Originally Posted by sactokid544
Each flip is independent IF that is the calculation you are trying to compute.
If you are trying to find the conditional probability that a coin lands on tails GIVEN that it's previous flip was tails, IT IS IMPOSSIBLE to NOT consider the previous flip, to make that calculation. Thus the previous flips have a bearing when calculating conditional probability.
I understand your point. The point I'm making is that using conditional probability to guide your actions in poker is a mistake.
Let's say the coin flipped 9 times in a row as tails (and let's make it a "fair" coin, no desire to get into rigged discussions). You'd be awfully tempted to think that this time it ought to come up heads, since 10 tails in a row would be statistically improbable. Let's say instead of taking even money for the flip, you're willing to bet w aggressive odds
(i.e., worse than even money) that it'll come up heads because it came up tails 9 times in a row. This is a mistake - it is still exactly 50/50 whether it comes up heads or tails, you're making a bad bet.
When somebody thinks that a bad run of cards means they should stop playing cuz they're more likely to continue w bad cards, OR that since they've had a bad run they're "due" for a good run, and change their playing behavior as a result of either line of reasoning, they are making a mistake - potentially a costly one.
You'll see players get gunshy all the time when they lose flips several times in a row thinking that they're cursed by a bad luck run, or overly aggressive when they lose flips (or other situations where it was appropriate to put money in the pot, like drawing with the correct pot odds
but missing) several times in a row thinking that they're due for the flips to come their way - both of these are responses that will cost them money relative to the correct plays.
bazerk, didn't get around to reading that paper, but thanks for posting!