Gambler's Ruin & Random Walk: Probability, Expectation
Gambler’s Ruin - University of Washington
MathPages
(PDF) Gambler’s Ruin: The Duration of Play
Gambler's Ruin Problem（赌徒破产问题）研究总结 - 简书
Week 4: Gambler’s ruin and bold play
1 Gambler’s Ruin Problem - Columbia University
Random Walks 1 Gambler’s Ruin - MIT
gambler's ruin
gambler's ruin - win
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Say what you want about the DCV, but Gambler's Ruin and Kell's Grave finally being removed is a huge win.
Seriously, how did these maps even get through play-testing? They play horribly as well as look awful. "Wow look at this beautiful environment where literally every wall or floor is the same exact rust texture." Please stop making maps on the Tangled Shore's interior. Crucible/Gambit maps set on the floating asteroids rather than the ugly rusted interior would be much better in my opinion.
Hi, I created this interactive dashboard to show the concept of gamblers ruin and how you can go bust very quickly even with favourable odds. I would love some feedback: - Are there any other graphs or stats you would find useful/important? - Is it easy to understand? How could it be made more user friendly? - General feedback https://gamblers-ruin1.herokuapp.com/ Thank you
Please do remove Gamblers ruin from all crucible playlists.
Gamblers ruin is the (previously ps4 exclusive) smallest map in the crucible, this has lead to it's spawns being in sightline and spawnkilling to be a constant on it. Due to it being a problem in every gamemode except doubles i reuest it be removed from all other playlists.
I was looking into the skybox and saw a giant ship. Is this the vestian web where the vestian outpost is located? Also is there any lore behind gamblers ruin or is it just some crucible map in the middle of the reef?
Gambler's ruin, kelly criterion, optimal bet sizing, and how to avoid losing all your tendies
What up autists, I know we all respect the YOLOs from the people who wave their giant smooth gorgeous bowling balls around and put 100% of their bankroll into huge trades, but my wife's boyfriend was telling me that this isn't always the smartest thing to do. According to some nerd math shit called Gambler's Ruin https://en.wikipedia.org/wiki/Gambler%27s_ruin, apparently even if you are bigly expected to win in any bet, if you bet too much or don't size down when you start losing, you'll eventually lose all your tendies. And since you need tendies to make tendies, no one wants that. So what is the optimal betting size then? Fortunately some other nerds have figured out this math thing called Kelly's Criterion that tells you how much you should bet. https://en.wikipedia.org/wiki/Kelly_criterion I know what you're thinking: "Math shit??!!?? I can barely read, much less do fucking math! Just tell me what to do!!!" Well fortunately, even if you can't do math, you can just go https://dqydj.com/optimizing-bet-sizes-with-the-kelly-criterion/ and input some numbers and it'll tell you what to do. For example, if you think that your 6/9 420 Tesla puts have a 50% chance to hit, and if you hit it pays off 2:1 (win 200 on a 100 dollar bet for 300 total dollars) and you have a bankroll of say 1000 bux, you can input those numbers into that website and it tells you you should bet 25% of your bankroll on each trade. The key thing here is that on the rare chance that you lose, YOU NEED TO SIZE DOWN YOUR NEXT BET TO 25% OF YOUR NEW BANKROLL. So, if you lose, you have to bet 25% * 750 (remaining money) and only bet 187.5 dollars for your next bet. If you don't size down when you lose, you will go broke, regardless of how good you are at picking options. And nobody wants to be out money to no longer be able to trade. TLDR: SPY 1 month 5% OTM puts with 10-20% of your bankroll (depending on how confident you are), size up or down repeat weekly with new bankroll size until you get all the tendies.
Personally I think it's a pretty cool map, with lots of different areas to fight in and around. I find this map not just people holding down lanes because there are so many avenues you can take, which makes it fun! All I see anytime this map is mentioned though is hate hate hate. Sure, MAYBE they could adjust spawns a little, but the map itself is fun, and interesting compared to all the other maps that are "pick one of 2-3 snipe lanes and hope you're better than the other guy".
