Problem with your book

[LittleOldLady]

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Why is there a little flame next to my thread now? I don't get it.

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Good grief, read the legend (that is, if you are merely clueless and not a troll).

[jman220]

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Holla,

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I stopped there.

[async]

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Are you telling me that if you miss a flush draw 99 times in a row by some crazy strike of probality, on the 100th time its the same chance?

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Yes.

Assume for the sake of argument that the odds of heads coming up on a coin are 50/50. (Which is supposedly true, but let's not bring in skilled flippers, weighted coins, etc)

The odds of heads are 50/50. When you flip, there are 2 possibilities:

(1) heads (50%)
(2) tails (50%)

When you flip 2 times in a row, the odds of it coming up heads both times is 25%, because there are 4 possibilities:

(1) heads, heads (25%)
(2) heads, tails (25%)
(3) tails, heads (25%)
(4) tails, tails (25%)

Now, if I flipped a coin, and it came up heads, and I asked you what the chances are that it would come up heads a second time, what would you say? If you say 50/50 now, then why is it exactly 50/50 for the 2nd time but not the 100th time? So if things should "even out" you'd expect tails to be more likely. The problem with this is that the heads has already happened.

Before we made the first coin flip, heads and tails were distinctly possible. So getting 2 heads in a row required 2 separate 50/50 events to happen a certain way, and the odds of that are 25%. However, after the first heads, it is no longer possible for the first flip to be tails, because it already happened. Now only 2 possible outcomes exist:

(1) heads, heads (50%)
(2) heads, tails (50%)

So the likelihood the second flip is heads is 50%. This can be taken to the extreme in the same way. If I have flipped a coin and it has been heads 99 times, then for flip #100, only 2 possibilities remain:

(1) heads, heads, [97 more heads], heads
(2) heads, heads, [97 more heads], tails

Each still remains 50% likely. If you asked what the odds were of heads coming up 100 times in a row were, I'd certainly tell you astronomically small. But if you say: What are the odds of heads coming up the 100th time AFTER already coming up heads 99 times, I'd say: 50/50.

The same thing applies to a flush draw. If you miss a flush draw 99 times in a row, you have been struck by a ridiculous event of probability. But if that's happened, the weird strike of probability HAS ALREADY HAPPENED, and as unlikely as it was, it won't help you suck out on the 100th time. We don't even hear about this because the 99 times in a row never happens. Neither does 98. Or 97.

The reason things don't "even out" over any observable time frame is that the time frame for things to "even out" is infinity. If there was an infinite string of random numbers, for example, any sequence of numbers you could enumerate would appear somewhere in the infinite string. Likewise, given infinite chances, any event, no matter how unlikely, will occur. This isn't possible to prove empirically. But I could write a random number generator (and have) which does a computerized "coin flip". It will come up 50/50 after millions of trials, out to several decimal places. Now, I could program the computer to make a special record of all "10th flips". That is, after it randomly chooses between, say, 0 or 1, and chooses the same one 9 times in a row, then record the outcome of the 10th flip. I guarantee you that even with it being 50.000%/50.000% after billions of trials, the odds on that 10th flip will also be 50/50, or so close it is irrelevent for any practical purpose. (The odds of having 9 flips go one way in a row are 1 in 256, or 1 in 512 if you specify WHICH way they go nine times... that is, heads or tails 9 times in a row is 1 in 256, but heads specifically 9 in a row is 1 in 512)

[MrGrob]

By this logic, if you have MADE 19 flushes in a row, and start with a 4 flush now, you should fold, as the odds of making this one (the 20th in a row) is going to be much less.

This is just wrong. You mistake comes from take into account information THAT HAS HAPPENED and applying it to a situation that is not relying on this same information.

Let me explain. If you were to say that it is going to be highly unlikely that I will miss 20 flushes in a row, I would say you are correct. The chances of me starting to draw to flushes NOW and missing 20 in a row is small. HOWEVER, once I already missed 19 flushes, the odds of missing 19 flushes in a row has already been reached. YOU ARE ALREADY at the freakish point for the odds. HOWEVER, these odds don't somehow add or influence the next flush draw, as that is going to be the same as the 1st. Since you have already reached the freak-of-the-odds point in missing 19, missing 20 is now the SAME AS MISSING 1, as there is ONLY 1 flush draw to go.

So, yes, missing 20 flushes IS HIGHLY UNLIKELY...FROM THE START...but once you have ALREADY MISSED 19 etc, the NEXT is not more likely to hit or miss then if you looked at missing only 1 flush draw...as this is only 1 flush draw. The freak of the odds has passed ALREADY, so the odds are not long NOW...they were already long and have already gotten there.

Make sense? The HISTORY of missed flushes, the long odds, have already been covered...it is not likely that it will, but once it happens, it has happened...the next flush doesn't know or does it care that 19 have missed...it is just the odds of making or missing 1.

I see how you are looking at it, but it is not right...I hope the above make sense....

[Fryguy]

Mathematical Induction at it's finest.

[Gregatron]

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I used to be a roulette player in the casino, I won some, and lost some, but overall I'm up. The reason why is I knew to only bet colors, and only bet a color that hadn't come up in a while, because the odds of red not coming up 10 times in a row are low.

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I love the internet. People can make any statement they want, no matter how rude or dumb, safely behind their computer screen.

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Seriously guys, why so much interest in this thread? This is some pretty obvious trolling. And not well done trolling either.

[ginko]

Hellmuth, you are wrong. I can tell you are trying to understand so I won't flame you.

[Haggis McHaggis]

Man, you guys are really close minded. Seriously, the thought that this guy is not a winning roulette player is as silly as it is pretentious. How do I know? Because I have been a high stakes roulette player for going on 5 years now. I have been banned from several casinos in Vegas and AC, and no I did not cheat... I WON! That's it. It's like card counters in BJ that get kicked out. Yeah I think it's BS, though I will admit the casinos are in their legal right to do it.

Anyway, master_hellmuth's main fault in this thread is his not willing to admit the complexity of winning as a roulette player. First, there is a lot of variance to the game. I mean a LOT, enough to make playing MTTs look like a 9 to 5 job. Second, you have to sit out some hands (another rouletter has mentioned that somewhere in this thread). You can't play every time. Third, you have to vary your bets, either doubling, or (depending on previous spins) sometimes tripling a previous (losing) bet.

Many of you buy into the idea that roulette can't be beat, and that is pretty sad. There is a pretty intelligent group of posters here at 2p2, but you are getting hoodwinked and avioding a very lucrative game. You can point out all the silly "math" and "logic" you want, but the empirical FACT is that you can win if you know how, and use the Law of Averages to your advantage.

[damaniac]

You work for a casino don't you?

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Hellmuth, if you are serious about fixing this (gigantic) misconception, please read and reread async's great post until you understand.

I vote Hellmuth is just trolling, especially given the username, but if he isn't, he probably plays roulette, loses money, but gets lucky enough not to be broke and brags how he "beats the game."

If not, he may simply be an astronomically lucky person (I guess Raymer isn't called lucky any more after his Kanter run-in?)!