Odds table from majorkong's new book

[Gar Pike]

So, trying to find a simple method of relating outs to odds (for Holdem) I graphed a couple of curves. Outs(x) vs Odds(y) looks like your normal 1/X curve. So you'd think (at least, I would think) that Outs times Odds would be a constant, right? Well, maybe not. From the table in S, M & Miller's new book, there's a definite slope down to the right. And it's not monotonic, it blips up at around 15 or 16 outs. Obviously I'm missing something, but what? Rounding error? Too simplistic an assumption?

Regards

Gar

[Lost Wages]

Sorry, I don't have the book in front of me so I can't comment on the chart, though I'm sure that it is correct.

If you have X outs then your odds (:1) are;

From flop to turn:
(1-X/47)/(X/47)

From turn to river:
(1-X/46)/(X/46)

From flop to river (hitting at least 1 out):
(1-(1-((47-X)/47)*((46-X))/46))/(1-((47-X)/47)*((46-X))/46)

Lost Wages

[Gar Pike]

Thanks for the reply, Lost Wages

Sadly, I'm still confused. My math is so rusty...

The way I intereperet the parens, (1-X/47)/(X/47) looks like it should simplify to (1-x)/x, which would imply increasingly negative odds with increasing outs.

(1 - (x/47)) / x/47 looks better, is that right? That looks like it simplifies to (47/x) - 1.

If that's right, then Odds X Outs = 47 - Outs, which would match the curve and that explains that.

Just thinking out loud... thanks again.

Regards,

Gar

[Lost Wages]

(1 - (x/47)) / x/47 looks better, is that right?

(1-X/47)/(X/47) and (1 - (x/47)) / x/47 are identical. Since division preceeds subtraction, the extra parenthesis are unnecessary but not incorrect. (1-X/47) is not the same as (1-X)/47.

That looks like it simplifies to (47/x) - 1

Correct. The unsimplified form just makes it eaiser to see how the answer is arrived at since:

Probability(P) = # of outs/# of unseen cards

and

Odds:1 = (1-P)/P

so with X outs on the flop

Odds = (1-X/47)/(X/47)

Lost Wages