Quote Originally Posted by Monty3038
That is the confusion on my part I think, guess it's back to basics for me... since it would seem you wouldn't put it in if the odds were bad...

Doing it the other way leads to 1/3.5 = 28.6% so I would need to be ahead of his range more than 28.6% of the time to make this profitable... if I understand it right.
it's an issue of converting ratios into percentages that makes most people lost on this. your risk:reward ratio is 10:25 because you are putting $10 at risk for a chance at the $25 that are already in there (the original pot of 15+his bet of 10). so in order to make this a break even endeavor your odds need to be 10:25, so for every 25 times you lose, you win 10 times. so there are 35 total scenarios (25 losses and 10 wins), so you win 10/35 or 28.6% times.

so you just "add the money you're putting in" just as a sort of shortcut to achieving the math, it's not actually what's logically taking place. what's really going on is that ratios compare how many wins happen for every loss, whereas percentages compare how many wins total over the course of 100 hypothetical scenarios. ratios apply more directly to the problem at hand but percentages are easier to calculate with/convert equity with