Robert: BJA3 Chapter 10, $ Won per 100 Question

[Robert]

Regarding Chapter 10 win rates....Are the ROR sims included in the win rates? I'll use a specific example to ask the question.

Playing 4.5/6, S17, DAS, BC Opt. (1-2), win rate of $37.75 per 100 observed.

Playing per the optimum chart as written, what is the win rate per 100 observed if we choose to ignore the possibility of going broke....i.e., the 13.5% of the sims? I assume that the other way to ask this is....What is the win rate of the bet scheme with an infinite bankroll?

[Don Schlesinger]

> Regarding Chapter 10 win rates....Are the
> ROR sims included in the win rates? I'll use
> a specific example to ask the question.

So far, I don't understand.

> Playing 4.5/6, S17, DAS, BC Opt. (1-2), win
> rate of $37.75 per 100 observed.

OK.

> Playing per the optimum chart as written,
> what is the win rate per 100 observed if we
> choose to ignore the possibility of going
> broke....

How do you ignore it??

> i.e., the 13.5% of the sims? I
> assume that the other way to ask this
> is....What is the win rate of the bet scheme
> with an infinite bankroll?

Sorry, but your question doesn't make much sense. You could have a million dollars, but if you still bet as in the chart, you'll win what the chart says you'll win, but with zero ROR. On the other hand, if you raise your bankroll and then bet in proportion to it, you'll win much more, with the same 13.5% ROR.

Don

[Robert]

> Sorry, but your question doesn't make much
> sense. You could have a million dollars, but
> if you still bet as in the chart, you'll win
> what the chart says you'll win, but with
> zero ROR. On the other hand, if you raise
> your bankroll and then bet in proportion to
> it, you'll win much more, with the same
> 13.5% ROR.

Got it, thanks. If you run 1000 sims of 1 million hands each, I assume then that you would tap out in 135 sims, and in the other 865 sims you would win, on average, $37.75 per 100 hands observed. I guess I was thinking that if you "averaged in" the lost sims, the $ won/100 would be lowered (slightly), instead, these sims are "thrown out" and treated separately, regardless of how long they take to occur, is that correct?

[Don Schlesinger]

Norm pointed out to me that what I had written above (now deleted), in the last paragraph, isn't correctly worded. I apologize for the confusion and will amend what I had written, in this new post, below.

> Now, say you play 1,000 hours. You might win
> 1,000 x hourly win rate, or, you might tap
> out before getting to 1,000 hours.

No problem yet.

> On average, you will tap out 135 times and
> manage to play all 1,000 hours the other 865
> times.

Still fine.

> When you tap out, you will, of
> course, have lost all of your money.

No argument there.

> For the other times when you succeed in reaching
> the end of the 1,000 hours, you will have
> averaged your hourly win rate per hour.

This is the confusing part. Every result that you obtain goes into making up your hourly win rate. So, when you tap out, that's a big negative, and, to maintain your average, when you have winning sessions, they must exceed the average, to restore the balance. Since you tap out 135 times, for the 865 times that you don't go broke, those sessions will reflect higher win rates than the average.

Here's a simple way to look at it: Suppose I average making $100 per hour. I play for one hour and tap out, losing, say, $3,000. Now, I play a second hour. I can't now say that to maintain my average, I'm going to win $100; that would be ridiculous. So, I need to win $3,200, so that, after two hours, I'm up $200, to make the average $100 per hour.

Of course, this is a simplistic example, but it illustrates the point.

The idea is that when you lose, your average losing session is much more than your hourly average, and when you win, your average winning session is much more than your average. I actually have a whole discussion of this on pp. 298-301 of BJA3. Should have reread it before I answered you! :-) Sorry.

Don

P.S. The part about having an infinite bankroll is somewhat of a red herring. If you play for the same stakes and have all the money in the world, you will have some "lifetimes" in which you will lose even more than you would have when you had a smaller bank. The distribution of your results will look somewhat different, but your hourly win rate won't really be affected. It will just take you a shorter period of time to achieve your hours, because, since you never tap out, you never have any "down time" building another bankroll.

[bfbagain]

[Robert]

Thanks Don, that is what I thought was going on in my original post..."Playing per the optimum chart as written, what is the win rate per 100 observed if we choose to ignore the possibility of going broke"?

I know it's more academic than practical maybe, but another interesting fact to me is....with a fixed chance of going broke in 13.5% of sims, it seems like a win rate of $60 per 100 observed hands gets "dragged down" more than a win rate of $30 per 100 observed hands....i.e., if you ignore the ROR possibility, the $60 will go up more than the $30.