Myooligan: Don's Early Payout Formula

[Myooligan]

Hullo Don and company,

Got a question on your formula from BJA p298. I punched it into a spreadsheet, and I matched your results when I ran the numbers from your example. I also included your "doublecheck," and it indicates that the numbers are all adding up, even when I change the variables.

Here's what's puzzling me: When I put in a number of rounds equal to or slightly greater than the number of rounds at which your total EV = the size of the original bank, it gives me a number around 47%. To get it up to 50%, I have to put in a number of rounds far higher than what should be required to double the bank. But, no matter how high the number of rounds, it never goes above 50%, which seems right.

Could it be that the formula breaks down at high round values? Or maybe my spreadsheet is broken. . .

Anyway, hope yer all doin well over here at ap.com. s'been too long

Myooligan

[Don Schlesinger]

> Hullo Don and company,

> Got a question on your formula from BJA p298. I
> punched it into a spreadsheet, and I matched your
> results when I ran the numbers from your example. I
> also included your "doublecheck," and it
> indicates that the numbers are all adding up, even
> when I change the variables.

So far, so good! :-)

> Here's what's puzzling me: When I put in a number of
> rounds equal to or slightly greater than the number of
> rounds at which your total EV = the size of the
> original bank, it gives me a number around 47%. To get
> it up to 50%, I have to put in a number of rounds far
> higher than what should be required to double the
> bank. But, no matter how high the number of rounds, it
> never goes above 50%, which seems right.

Should your last remark be, "which doesn't seem right"?

> Could it be that the formula breaks down at high round
> values? Or maybe my spreadsheet is broken. . .

The formula is based on the fact that a 50-50 split is mandated as "correct" when you have played just enough hours to double the bank. So, it's possible that, if you play more than that number of hours, the formula gets "confused," as to why you're exceeding the smallest number of hours sufficient to already achieve the 50-50 split. In other words, what more could you hope for?

Try using Griffin's alternative approach, on p. 301, and let me know if it changes anything.

> Anyway, hope yer all doin well over here at ap.com.
> s'been too long

Nice to see you. Please visit more often.

Regards,

Don

[Myooligan]

Whoops, sorry for the belated reply. I went on a trip the day after posting this. Was planning to reply the next day, but it doesn't look like ap.com is accessible on the mobile web. Anyway, thanks for the reply. . .

> Should your last remark be, "which doesn't seem right"?

Maybe so. The number I end up with might be a short-term cut for x hours equivalent to a long-term 50/50 share for an infinite number of hours. I know that's not what the formula is supposed to produce, but it looks like that's what I'm getting. That's why I said it "seems right" for the percentage to top out at 50%. I'll triple check it tomorrow.

> The formula is based on the fact that a 50-50 split is
> mandated as "correct" when you have played
> just enough hours to double the bank. So, it's
> possible that, if you play more than that number of
> hours, the formula gets "confused," as to
> why you're exceeding the smallest number of hours
> sufficient to already achieve the 50-50 split.

The problem is, even when I use exactly the number of hours required to double the bank, it comes up with a number around 47%, while it should be 50%.

> Try using Griffin's alternative approach, on p. 301,
> and let me know if it changes anything.

Ok. I'll post what I come up with.

> Nice to see you. Please visit more often.

Will do.

[Myooligan]

So, I tried Griffin's method. Once again, I get exactly the same outcome -- 33.4% -- as you ended up with. Moreover, when I change the variables, the Griffin Method, your method, and your double-check all corroborate the results. And once again, it produces a payout in the 47% range when n = h.

Is it possible that we're looking at the short-term equivalent payouts for an infinite-time 50/50 split (Rather than a 50/50 split at a number of hours such that expected win = starting bank)? That's my hunch, and one bit of supporting evidence is the following: Although you use the "240 total hours" (h) figure in your original formula, it doesn't appear in the Griffin version. We only find the "40 hours" (n) figure there. Of course, it's easy to derive the number of hours necessary to double the bank from the other variables in the Griffin equation. But since the Griffin formula doesn't look directly at the "h" figure, I suspect the results it produces are independent of it.