Comments on: The gambler's fallacy killed by pure maths http://altentee.com/blogs/2007/the-gamblers-fallacy-killed-by-pure-maths/ Performance and Test Automation Experts Mon, 09 May 2011 03:51:22 +0000 hourly 1 http://wordpress.org/?v=3.0.3 By: Tim http://altentee.com/blogs/2007/the-gamblers-fallacy-killed-by-pure-maths/#comment-4400 Tim Mon, 18 Jun 2007 04:40:19 +0000 http://90kts.com/blog/2007/the-gamblers-fallacy-killed-by-pure-maths/#comment-4400 Karps, if we were to write a dictionary definition of <em>gambler's fallacy</em> we could use your belief almost verbatim. No offence! Even though you acknowledge statistical independence for each play, you still refer to patterns. That is a common mistake. For example, we know that the probability of losing any spin is: <code>20/38 * 100 = 52.6%</code> So we can say <em>before</em> we play that the probability of losing six times in a row is: <code>0.526 ^ 6 = 2.12% chance or 1 in every 47 possible outcomes</code> However whilst that theory acknowledges the possibility for a particular pattern to occur (black, red, black, red, black, red) it still does not nullify the statistical probability that between every spin, we always have a 52.6% of choosing the wrong colour! <blockquote>A more subtle version of the fallacy is that an "interesting" (non-random looking) outcome is "unlikely" (e.g. that a sequence of "black,red,black,red,black,red" in a roulette result is less likely than any other individual outcome). Even apart from the debate about what constitutes an "interesting" result, this can be seen as a version of the gambler's fallacy because it is saying that a random event is less likely to occur if the result, taken in conjunction with recent events, will produce an "interesting" pattern.</blockquote> Using your suggested strategy, I ran it through the simulation 2,000 times: <code>./Roulette.pl -nightsOut 2000 -atm 200 -maxBets 250 -quit 1.75</code> In that simulation I am betting a maximum of 250 times per night (about 1 bet every 1.5 minutes = approx 6 hours at the table) over 2000 nights (to build some statistical validity into our results) and quitting when I am 1.75 times ahead (or $150 winnings as you said) or I have lost my atm balance for that night ($200). Sadly, it is nowhere near to winning 80% of the time as you predict. In my simulation, it was closer to 48.2% of the time. A net loss after 2000 nights of $57,500 ... I also modified my code to remove the casino's edge with an addtional argument <code>./Roulette.pl -nightsOut 2000 -atm 200 -maxBets 250 -quit 1.75 -fair true</code> This removes the max bet limitation of $500 per table (not applicable for a $200 atm bankroll) and also eliminates the two green positions. Both of which give the casino the slight edge required. This time I was winning approximately 62.8% of the time, which gave me a net gain of $46,000 ... So you can see quite simply, over time you will always lose as long as the casino maintains an edge. This does not rule out sheer luck, perhaps on the nights you have gone out you have fallen onto the right side of the distribution, but ultimately, if you stick to the same strategy with the same environmental conditions, I can guarantee you 99.999% that you will lose ... Bloody good fun though. See you next time at the black jack table! ;) Karps, if we were to write a dictionary definition of gambler’s fallacy we could use your belief almost verbatim. No offence! Even though you acknowledge statistical independence for each play, you still refer to patterns. That is a common mistake. For example, we know that the probability of losing any spin is:
20/38 * 100 = 52.6%
So we can say before we play that the probability of losing six times in a row is:
0.526 ^ 6 = 2.12% chance or 1 in every 47 possible outcomes

However whilst that theory acknowledges the possibility for a particular pattern to occur (black, red, black, red, black, red) it still does not nullify the statistical probability that between every spin, we always have a 52.6% of choosing the wrong colour!

A more subtle version of the fallacy is that an “interesting” (non-random looking) outcome is “unlikely” (e.g. that a sequence of “black,red,black,red,black,red” in a roulette result is less likely than any other individual outcome). Even apart from the debate about what constitutes an “interesting” result, this can be seen as a version of the gambler’s fallacy because it is saying that a random event is less likely to occur if the result, taken in conjunction with recent events, will produce an “interesting” pattern.

