Gamblers Fallacy & Progressive Betting

I'm pretty sure I already know this isn't going to work, but I'm really more interested in why. My background isn't in statistics, but I'm starting to work more and more closely with stats and need to learn more.

So I primitively understand why the gambler's fallacy is a fallacy, and why progressive betting (or any betting system in general) won't work.

What I don't understand is if you were to combine the two together why they wouldn't work. Please know I understand how dumb that sounds.

As just a quick example with coin flips: If I were to only bet after seeing 9 heads in a row, and then begin to bet on tails exponentially until I won... what the math look like? Say on the 10th flip I were to bet $1, then on the 11th flip $10, then $100, and so forth.

Is the answer that I could remove the gambler's fallacy and just bet like this on any coin flip, having the same 50/50 odds per flip? I feel like it's the answer, but having a hard time visualizing it. So if I only bet after 9 heads, over time, I'd have the same "return" or loss, because eventually there's bound to be another 9 heads in a row... which would bankrupt Bill Gates? Therefore I could have just started betting on the first flip and have no consideration for past flips?

Quote: thep0e

I'm pretty sure I already know this isn't going to work, but I'm really more interested in why. My background isn't in statistics, but I'm starting to work more and more closely with stats and need to learn more.

So I primitively understand why the gambler's fallacy is a fallacy, and why progressive betting (or any betting system in general) won't work.

What I don't understand is if you were to combine the two together why they wouldn't work. Please know I understand how dumb that sounds.

As just a quick example with coin flips: If I were to only bet after seeing 9 heads in a row, and then begin to bet on tails exponentially until I won... what the math look like? Say on the 10th flip I were to bet $1, then on the 11th flip $10, then $100, and so forth.

Is the answer that I could remove the gambler's fallacy and just bet like this on any coin flip, having the same 50/50 odds per flip? I feel like it's the answer, but having a hard time visualizing it. So if I only bet after 9 heads, over time, I'd have the same "return" or loss, because eventually there's bound to be another 9 heads in a row... which would bankrupt Bill Gates? Therefore I could have just started betting on the first flip and have no consideration for past flips?

Coins don't have a memory.

Quote: thep0e

As just a quick example with coin flips: If I were to only bet after seeing 9 heads in a row, and then begin to bet on tails exponentially until I won... what the math look like? Say on the 10th flip I were to bet $1, then on the 11th flip $10, then $100, and so forth.

Why not just start with the first flip? The odds of flipping x tails in a row starting from the first flip are no different than flipping x more tails in a row after tails has already been flipped nine times. Coin flips, assuming you get paid even money, have an Expected Return of 0%, so the long-term expectation is you'll be even regardless of what system you use.

Although, if you are ever tossing coins for cash, a Stanford study concluded a coin is slightly more likely to land on the same side that was facing up when it was tossed.

Quote:

Is the answer that I could remove the gambler's fallacy and just bet like this on any coin flip, having the same 50/50 odds per flip? I feel like it's the answer, but having a hard time visualizing it. So if I only bet after 9 heads, over time, I'd have the same "return" or loss, because eventually there's bound to be another 9 heads in a row... which would bankrupt Bill Gates? Therefore I could have just started betting on the first flip and have no consideration for past flips?

Exactly, except it's a break-even proposition, so your long-term expectation is to neither win nor lose. The only difference using the Martingale system and waiting until nine Heads are flipped instead of just using it from the beginning is that it will take longer (in terms of time, not betting attempts) to reach the long-term.

Gambler's Fallacy: Waiting is worthless. Yeah, after an infinite number of events, the average will approach the predicted percentage. But read that carefully. "Ten" is far less than infinity, and "approach" is somewhat vague.

Systems: Sooner or later you'll run into such a bad streak that you'll lose the entire bankroll, or your bet size will exceed the table limit.


Here's my take on it. Ya know those displays at the roulette table? For every guy that ever said "Look honey. 8 reds in a row. Let's bet on black", there was a guy a minute earlier that said "Look honey. 7 reds in a row. Let's bet on black"

If you wanna play the streaks, play WITH them. 8 reds in a row? Bet on red, not black. If red hits, great. Keep working the streak. If not, OK, streak is over, and you won't lose a fortune chasing your money.

There are two things you have to remember.

First, on a 50/50 coin flip, the probability of 10 heads in a row is 1/1024 - but the probability of 9 heads followed by a tail is also 1/1024.

Second, even if the coin had "memory", do you have a listing of how the coin tossed before you started betting? Maybe the 9 heads in a row was after a run where tails came up 800 times out of 1000 - wouldn't heads be "due" in this case?

As for your math, you would be making a profit when it came up tails - if it comes up tails before you run out of money to bet. After 6 heads in a row (probability 1/32), you are behind $111,111, and your next bet is supposed to be $1,000,000. This is one reason table games have maximum bets - to make systems like this much less likely to work by having you reach a point where the next bet that you have to make in order to get ahead is above the maximum.

On a coin flip, yes it is true, that the number of heads and tails will approach expectation (50/50). The fallacy is including the previous heads/tails on what will expect to happen. The expectation is only on future events.

For example, you flip a coin 10 times and it lands on heads all 10 times. So you have H:T (Heads:Tails) right now at 10:0. If you flip the coin 100 more times, you expect that figure to approach 60:50 (110 flips), NOT 55:55.


People also have this idea that EV or expected results are only for the long term, this idea that "if I flip a coin 10,000 times, I can expect the results to be close to 5000:5000....but if I flip a coin 10 times, anything can happen". While that is true to an extent, that is very misleading. Yes, anything CAN happen, but, your expectation for 10 flips is still going to be 5:5.


So, that rules out 2 "fallacies" --

1) Future expectation is based on previous expectation.
2) Expectation only shows up in the long run.

Quote: thep0e

As just a quick example with coin flips: If I were to only bet after seeing 9 heads in a row, and then begin to bet on tails?

Why 9 in a row? Is 9 the magic number?

Why not sell everything you have borrow as much money as you can. Come to Vegas and wait for 10, 11, 12, 13, 14 or 15 losses in a row? Whatever you believe to be almost impossible? then bet 1/4 th of everything you have. Surly almost impossible + 1 more bet must be a lock. If you lose that, bet the rest, A lock + a lock = destiny.

I really don't understand how ANYONE including even the mathematically challenged cannot grasp this(Gamblers fallacies).

a streak of 10 will happen half as many times as a streak of 9.... why? because its 50/50 so that 10th willbe heads or tails.. a streak of 11 will happen half as many times as 10...
you will lose half the time on your 10 bet and 11 bet just like you would lose half the time on 1 or 2 if you did not wait..

you would just bet less often..

A good way to think of it is this: you aren't making that last bet that heads will come up 10 times in a row; you are making that bet that heads will come up 10 times in a row after the first 9 have already happened. 50/50.