A math question

First off, I realize all betting systems fail. In my younger days, I tried many, I lost money, I get it. Tying to make a betting system work isn't at all the purpose of this question. But i am interested in the math.

So, I was playing Ez Bacc today watching a guy losing money playing a betting system and it made me curious about a math question.

So, here's the set up. Say I'm playing a la Boucher system (this guy was) where I start by betting 1 unit, if I loose I tack my loss on to the end and bet the first and last number of units (in this case 1 and 1 so 2 units). Lose again, 2 goes on the end and repeat. Win and cross off first and last numbers and play the next number of units in the column.

Ok, here's the question. Let's say I have $1000 to play and I want to win $100. If my unit is $100 I have to win 1 set to hit my goal. If my unit is $25 I have to win 4 sets to hit my goal.

So my question is, am I 4x less likely to hit my goal if I play $25 since I have to win 4x as ma y sets? Are my odds for hitting my goal the same no matter what my unit is? My assumption is that the odds of hitting my goal is the same no matter what because using the system doesn't change the house advantage. But instinctively it seems like the more sets you have to play, the more likely you are to approach the house advantage and lose.

Thanks friends!

(P.s. Stopped by the roulette table to have argument with guy playing all 3 12's.... Funny night)

Quote: Cowpie

Ok, here's the question. Let's say I have $1000 to play and I want to win $100. If my unit is $100 I have to win 1 set to hit my goal. If my unit is $25 I have to win 4 sets to hit my goal.

So my question is, am I 4x less likely to hit my goal if I play $25 since I have to win 4x as ma y sets? Are my odds for hitting my goal the same no matter what my unit is?

Hi, Welcome to the forum.
There's not much in it.
The probability is approximately the same for pretty much any system: You'd have a little less than 90% probability of hitting goal.

P<=1000/(1000+100)

See here https://wizardofvegas.com/member/oncedear/blog/#post1370

I really cannot be bothered to do or explain the more complicated maths for your specific example. sorry.

House edge would have a modest impact because, on average you would not need to lay much 'action' on the table before either hitting goal or losing all.

:). Thanks for the quick reply.

Quote: Cowpie

Let's say I have $1000 to play and I want to win $100.
If my unit is $100 I have to win 1 set to hit my goal.
If my unit is $25 I have to win 4 sets to hit my goal.

So my question is, am I 4x less likely to hit my goal if I play $25 since I have to win 4x as ma y sets?
Are my odds for hitting my goal the same no matter what my unit is?

using the Gambler's Ruin Formula and 49.35% as an average success rate (at EZ Bacc)

the probability of $1000 into $1100 betting $100 = 89.68%
so make it 90% or 9 out of 10
9 times WIN $100 = $900
1 TIME LOSE $1000 = net -$100
sweet!
so one must do better

how about that $25 bet instead?
85.5% success rate

not better
not good

but gamble for fun!
watching others gamble and lose can also B fun 2 4 sum
fun question
Sally

Thanks a lot. That seems to answer the question. It seems it would be better, though only slightly, to play $100 units instead of $25. Many thanks!!!

By the way, that gamblers ruin formula is exactly what I was looking for! Perfect! Thank you.