, it is due to variance.  Trends can be astonishingly long.

I'll explain in two different manners:

1)  If both chances of winning or losing are equal, in the long run, cal it the law of large nrs or whatever, this mathematically even chance will overcome variance and the sum of all results will tend towards zero.  So as said before, all 512u bets will even out, all 8u bets will even out...

2) Step by step.
Spin nr 1 with 1u.  50% chance of +1, 50% chance of -1.  Even out.
Spin nr 2 following a loss, with 2u. 50% chance of +2, 50% chance of -2.
                                                             75% chance (3/4) of +1, 25% (1/4) of -3.  Even out.
Spin nr 3 following a loss, with 4u. 50% chance of +4, 50% chance of -4
                                                             7/8 chance of +1, 1/8 chance of -7 (-1-2-4)  Even out.
Spin nr 4 following a loss, with 8u. 50% chance of +8, 50% chance of -8.
                                                             15/16 chance of +1, 1/16 chance of -15  (-1-2-4-8)
So on.


Running a macro now to show results after 10 million spins.               

[Bigbroben]

So,

10 million spins later.

See the result of 10k runs of 1000 spins, playing Martingale without zero, stopping at 64u.

The score varies but tends towards zero, the edge even more direction zero.

[ati]

Thanks for the charts. So it's fair to say that in the extreme long term your expected result can be break even, but you might lose more than you win in the next couple million spins. If I understand correctly and the left chart shows the full 10 million spins.

[Bigbroben]

Yes.