Bungie, pls remove Gambler's Ruin map from 6v6 crucible game modes
Gambler's ruin is one of the most broken maps I have ever played in destiny's history. It is way, way too small for 6v6, there is no sense of flow or control, spawns will often place you right in the middle of the enemy team, capture points are completely broken in control, heavy spawn favors outside way more than inside, and the list goes on and on. It has a very similar layout to vostok (major sections of the map divided by a single, central tunnel/pathway), but its probably around a third of the size. Vostok is already a pretty unpopular map, but gamblers ruin is just a much smaller, and significantly more broken version of it in nearly every way. Vostok has three major areas; A flag, the lone building that overlooks the very long, straight sightline on the left side of the map, when facing B flag. Then, you have B flag itself, a large platform with two towers on either side, that provides a great control point for central map control, as it gives you access to heavy, as well as allowing you to see all three major sightlines. Finally, C flag, the domed building, which offers a good amount of protection, as well as the best sightline for accessing mid tunnel/B flag. Despite this map's flaws, it still does manage to be decently balanced, at least compared to gambler's ruin. However, when we take a look at gamblers ruin, there are only two major areas, as opposed to three. The two major areas in gambler's ruin are inside and outside. Playing control on this map is absolutely atrocious because inside is given only 1 flag, whereas outside is given not only 2 flags, but heavy as well. In addition, it is far easier to counter players on the inside trying to push outside, due to how the sightlines work, where outside almost always has the upper hand, especially in the tunnel, where outside has two points of entry on either side, whereas inside only has one point of entry, which is smack dab in the middle, making it extremely easy to corner players trying to go outside via the central tunnel. The spawns are also absolutely broken, as I think anyone who has played on this map can attest to. The game will so often put you in direct line of sight of the other team, or just flat out spawn you in the enemy's spawn, leaving you defenseless as three other players spawn up right behind you. More than any other map, I have been killed instantly off of spawn, by a sniper, shotgunner, super, etc. Spawns are also constantly switching due to how the majority of people play the map, especially in QP, where players will just randomly run around the map, creating utter chaos as there are no clear areas of control, since every minute or so, the spawns will be flipped, making it very difficult for players to read spawns, and take advantage of their map knowledge. TL;DR gambler's ruin is broken, should be (at the very least) be removed from 6v6 gamemodes due to broken spawns and unfair map advantages.
Gambler's Ruin, Finding the Variance of Final Wealth?
Hi, I have been trying to solve this problem for ages and gotten feedback from my professor for having the wrong answer. "Alfred and Daniel decide to gamble against each other by rolling a fair dice until one of them runs out of money. At the beginning, Alfred has $40 while Daniel has $50. When the dice lands on 1, 3, 4, or 6, Alfred wins $1 and Daniel loses $1. When the dice lands on 2 or 5, Daniel wins $1 while Alfred loses $1. Find the variance of Daniel's final wealth." The way I approached this problem was finding the probability of Daniel ending up with $0 and the probability of him ending up with $90. Then, I used first principles to find E[X] where X = Daniel's final wealth, found E[X^2], and then found the variance. I used this formula to help me find the probabilities: https://imgur.com/a/C0X0jpV Any help would be appreciated!
Why is gamblers ruin so small when it's in every 6vv6 mode.
It is the smallest map in the game with spawns in direct sight of eachother yet it is in every 6v6 mode. It's like the size of a doubles map or something or a 3v3 map but not 6v6.
Gambler's Ruin would not be missed if it was removed from the map rotation.
I play on Playstation and I have not met a single Guardian in the last year that enjoys this map. It draws a similar ire as Equinox amongst every PvPer. The spawns are truly awful due to the puny map size and has no business being in the game in its current state.
Hi, I have been trying to solve this problem for ages and gotten feedback from my professor for having the wrong answer. "Alfred and Daniel decide to gamble against each other by rolling a fair dice until one of them runs out of money. At the beginning, Alfred has $40 while Daniel has $50. When the dice lands on 1, 3, 4, or 6, Alfred wins $1 and Daniel loses $1. When the dice lands on 2 or 5, Daniel wins $1 while Alfred loses $1. Find the variance of Daniel's final wealth." The way I approached this problem was finding the probability of Daniel ending up with $0 and the probability of him ending up with $90. Then, I used first principles to find E[X] where X = Daniel's final wealth, found E[X^2], and then found the variance. Work: I found P(Daniel ends up with $0) = 1 and the P(Daniel ends up with $90) = 1-1 = 0. Thus, E[X] = 1*0 + 0*90 = 0, E[X^2] = 0 and Var[X] = 0. Apparently, P(Daniel ends up with $0) is not 1. Where did I go wrong in this logic? Edit: I used this formula to help me get the probabilities. https://imgur.com/a/C0X0jpV Any help would be appreciated!
Gambler's Ruin Spawns are atrocious; Please spawn me with my team
This map was NOT designed for the flow of PC gameplay and the spawns directly reflect that. If you're going to give me MLG pro's to play against at least spawn me with my team bungie. Everytime i play this map it's just a pacer test with spawning enemies at the end, you run down, shoot 1-2 guys with your entire team as they spawn and race to the other side to farm whoever spawned over there.
