Help me understand probability

So I was on the qfit website where they have calculators used for the Casino Veritae (sp?) software (based on tables from blackjack attack I believe). So I was casually playing with the 'probability of reaching your goal based on a time constraint' calculator. I strted playing with some numbers worked out from other calculators, so explain this:

Say someone's ONLY goal was to make 5 units out of a starting 4 units, so basically 1 win.

ROR = 19.72%.

Say the number hands you play is only as many as it would take to lose all 4 units, so 4 hands. So the probability of reaching your goal before going bankrupt or reaching your number of hands is:

80.11%

And finally, the number of hands to reach goal if you had no time constraint but the probability and goal is:

24 hands.

Now, putting that together, it's basically saying that if someone's only goal is to increase their unit betting by 1, ie just win once, bankroll independent, there is an 80% chance of success and just under 20% chance of losing it all. So what is stopping someone just settling down and really very very slowly grinding away and increasing their betting units this way? Once you start increasing your units, the probability of success keeps increasing. How can this make sense? Obviously this will be dependent on variance etc AND I haven't changed the standard deviation or wins rate per 100 hands (If I understand these are from tables on the actual software). But I really don't quite understand this, even when you put in playing for 1 hand, you appear to have a 71% chance of reaching your goal.

I'm obviously missing something simple here, can anyone clear up my understanding of this?

first, i'm not sure your ROR is correct. if the game were fair (50-50 for 1 unit wagered) you would have exactly a 20% chance to lose 4 units before winning 1, so you would have to increase the edge in your favor to get a ROR less than 20%.

second, you are having a 80% chance of winning 1 and a 20% chance of losing 4.. you are not considering that you lose more relative to what you win.

I think I follow you. The ROR was from that website.

Quote: chrisr

first, i'm not sure your ROR is correct. if the game were fair (50-50 for 1 unit wagered) you would have exactly a 20% chance to lose 4 units before winning 1, so you would have to increase the edge in your favor to get a ROR less than 20%.

second, you are having a 80% chance of winning 1 and a 20% chance of losing 4.. you are not considering that you lose more relative to what you win.