Using your suggested strategy, I ran it through the simulation 2,000 times:
./Roulette.pl -nightsOut 2000 -atm 200 -maxBets 250 -quit 1.75

In that simulation I am betting a maximum of 250 times per night (about 1 bet every 1.5 minutes = approx 6 hours at the table) over 2000 nights (to build some statistical validity into our results) and quitting when I am 1.75 times ahead (or $150 winnings as you said) or I have lost my atm balance for that night ($200). Sadly, it is nowhere near to winning 80% of the time as you predict. In my simulation, it was closer to 48.2% of the time. A net loss after 2000 nights of $57,500 …

I also modified my code to remove the casino’s edge with an addtional argument
./Roulette.pl -nightsOut 2000 -atm 200 -maxBets 250 -quit 1.75 -fair true

This removes the max bet limitation of $500 per table (not applicable for a $200 atm bankroll) and also eliminates the two green positions. Both of which give the casino the slight edge required. This time I was winning approximately 62.8% of the time, which gave me a net gain of $46,000 …

So you can see quite simply, over time you will always lose as long as the casino maintains an edge.

This does not rule out sheer luck, perhaps on the nights you have gone out you have fallen onto the right side of the distribution, but ultimately, if you stick to the same strategy with the same environmental conditions, I can guarantee you 99.999% that you will lose …

Bloody good fun though. See you next time at the black jack table! ;)

]]> By: Ted http://altentee.com/blogs/2007/the-gamblers-fallacy-killed-by-pure-maths/#comment-4399 Ted Mon, 18 Jun 2007 01:49:42 +0000 http://90kts.com/blog/2007/the-gamblers-fallacy-killed-by-pure-maths/#comment-4399 I was telling you at lunch "It is best just not to gamble". I think you have said it best with "Statistically you will lose". We both mean the same thing. I was telling you at lunch “It is best just not to gamble”. I think you have said it best with “Statistically you will lose”. We both mean the same thing.

]]> By: Karpa http://altentee.com/blogs/2007/the-gamblers-fallacy-killed-by-pure-maths/#comment-4398 Karpa Mon, 18 Jun 2007 01:49:20 +0000 http://90kts.com/blog/2007/the-gamblers-fallacy-killed-by-pure-maths/#comment-4398 Hey koops, interesting. Statistically you are right. But patterns do occur in nature, and the table most of the time does follow runs of colour rather than alternating. You have seen it and i have seen it. We have won both times, and i have lost only 3 times that i can remember using this strategy. Providing you stick to the limit you start out with to lose and win, if you win most of the time you will stay ahead reguardless of what statistics states. Remember they are an approximation of the real world, in the real world over 1000 or whatever spins the casino seems ahead statistically but generally isn't when you use this strategy. When you lose, only lose the amount you started with limiting your losses. Each time you go if you start with 200 max, leave at say $150 winnings, generally win most of the time, say 80% which is conservative given my experience so far, then after 10 visits you have lost $400 but won $1200 therefore ahead $800. To break even using this strategy using these limits you would have to lose more than 40 % of the time. My experience does not even come close to this. I agree if you keep betting and playing forever with out stopping and starting again with limits then you will lose as those 6 in a row alternating numbers come up then a green, you reach the maximum bet and are cleaned out, but if you stick to the limits you will hopefully avoid that particular moment in time in which the nightmare event occurs occurs, because it DOES occur uncommonly. Each spin is independent and 50:50 but the statistical chance of alternating for six spins is low. You can do the maths. Love ya Hey koops,
interesting. Statistically you are right. But patterns do occur in nature, and the table most of the time does follow runs of colour rather than alternating. You have seen it and i have seen it. We have won both times, and i have lost only 3 times that i can remember using this strategy. Providing you stick to the limit you start out with to lose and win, if you win most of the time you will stay ahead reguardless of what statistics states. Remember they are an approximation of the real world, in the real world over 1000 or whatever spins the casino seems ahead statistically but generally isn’t when you use this strategy. When you lose, only lose the amount you started with limiting your losses. Each time you go if you start with 200 max, leave at say $150 winnings, generally win most of the time, say 80% which is conservative given my experience so far, then after 10 visits you have lost $400 but won $1200 therefore ahead $800. To break even using this strategy using these limits you would have to lose more than 40 % of the time. My experience does not even come close to this. I agree if you keep betting and playing forever with out stopping and starting again with limits then you will lose as those 6 in a row alternating numbers come up then a green, you reach the maximum bet and are cleaned out, but if you stick to the limits you will hopefully avoid that particular moment in time in which the nightmare event occurs occurs, because it DOES occur uncommonly. Each spin is independent and 50:50 but the statistical chance of alternating for six spins is low. You can do the maths.

Love ya

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