It was the worst fucking experience I've had in pvp in a while. Seriously, the map is the size of a tick and the spawns flip like a skateboard, got constantly spawned in the middle of the enemy team, rushed on corners by one eyed apes, sniped from angles, boxed in by grenades and all that in under a minute, not to mention all the folks that left the first 30-or-so-seconds in the game, well, now I know better. I swear, they got at least 10 easy kills by snipe spawning me. Bungie removed some maps from crucible rotation, but they seriously didn't even CONSIDER taking this one down? Is there any strategy to this map other than just bailing back to orbit?
The Gambler’s Ruin Problem. The above formulation of this type of random walk leads to a problem known as the Gambler’s Ruin problem. This problem was introduced in Exercise [exer 11.2.22], but we will give the description of the problem again. A gambler starts with a “stake" of size \(s\). Gambler’s Ruin: Probability of Winning (when p = q and when p ≠ q) Let’s now calculate the probability of a player winning the entire game given k dollars and with a total of N dollars available, both for when that player’s probability of winning a given turn is 1/2 and for when it’s not 1/2. 1 Gambler’s Ruin Problem Consider a gambler who starts with an initial fortune of $1 and then on each successive gamble either wins $1 or loses $1 independent of the past with probabilities p and q = 1−p respectively. Let R n denote the total fortune after the nth gamble. The gambler’s objective is to reach a total The Gambler’s ruin for fair games: We brie y discuss the case of fair game p= q. In that case the equation for the ruin’s probabilities x j simplify to x j+1 2x j + x j 1 which gives the quadratic equation 2 2 + 1 with only one root = 1. So we have only one solution x j = C. To nd a second solution after some head-scratching and we try the Gambler’s Ruin Math 394 1 The General Problem Suppose two players play consecutive games, where player #1 as probability p of winning any game, independently of the others, and player #2 has winning probability1−p =q. Suppose also that player#1 starts with a capital of c1, and player #2 with a capital of c2. Each time a player wins one unit The Gambler’s Ruin problem involv es a gambler, starting with initial wealth S 0 = M ≥ ν (a positive integer) and playing a series of games, in which the payoff of game t ( t = 1 , 2 , 3 Gambler's ruin applies to any game of chance in which the house has an advantage over the gambler. This includes any casino game played against the casino, such as blackjack, craps, roulette, Keno, and slot machines. The only way to avoid gambler's ruin is to accept that fact that you can't gamble to win, so you should only gamble for the Gambler's Ruin Problem（赌徒破产问题）研究总结 导语. 以下是对“赌徒破产”系列问题的研究总结。通过数学证明，可见“十赌九输”并非虚言。 PS：由于MarkDown不支持数学公式，所以下面问题的证明过程是通过 Daum Equation Editor 来撰写，然后导出图片来展示。 6.042/18.062J Mathematics for Computer Science December 12, 2006 Tom Leighton and Ronitt Rubinfeld Lecture Notes Random Walks 1 Gambler’s Ruin The Gambler's Ruin . You always said the cards would never do you wrong; The trick you said was never play the game too long. Bob Seger . Consider a game that gives a probability α of winning 1 dollar and a probability β = 1–α of losing 1 dollar. If a player begins with (say) 10 dollars, and intends to play the game repeatedly until he
STAT 333 bonus assignment Finite Math: Markov Chain Example - The Gambler's Ruin.In this video we look at a very common, yet very simple, type of Markov Chain problem: The Gambler's R... This video is the fifth in a six-part series on the Gambler’s Fallacy. In this video I show how to calculate the “expected value” of an act, and use this ill... MIT RES.6-012 Introduction to Probability, Spring 2018View the complete course: https://ocw.mit.edu/RES-6-012S18Instructor: Patrick JailletLicense: Creative ... Here’s Gameplay Of PS4 Exclusive Crucible Map Called “Gambler’s Ruin” In Destiny 2’s Forsaken Expansion Destiny 2 Forsaken Is Out Now On PS4 , Xbox One and B... Calculates the probability of obtaining a fortune of N dollars before going bust by betting on red in roulette. We analyze the gambler's ruin problem, in which two gamblers bet with each other until one goes broke. We then introduce random variables, which are essentia...
![[University Maths : Markov chains - Alternating p&q gamblers ruin] how do you find the probability of reaching N for non constant p&q](https://b.thumbs.redditmedia.com/wclr8WsiEq_kw2tprZyr_k1BTtntMUGt2qXn3jHZXVg.jpg "[University Maths : Markov chains - Alternating p&q gamblers ruin] how do you find the probability of reaching N for non constant p&q")
