Hello everyone. This is a follow-up on my previous post, which can be found here: https://www.torn.com/forums.php#/p=threads&f=15&t=16156344&b=0&a=0 This may be useful to read, just to catch up on some terminology I use. But it's not necessary.
I was a bit butthurt about some comments on the last post xD, so I figured (since I am in lockdown anyway) I had to come up with something.
I know that this is probably a post that belongs into the gambling section, but, since there are merits to be gained in RR, every torn citizen - gambler or not - will eventually step foot in the casino, or, may otherwise get in touch with this gambling scheme.
The purpose of this post is to elaborate on the infamous martingale betting system and inform people about its severity by providing some intuition without using any mathematics. Imo abstract concepts are best explained using simulation, as human intuition is usually crap when it comes to these things. I am also hoping to encourage discussions.
So what exactly is the martingale system?
It is a betting strategy, where the gambler doubles his bet after every loss, so that an eventual success (after a sequence of losses) will recover all previous losses plus win a profit equal to the original stake. This betting strategy has its origins in the 18th century in France. For those interested, you can read up on it here: https://en.wikipedia.org/wiki/Martingale_%28betting_system%29
I will show an application of this scheme to RR. So let's set the scene:
We suppose that you're always the initiator and that both players are beginners (i.e. no double shots). You go to the casino with a total bankroll of $3 (yes you're poor) and your initial bet is $1. You apply the martingale betting system (because you're a twatwaffle). This means that you bet $1 and if you win, your next bet will be $1 again. But whenever you lose, you have to double your bet, and, you have to continue doing so until your loosing streak ends.
Assume further, that your friends are enablers, and that everytime you go broke, they will give you $3 again so that you can start over. Here, going broke means that the bet that you'd have to place is higher than the money you have available at this moment. It does not mean that you lost all your money.
So now, that we set a scene that is toxic yet still reasonably close to reality, we'll be able to answer some questions.
The first question is: Will you eventually go broke? And the answer is a big YES. If you keep applying this strategy you're bound to fail at some point. But where is that? To answer such a question, one has to understand the distribution of this phenomenon.
So let's play one thousand games (not a very high number) of RR, in the above setting, and let's do this 3 times and have a look at the (empirical) distributions of this phenomenon in each case. This is going to look somewhat like this:
[image: i.imgur.com]
A streak is the amount of games you can play until you go broke. A histogram is a way to look at a distribution. Notice that I had to cut those off on the right, so that you can actually see something. There seems to be some variation in the data.
In the first data-set, represented by histogram of steaks 1, on average, you played 13.88 games before going broke. Best streak was a staggering 1607 games. Which is insane, considering that you started with only $3.
In the second data-set, represented by histogram of steaks 2, on average, you played 12.6 games before going broke. Best streak was 796 games. Which is still high, considering that you started with only $3.
In the third data-set, represented by histogram of steaks 3, on average, you played 13 games before going broke. Best streak was a staggering 895 games. Which is still high, considering that you started with only $3.
So; last but not least, let's look at how one particular steak could look like:
[image: i.imgur.com]
First thing to notice, is that I superimposed (which is a fancy word for lay on top of each other) those two graphs. They both have different scales. The red scale on the left is for the money you have, and the scale for the green one is on the right. It represents the bets you've placed. We are looking at a streak that ended after 17 games. Max money ($12) is at game 13.
$mvec
[1] 3 4 3 5 4 6 7 6 4 8 9 10 11 12 11 9 5
above is the money vector
$bvec
[1] 1 2 2 2 2 1 2 4 4 1 1 1 1 2 4 8 16
above is the betting vector.
Thanks everyone for reading, I hope you enjoyed it! Please comment, discuss and ask questions.
Cheers, Alfred
I was a bit butthurt about some comments on the last post xD, so I figured (since I am in lockdown anyway) I had to come up with something.
I know that this is probably a post that belongs into the gambling section, but, since there are merits to be gained in RR, every torn citizen - gambler or not - will eventually step foot in the casino, or, may otherwise get in touch with this gambling scheme.
The purpose of this post is to elaborate on the infamous martingale betting system and inform people about its severity by providing some intuition without using any mathematics. Imo abstract concepts are best explained using simulation, as human intuition is usually crap when it comes to these things. I am also hoping to encourage discussions.
So what exactly is the martingale system?
It is a betting strategy, where the gambler doubles his bet after every loss, so that an eventual success (after a sequence of losses) will recover all previous losses plus win a profit equal to the original stake. This betting strategy has its origins in the 18th century in France. For those interested, you can read up on it here: https://en.wikipedia.org/wiki/Martingale_%28betting_system%29
I will show an application of this scheme to RR. So let's set the scene:
We suppose that you're always the initiator and that both players are beginners (i.e. no double shots). You go to the casino with a total bankroll of $3 (yes you're poor) and your initial bet is $1. You apply the martingale betting system (because you're a twatwaffle). This means that you bet $1 and if you win, your next bet will be $1 again. But whenever you lose, you have to double your bet, and, you have to continue doing so until your loosing streak ends.
Assume further, that your friends are enablers, and that everytime you go broke, they will give you $3 again so that you can start over. Here, going broke means that the bet that you'd have to place is higher than the money you have available at this moment. It does not mean that you lost all your money.
So now, that we set a scene that is toxic yet still reasonably close to reality, we'll be able to answer some questions.
The first question is: Will you eventually go broke? And the answer is a big YES. If you keep applying this strategy you're bound to fail at some point. But where is that? To answer such a question, one has to understand the distribution of this phenomenon.
So let's play one thousand games (not a very high number) of RR, in the above setting, and let's do this 3 times and have a look at the (empirical) distributions of this phenomenon in each case. This is going to look somewhat like this:
[image: i.imgur.com]
![[image: i.imgur.com]](https://i.imgur.com/wJ9Ugdu.png){kind=link}
A streak is the amount of games you can play until you go broke. A histogram is a way to look at a distribution. Notice that I had to cut those off on the right, so that you can actually see something. There seems to be some variation in the data.
In the first data-set, represented by histogram of steaks 1, on average, you played 13.88 games before going broke. Best streak was a staggering 1607 games. Which is insane, considering that you started with only $3.
In the second data-set, represented by histogram of steaks 2, on average, you played 12.6 games before going broke. Best streak was 796 games. Which is still high, considering that you started with only $3.
In the third data-set, represented by histogram of steaks 3, on average, you played 13 games before going broke. Best streak was a staggering 895 games. Which is still high, considering that you started with only $3.
So; last but not least, let's look at how one particular steak could look like:
[image: i.imgur.com]
![[image: i.imgur.com]](https://i.imgur.com/I2ZIeAz.png){kind=link}
First thing to notice, is that I superimposed (which is a fancy word for lay on top of each other) those two graphs. They both have different scales. The red scale on the left is for the money you have, and the scale for the green one is on the right. It represents the bets you've placed. We are looking at a streak that ended after 17 games. Max money ($12) is at game 13.
$mvec
[1] 3 4 3 5 4 6 7 6 4 8 9 10 11 12 11 9 5
above is the money vector
$bvec
[1] 1 2 2 2 2 1 2 4 4 1 1 1 1 2 4 8 16
above is the betting vector.
Thanks everyone for reading, I hope you enjoyed it! Please comment, discuss and ask questions.
Cheers, Alfred
Mentions: How 'random' is RR really?
![[image: media.giphy.com]](https://media.giphy.com/media/lnz5AsSJTwnkusAOJe/giphy.gif){kind=link}