Curious Stats Question

#1
Hi all,

I have a curious statistical question for ya'll.

Theoretically speaking wouldn't the following be true:

1) if a game was exactly breakeven (Win/hr = $0.00) and had a std/hr > $0.00 then RoR = 100% given an infinite number of hours of play.

but if #1 true then wouldn't #2 be true as well

2) Everygame with a std/hr > $0.00 has a RoR = 100% given an infinite number of hours.

Should I not even bother with the idea of infinite hours of play and just accept the fact that the probability of a losing streak of -$9999999999999999... while very nearly impossible is not 0%, but is still virtually impossible.

I feel like this is starting to maybe stumble into N-zero territory, is that right? Can you please recommend a book for N0 reading?

Thanks in Advance.
 

KewlJ

Well-Known Member
#2
I'll leave it to Mr. Schlesinger or one of the other math guys to give a mathematical answer, but it seems to me, your question is incomplete and can't be answered because there is no mention of bankroll. I mean what if your bankroll is infinite as well? ;)

Also the concept of infinite hours of play is silly. Even if you play fulltime (grinder status, so playing many hours) and you do that for 30 years, that is a very finite number of hours.

I can tell you this much from my own experience. Just finishing 17 years, and I haven't hit "ruin" yet. :p And I started very underfunded with a small inadequate bankroll and have never added an outside dollar to my bankroll. So the idea of 100% RoR seems a stretch to me. Maybe it's coming I don't know. :oops: After this year (on so many levels) I feel like almost anything is possible.
 

DSchles

Well-Known Member
#3
AC3SrW1LD said:
Hi all,

I have a curious statistical question for ya'll.

Theoretically speaking wouldn't the following be true:

1) if a game was exactly breakeven (Win/hr = $0.00) and had a std/hr > $0.00 then RoR = 100% given an infinite number of hours of play.

but if #1 true then wouldn't #2 be true as well

2) Everygame with a std/hr > $0.00 has a RoR = 100% given an infinite number of hours.

Should I not even bother with the idea of infinite hours of play and just accept the fact that the probability of a losing streak of -$9999999999999999... while very nearly impossible is not 0%, but is still virtually impossible.

I feel like this is starting to maybe stumble into N-zero territory, is that right? Can you please recommend a book for N0 reading?

Thanks in Advance.
Think about what you're saying. If the s.d. is zero, that means that there is no fluctuation of outcomes around the mean. It implies that it is a certainty that, for each hour of play, you are guaranteed to break even. Why wpould you say that your RoR is 100% under those circumsatnces? In fact, your RoR is zero. It's impossible to lose any money with a s.d. of zero.

One such way this could happen would be for every hand to be a push. You would always break even and there would never be any fluctuation in your bankroll.

Do you have BJA3? Read the RoR chapter.

Finally, the huge work The Kelly Capital Growth Investment Criterion edited by, among others, Ed Thorp, is the definitive work on the subject.

Don
 
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#4
DSchles said:
Think about what you're saying. If the s.d. is zero, that means that there is no fluctuation of outcomes around the mean. It implies that it is a certainty that, for each hour of play, you are guaranteed to break even. Why wpould you say that your RoR is 100% under those circumsatnces? In fact, your RoR is zero. It's impossible to lose any money with a s.d. of zero.

Don
Hi Don you may have misread #2 above. The assumption is not SD = 0 but SD > 0. Either way this is just a thought experiment that popped into my head and was wondering if there was any math that proved it otherwise (though, most math breaks down when you mention infinity). I think I heard from one of BJA videos (or maybe somewhere else) that #1 was true but then I thought well why wouldn't that be the case for all games SD > 0 (and I suppose another assumption needed would be at least one possible negative outcome). I think it's ultimately a pessimistic point and as KewlJ pointed out "well, what if your bankroll was infinite"

I recently purchased BJA3 but have not read the RoR chapter. I looked briefly at formulas and was surprised to see trig equations! Interesting. I haven't had the time to really dig too far into BJA3 as it reads almost more like a textbook than a casual read.
 

DSchles

Well-Known Member
#5
"Hi Don you may have misread #2 above. The assumption is not SD = 0 but SD > 0."

I did. Sorry about that. Not like me.

"Either way this is just a thought experiment that popped into my head and was wondering if there was any math that proved it otherwise (though, most math breaks down when you mention infinity). I think I heard from one of BJA videos (or maybe somewhere else) that #1 was true"

Yes, sure it's true. If you have no edge, and there is variability of outcome, sooner or later (and you're playing forever!) a bad streak will wipe you out.

"but then I thought well why wouldn't that be the case for all games SD > 0"

No, definitely not. Tha's exactly what N0 measures. Sooner or later, e.v. catches up to and begins to dominate s.d. Far from going bust, if you play forever, you win all the money in the world -- if you don't go broke first.

"(and I suppose another assumption needed would be at least one possible negative outcome). I think it's ultimately a pessimistic point and as KewlJ pointed out "well, what if your bankroll was infinite"

Doesn't matter.

"I recently purchased BJA3 but have not read the RoR chapter. I looked briefly at formulas and was surprised to see trig equations!"

Well, yeah, the double-barrier formulas are a bit intimidating, but don't let them scare you. You don't need to know them to understand the gist of the section.

"Interesting. I haven't had the time to really dig too far into BJA3 as it reads almost more like a textbook than a casual read."

It's certainly not a casual read! Take your time and read it slowly -- more than once for the chapters that are important to you.

Don
 
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