Double21: BJRM Software Question

[Double21]

Maybe John or someone else can answer this question for me.

In using the trip simulator feature of BJRM, I have tried to ascertain the probability of winning a one hour trip. I input a trip goal of $1 and get a probability of achieving this or better at over 99%. Is this telling me that, when I win, the probability of walking away with $1 or better is over 99%? I can't believe it means the probability of being ahead after one hour is better than 99%!

Thanks for the help.

[John Auston]

> Maybe John or someone else can answer this
> question for me.

> In using the trip simulator feature of BJRM,
> I have tried to ascertain the probability of
> winning a one hour trip. I input a trip goal
> of $1 and get a probability of achieving
> this or better at over 99%. Is this telling
> me that, when I win, the probability of
> walking away with $1 or better is over 99%?

It is if you walk away as soon as you are up $1,
which is what the stat means, even if that is after the very first hand.

The pop-up help text says you have to leave as soon as goal is reached.

Maybe Don can help here, but it might also be true that some of these formulas break down a bit when given extreme parameters (like 1 hour of play only).

John

[Double21]

Thanks for the respose John---it is so great to have help like you and Don so graciously offer.

[Karel]

> Maybe Don can help here, but it might also
> be true that some of these formulas break
> down a bit when given extreme parameters
> (like 1 hour of play only).

That is true:
The mathematical formulas assume the so-called Brownian motion , which is a continuous version of the so-called random walk. For a play of 1 hour the approximation is not bad since 1 hour results can already be approximated by normal distribution with not too much error.

However, a large error could be caused by "overshooting" the goal. In other words, the winning goal should be large relative to the maximum bet size, for example.

The formula is grossly wrong in the example above, with $1 winning goal. The actual probability that the player walks away with at least $1 is smaller since in most cases he would win signification more than $1.