Doubling bet after a losing hand..

SleightOfHand said:
I was agreeing with you, showing the growth in bankroll over 1 million hands (although that is a smallish sample). Common sense seems to prove that Martingale will work with the conditions of an infinite roll, no table limits, and infinite play time. A losing streak can't last (literally) forever.
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When you assume that you have an infinite bankroll and infinite time, then you must also accept that a losing streak CAN last literally forever. In fact, you WILL have an infinite losing streak. This is a common mistake. When you start talking about infinity, everything changes. You can't assume infinity for part of the equation and ignore the impact of infinity on another part.
 
QFIT said:
When you assume that you have an infinite bankroll and infinite time, then you must also accept that a losing streak CAN last literally forever. In fact, you WILL have an infinite losing streak. This is a common mistake. When you start talking about infinity, everything changes. You can't assume infinity for part of the equation and ignore the impact of infinity on another part.
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Oh really? That is interesting. I didn't think that an infinite losing streak can occur. So does this mean that in our theoretical situation, we can have both an infinite winning AND losing streak? What does that mean? How can 2 opposing events both occur infinitely?
 
SleightOfHand said:
Oh really? That is interesting. I didn't think that an infinite losing streak can occur. So does this mean that in our theoretical situation, we can have both an infinite winning AND losing streak? What does that mean? How can 2 opposing events both occur infinitely?
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That's the problem with handling infinite values; you get funny results. If you have a divergent series (like this one) the concept of a "sum" (win) doesn't really work.

http://en.wikipedia.org/wiki/Divergent_series
 
oh Lord, i dunno :confused: what the heck i'm talking about, just this seems sort of interesting. so Sleight maybe QFIT means it this sort of way.

SleightOfHand said:
.... So does this mean that in our theoretical situation, we can have both an infinite winning AND losing streak?
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yes, potentially speaking.

What does that mean?
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just that the potential for one or the other exists.

How can 2 opposing events both occur infinitely?
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as far as say it happened, lmao well i don't think you could say that, since it would never finish.
maybe you could say if something like that was to happen then the sum of the two would be zero.
but all that doesn't seem to be the point, the point would seem to be the possibility of such potentials.

weird stuff as you know can be like that in quantum mechanics, far as cards it doesn't seem practical. :laugh:
 
QFIT said:
When you assume that you have an infinite bankroll and infinite time, then you must also accept that a losing streak CAN last literally forever. In fact, you WILL have an infinite losing streak. This is a common mistake. When you start talking about infinity, everything changes. You can't assume infinity for part of the equation and ignore the impact of infinity on another part.
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Is that to say that one would be more likely to be a winner using a martingale, if one had simply a very large bankroll and a normal lifetime against a house game with no established maximum? Or are you admitting to the possibility that an infinite bettor with an infinite bankroll might never encounter an infinite losing streak, even though it theoretically lies within the realm of possibility; i.e., go on forever not encountering an infinite losing streak? Is it even possible to talk in terms of infinities?
 
QFIT said:
In an infinite amount of time, all things that can occur, must occur.
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An infinite losing streak and an infinite winning streak are not possible, because if one starts happening, then it precludes the other from happening, therefore, the statement that all things must occur cannot be true, except as a mathematical convention, just not in the real world.

It does seem possible that one or the other could "start" happening, but it could never happen (past tense), because it could never come to a conclusion (i.e., it is infinite). So, if one is happening, the other can never happen.
 
"To infinity ... and beyond"

QFIT said:
When you assume that you have an infinite bankroll and infinite time, then you must also accept that a losing streak CAN last literally forever. In fact, you WILL have an infinite losing streak. This is a common mistake. When you start talking about infinity, everything changes. You can't assume infinity for part of the equation and ignore the impact of infinity on another part.
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Is there not a difference between actually playing for infinitely long with an infinite bankroll, and merely having those infinite resources available to you?

In the latter case, can we have an infinite losing streak, starting right 'now'? If not, then surely a progression always 'works'. At any (finite) stage, you are still just one win away from success.
 
London Colin said:
Is there not a difference between actually playing for infinitely long with an infinite bankroll, and merely having those infinite resources available to you?

In the latter case, can we have an infinite losing streak, starting right 'now'? If not, then surely a progression always 'works'. At any (finite) stage, you are still just one win away from success.
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We can have an infinite losing streak starting anytime. :eek: It's just not very probable. :p
 
aslan said:
An infinite losing streak and an infinite winning streak are not possible, because if one starts happening, then it precludes the other from happening, therefore, the statement that all things must occur cannot be true, except as a mathematical convention, just not in the real world.

It does seem possible that one or the other could "start" happening, but it could never happen (past tense), because it could never come to a conclusion (i.e., it is infinite). So, if one is happening, the other can never happen.
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QFIT never really said that both can happen, just gave us a philosophical/mathematical cliche :laugh:. If one event prevents the other from occurring, a single infinite session can and will have a single "occuring" infinite win OR lose streak. However, given an infinite number of sessions, there can be an infinite number of infinite losing and winning streaks. Valid?

