[jtr]

Hi, Vanquish.

Good questions.

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My instinct is to go with math, and not to trust sites that base odds on however many simulated hands. I mean, why go with a simulation when I can calculate precisely how often that third Ace I need is going to come up?

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As someone who basically does simulations for a living, I can appreciate your scepticism here. But rest assured that simulating deals (as opposed to realistic play) in poker is pretty easy and a tool like pokenum is effectively doing the same thing as the enumeration you do in a pen-and-paper probability calculation.

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I saw one site that calculated the odds of you NOT getting the cards you need, since that can be an "AND" situation and you can multiply. It was like this:

Odds you'll complete your inside straight draw:

Start with odds you won't hit on turn AND won't hit on river: (43/47)*(42/46) = 83.53%

Subtract this number from 100% to find out chances that this WON'T happen (i.e. chances you'll have you straight by the river): 100% - 83.53% = 16.47%

Is this correct? Is there another way?

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This is exactly the right way to go about it. Don't let anyone convince you otherwise. One small caution: don't say "odds" if you're going to work with stuff like 43/47 in your working above. This is a probability (in this case the prob. of not hitting your gutshot on the turn) -- it's not an odds ratio. Odds ratios are the probability of an event happening, divided by the probability of its not happening. So heads on a fair coin is 50% as a probability, but 1 (or 1:1) as an odds ratio. I don't mean to be a geek about this, but there's a real danger of confusion if aren't clear about which one you're using.

Also, the popularity of odds ratios over probabilities in poker reasoning is not an accident. Odds ratios make it very easy to compare the return the pot is potentially offering you on your bet, and the likelihood of your draw hitting.

Finally, I think the disagreement you had in your example was a disagreement about counting outs, not a disagreement about how to calculate probabilities.