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.
Doubling bet after a losing hand..
- Thread starter archer1131
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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
http://en.wikipedia.org/wiki/Divergent_series
oh Lord, i dunno 
what the heck i'm talking about, just this seems sort of interesting. so Sleight maybe QFIT means it this sort of way.
yes, potentially speaking.
just that the potential for one or the other exists.
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:
what the heck i'm talking about, just this seems sort of interesting. so Sleight maybe QFIT means it this sort of way.yes, potentially speaking.
just that the potential for one or the other exists.
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:
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?
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.
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"
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.
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.
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.
Perhaps you can't combine infinite sessions, as a session has a defined length of time.
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.
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.
It really makes no sense to talk about statistics in a situation that includes infinity. Any discussion of statistics must include bounds.
Nice explaination
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.
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.
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.