Imagine you are participating in a game with a prize money, but there's a entry fee of $5,000.The game has 1 challenge requiring skill (it's not hard, 99% of people can complete it), and then a coin toss game (gamble).1) If you complete the 1st challenge, you get $10,000 and can obtain the money OR continue to the gamble.2) The gamble goes as follow: You can lose your $10,000, or you can gain another $20,000, for a total of $30,000.What is the, matematically, the optimal play, considering hundreds of people will play the game?A) Always stop after the 1st challenge and take $10,000B) Always gamble and either lose everything (including the entry fee) OR gain 3x more than you would gain for stopping.
>>16546395Dumb problem that uses too many words for 1 (one) multiplication for expected value
>>16546398What do you do then, if you'd play many times?Sorry about the use of many words, I wanted to be as clear as possible
>>16546402Unironically ask chatgpt these kinds of homework questions.
>Is the expected reward given a 50/50 to either gain $20k or lose $10k greater than $0kProbability is hard, but it's not that hard.
>>16546395>matematically, the optimal playYou don't give enough information about that, you would need a utility function for an individual to have any idea. To some people losing 5000$ is devastating, to others they'd easily forgo 5000$ to make more, some wealthy people could make more money in the time they would spend playing this game.
>>16546395You have 5,000You spent 5entry and won 10.You get offered a bet to either leave at 5,000, or gamble and either lose 10,000 (your worded differently, but same result "-5,000" if lose or win 25,000(you'd go from 5,000 to 30,000).A 10,000 bet returning 30,000 is generally considered 'fair odds' when the probability is 50%.Any way you manipulate the semantics the value isn't attractive enough to really create a dilemma. Personally? I walk up $5,000. Outside my circle of competence and edge. "Leave your luck while winning, all the best players do it."
>>16546395>50% chance to miss out on winning 10k$>50% chance to miss out on winning 30k$>100 goes -50 for the 10, and 50 for the 30>50 for the 10 = 500>50 for the 30(accounting for the 50% loss rate) = 750>so """statistically""" there's some logic to the 'dontcaredidntread' gambit>but that means you're hedging your bet to the whims of a 50/50 rollI mean, this question has multiple ""answers"".If you are an entity with multiple representatives that are playing this game, then the answer seems to point towards shooting for the three-o-k.If your current circumstances would see significant gain from that 10k, then it's not necessarily unreasonable to go for the secured benefit of the lesser quantity.Idk, it sounds more like a personal problem, more /his/biz/pol/, because in this situation(in this economy?!), it doesn't seem as applicable to attach mathematically-calculable functions to get your answer to the problem.
tldr chatgpt says thisTo determine the optimal play mathematically, we need to calculate the expected value (EV) for both strategies and compare them.Step 1: Entry Fee and Game Costs Entry fee = $5,000 Challenge reward if completed = $10,000The initial out-of-pocket cost for each player is $5,000, regardless of the choice they make.Step 2: Scenario A (Always Stop After the Challenge)In this scenario, after completing the challenge and earning $10,000, the player stops and takes the $10,000.The player's net profit will be: $10,000 (reward) - $5,000 (entry fee) = $5,000 net profitStep 3: Scenario B (Always Gamble)In this scenario, after completing the challenge and earning $10,000, the player decides to gamble, where: If the coin toss results in a loss, they lose the $10,000 they earned, effectively losing $5,000 (the entry fee). If the coin toss results in a win, they gain $20,000 on top of the $10,000 they already earned, for a total of $30,000. Their net profit will then be: $30,000 (total money) - $5,000 (entry fee) = $25,000 net profitWe can calculate the expected value (EV) of gambling. The probabilities of winning and losing are each 50% (since it’s a fair coin toss).Expected Value of Gambling (EV): 50% chance of losing $5,000 (net) 50% chance of gaining $25,000 (net)EV = (0.5 * -$5,000) + (0.5 * $25,000) EV = -$2,500 + $12,500 EV = $10,000Step 4: Comparison Scenario A (Always Stop) gives a net profit of $5,000. Scenario B (Always Gamble) gives an expected net profit of $10,000.Since the expected value of gambling ($10,000) is higher than the net profit from stopping ($5,000), the optimal strategy is to always gamble.Conclusion:The optimal play, mathematically, is: B) Always gamble and either lose everything (including the entry fee) OR gain 3x more than you would gain for stopping.
>>16546395Nah
>>16546993>ChatGPT doesn't even understand diminishing marginal utility/prospect theorygrim>>16546395read Uncertainty, Expectations, and Financial Instability by Eric Barthalon
>>16546993ThanksI made an error >A 10,000 bet returning 30,000 is generally considered 'fair odds' when the probability is 50%.*33% (which means 50% is a value and would be 'fair' 50% at '20,000')Utility / lack of funding or bankroll could change the optimum decision for a specific case, but yes... long-term always bet in this problems scenario
>>16550204Another one that most noobs lack is understanding the Kelly Criterion I've been a gambler in horse racing. The math is very important to understand. Generally not skimming small edges, so it's not a calculation, but it has to be relatively accurate in your understanding, and the edge that you found and opportunity you choose has to be strong
Kelly does a reasonably good job at teaching you appropriate wager size given your bankroll size. It can be smaller than many action gamblers would guess or wantAaron Brown AQR firm..."Poker Face of Wall Street" ...Taught me some additional Kelly Criterion stuff
The markets themselves, in most skill based gambling games should not be ignored.If the bad team (Jets) plays the Good Team (Chiefs) and the line is oddly low (attractive to bet your beloved CHEIFS!!), AND 85% money is on cheifs-6 yet the line doesn't adjust to make any attempts to balance- proceed cautiously. Postmortem analysis the refs called back 2 Chief touchdowns, Chief 14 Jet 10So you note that Jets with bias(downgrade), Chief vs biasHave notes for each performanceIt's a bunch of work.Low hanging fruit is seldom a rare value insight of mispriced offerings
Got me a goddess, show her how to divide it, she still down, and she don't get none of the profits. Pari-mutuel markets, fans pick the favorite, i look for the opposite, Dashing through the city, old S500, flawed favorite, let the power rear sun shade hide me, that's a cold MTHFKR whoever inside it
>>16546993This is why you don't take advice from AI because the quality of the answer reflects the quality of the question and the lack of ability to determine quality. This is also why people especially of the anon variety keep participating in games that only benefit a part of the participants hoping their entire lives that one day they will be in the winner's group. They watch the news and listen to their favorite politicians that the economy is growing, blooming even, with so much fair chance opportunity to win......well you had your fair chance but here you are jacking off to 2D pictures on a Swiss Marine board.
>>16550529can you state this in a way that doesn't involve niggerball? Thank you.