Perhaps you can't combine infinite sessions, as a session has a defined length of time.
 
London Colin said:
Is there not a difference between actually playing for infinitely long with an infinite bankroll, and merely having those infinite resources available to you?

In the latter case, can we have an infinite losing streak, starting right 'now'? If not, then surely a progression always 'works'. At any (finite) stage, you are still just one win away from success.
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If you can have an infinite bankroll and infinite period of time, then you can have an infinite losing streak starting right now. Again, you cannot assume infinity for part of the problem and ignore infinity for the rest of the problem. If you run an infinite number of such potentially infinite tests and average the results, then YES, you WILL have an infinite losing streak starting at the first bet in one of those tests. (Actually, this will occur not once but an infinite number of times.) And the average EV will be negative.

Once you bring infinity into a problem, what goes for common sense isn't so common.
 
It's important to understand that infinity is NOT a really big number. It is something very different. As an example, there are an infinite number of positive integers. There are also an infinite number of negative integers. There are also an infinite number of real numbers between any two integers, say between 1 and 2. And that's just one dimension. Add one more dimension and you multiply by even more infinities. The odds of picking any one of those infinite numbers is infinitesimal. Yet, if you pick a number, it is picked even though the chance is of it being picked is infinitesimal. An infinite number of infinitely unlikely events exists in infinity.

It really makes no sense to talk about statistics in a situation that includes infinity. Any discussion of statistics must include bounds.
 
QFIT said:
It's important to understand that infinity is NOT a really big number. It is something very different. As an example, there are an infinite number of positive integers. There are also an infinite number of negative integers. There are also an infinite number of real numbers between any two integers, say between 1 and 2. And that's just one dimension. Add one more dimension and you multiply by even more infinities. The odds of picking any one of those infinite numbers is infinitesimal. Yet, if you pick a number, it is picked even though the chance is of it being picked is infinitesimal. An infinite number of infinitely unlikely events exists in infinity.

It really makes no sense to talk about statistics in a situation that includes infinity. Any discussion of statistics must include bounds.
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Mmm I see. Yea, I agree that using infinite is not very useful for our discussion, but it sure is fun :)
 
Nice explaination

QFIT said:
If you can have an infinite bankroll and infinite period of time, then you can have an infinite losing streak starting right now. Again, you cannot assume infinity for part of the problem and ignore infinity for the rest of the problem. If you run an infinite number of such potentially infinite tests and average the results, then YES, you WILL have an infinite losing streak starting at the first bet in one of those tests. (Actually, this will occur not once but an infinite number of times.) And the average EV will be negative.

Once you bring infinity into a problem, what goes for common sense isn't so common.
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To add-on:

Consider sample of 2 trials: Assume win prob=0.49
You will lose both = (0.51)^2 == 1 out of 4 player will go broke

Now n=3, prob(lose all)=(0.51)^3 >0 == 1 out of 9 player will go broke
Now n=4, prob(lose all)=(0.51)^4 >0 == 1 out of 16 player will go broke
Now n=100000, prob(lose all)=(0.51)^100000 >0
1 out of <.....> will go broke

For every n, there will be a probability that you'll lose it all which can be very small tends to zero but will always be greater than zero.
For n=infinity,
1 in (infinity)*(infinity)=(infinity) player will go broke due to infinite losing streak.. sounds fun :)


On the graph posted here http://www.blackjackincolor.com/useless4.htm

Player's bankroll is actually growing/moving downward with time. It'll be up 99% of the time, but 1% of the time when it is -ive. -ive(value of -ive) will overcome the +ive. Whether u ends as a winner or loser, depends on when u ends the sample. But with time, your average bankroll is keep decreasing oscillating around -ev of the game.
 
QFIT said:
It's important to understand that infinity is NOT a really big number. It is something very different. As an example, there are an infinite number of positive integers. There are also an infinite number of negative integers. There are also an infinite number of real numbers between any two integers, say between 1 and 2. And that's just one dimension. Add one more dimension and you multiply by even more infinities. The odds of picking any one of those infinite numbers is infinitesimal. Yet, if you pick a number, it is picked even though the chance is of it being picked is infinitesimal. An infinite number of infinitely unlikely events exists in infinity.

It really makes no sense to talk about statistics in a situation that includes infinity. Any discussion of statistics must include bounds.
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Infinity is not a number at all. As Qfit stated it is merely a word to describe a process or situation without bounds. And without bounds... all is possible. :whip:
 
What really makes the discussion all the more ridiculous is the concept of an infinite bankroll. This is a contradiction in terms. The existence of a bankroll presupposes that society has divvied up limited wealth in some manner and that your bankroll consists of countable script of some sort (money, chips, seashells, whatever) to represent your share of existing wealth. Bankroll has no meaning if wealth is infinite.
 
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