Talk:Gambler's ruin

message: I'm removing the following text, and moving the external link to the end of the article:
A casino generally has:    
*many more pennies than any player thus ensuring that the player is much more likely than the casino to experience gambler's ruin;   
*odds that favor the casino resulting in negative expected return for the player; and
*various risk management techniques that limits their maximum loss.
The combination of the above ensures that the casino will in the vast majority of cases come out ahead in the long run. For an illustration, see this Gambler's Ruin simulation: 
The first point is misleading; as explained just above this text, the difference in capital does not change the casino's expected return, which is what it needs for long-term profit.  The second point is out of place, and is explained in the next section.  The third point is vague.  --Allen 03:36, 3 May 2007 (UTC)
thread_title:  Removing last part of coin-flip section 

message: I think P1 and P2  exprssions should be exchanged. To see this let p/q -> 1 . then the expression for P1 and P2 in fair case are reversed
87.8.225.48 (talk) 21:32, 23 November 2007 (UTC)
thread_title:  Typo 

message: I also take objection to the notion that the man with more pennies has a negative expected value in this game. It is impossible for the winner of this game to be "scathed." He has won back any pennies he lost, plus all of his opponent's. I am striking the line.  —Preceding unsigned comment added by 75.65.196.71 (talk) 09:15, 31 May 2008 (UTC)
thread_title:  Expected value negative 

message: I hope people think it improves the article.
AaCBrown (talk) 14:57, 16 September 2013 (UTC)
thread_title:  I added a short section on history 

message: It's fine to just give the formulas and show how to use them with examples but there is the beginning of proof showing how to derive the formulas for unfair coins. This looks really promising but it suddenly ends with - look up the rest in a book! 
79.75.159.115 (talk) 13:48, 22 August 2018 (UTC)
replies: text: Not suddenly. This is a general encyclopedia, not a math textbook. Solution of a linear homogeneous recurrence relation is outside the scope of this article, but is explained in "Recurrence relation#Solving and Linear difference equation". Boris Tsirelson (talk) 17:10, 22 August 2018 (UTC)
thread_title:  Lack of mathematical explanation 

message: A constant gambler's ruin, will be inevitable.
But without the game, there'll be nothing.
— 154.48.253.21 (talk) 02:56, 11 February 2020 (UTC)
replies: text: Wikipedia is not a place to publish your own thoughts and analyses WP:NOTFORUM. And, this has absolutely nothing to do with freedom of speech. O3000 (talk) 13:10, 16 February 2020 (UTC)
thread_title:  But isn't our life a constant gambling?.. 

message: For N = 2 and large initial capitals x₁, x₂ the solution can be well approximated by using two-dimensional Brownian motion. (For N ≥ 3 this is not possible.) 
This is completely bogus.  First of all, with N players the question is equivalent to a random walk in an N-1-dimensional simplex (see the quoted reference to Ferguson).  So it is approximated by 1-dimensional Brownian motion.  Second, N-dimensional Brownian motion is a perfectly valid notion — contrary to what an anonymous claimed above.  --Ilya-zz (talk) 08:41, 3 April 2021 (UTC)
thread_title:  N-dimensional Brownian motion