I've being reading and reshearching for so long and with your video I understood in 10 min what I didn't in days of reading, thanks.
@KBRATM895
7 жыл бұрын
This is the 3rd video I watched in the channel today, and the straightforwardly explanation is amazing! Thank you Ronald!
@ShwetankT
5 жыл бұрын
Please correct me if I am wrong. X = number of tosses for the first tail. E[X] = 2. Thus expected payoff = 2^2 = 4. Thus, one should not care much about this came in a Casino.
@jacqueshollands5630
Жыл бұрын
Excellent explanation, thank you.
@Knot2goodAtIt
9 жыл бұрын
Its so convenient that I just got homework on this and this video was just made!
@EseKanayo
5 жыл бұрын
thanks this helped me clarify the paradox
@criticalvalue
7 жыл бұрын
great stuff!!
@cach_dies
6 жыл бұрын
I got that the expected utility is about 1.386 witch if used as the exponent of 'e' gives 3.999. So I think there is a mistake in the vid.
@suprajavadlamani8484
5 жыл бұрын
that's correct. $4 is the premium people would be willing to give to engage in such a gamble.
@robertbrandywine
5 жыл бұрын
The best treatment of the game I have read is here: medium.com/@thomasafine/the-saint-petersburg-paradox-is-a-lie-62ed49aeca0b
@mario34129
3 жыл бұрын
The expected value is a number which we should expect to be our average of n number of outcomes. For example, if you roll a dice 1000 times, you can expect that the average outcome is 3.5. Now if we simulate St. Petersburg experiment for as many times as we like, I am pretty sure the average outcome will never be anything "close" to infinity. For example, we will never encounter a series of, let's say 100 tails or more. That's why I can not accept that the expected value of this game is infinity, it will never happen in real life. The real expected value should be what we can observe empirically by making n number of simulations, n being a big number.
@asmaoli7064
3 жыл бұрын
thank's so much this is so helpful
@ronmatthews1738
6 жыл бұрын
The rational gambler would definitely not pay large amounts of money to play this game. Expected value is infinite, but it is infinitely unlikely that the gambler will get the infinite payout. Try running this simulation of a $20 stake to see how quickly you start losing money and how much you lose in reality. www.mathematik.com/Petersburg/Petersburg.html This is not a paradox, but a fallacy.
@Knot2goodAtIt
9 жыл бұрын
Quick question, how did we know to choose log($)?
@Tadesan
5 жыл бұрын
Knot2goodAtIt im surprised nobody answered. Im curious too. I wonder if it’s just a guess.
@nickergodos1554
5 жыл бұрын
@@Tadesan It's just a guess.
@petrosprastakos
4 жыл бұрын
Any sort of concave function is fair game I believe. Could be sqrt($) for example. As long as f' > 0 and f" < 0
@robertbrandywine
5 жыл бұрын
I must not understand because why would I pay much more than $2? If I play, I stand a very poor chance of getting past the first toss.
@RonaldMoy
5 жыл бұрын
But that's he paradox. The idea is that we need to look at expected utility, not expected value.
@robertbrandywine
5 жыл бұрын
I mean the literal mechanics. If I play and lose after the first toss, is that the end of the game, or do I get to take the $2 I won and toss again?
@RonaldMoy
5 жыл бұрын
The game ends and you get your $2.
@robertbrandywine
5 жыл бұрын
Since I asked the question, I've decided it is just the opposite or the whole question makes no sense. The way you say it works, the entry fee is a BET on how the first round would turn out. Instead, I think it is an entry fee to play the game. So, you pay some entry fee, and then are allowed to play the game indefinitely -- you will never lose all your money since you always get $2 per coin toss OR the right to toss again, pushing off your payoff (but it is larger). And there, also, is the answer to the paradox. People are not understanding that it is a game entry fee. They view it as a bet. If people understood that this is a money-producing machine that pays on average $1 with each toss of the coin, how much they would pay to put themselves in this situation depends on how long they foresee themselves wanting to sit at a table watching coins getting tossed and part of the equation depends on how frequently the coin is tossed. One coin toss per 24 hours wouldn't be worth nearly as much as one coin toss every 5 seconds. It also depends on how wealthy they are. A wealthy person wouldn't want to play the game at all. An impoverished person would want to play as long as they could stay awake.
@ShwetankT
5 жыл бұрын
@@robertbrandywine Hi, I still could not get it. This is how I thought of it when I read it first: X = number of tosses for the first tail. E[X] = 2. Thus expected payoff = 2^2 = 4. And thus, one should not care much about this came in a Casino.
@ancyjohn7750
4 жыл бұрын
Why it is called st petersburg paredox??
@RonaldMoy
4 жыл бұрын
The paradox takes its name from its resolution by Daniel Bernoulli, one-time resident of the eponymous Russian city, who published his arguments in the Commentaries of the Imperial Academy of Science of Saint Petersburg (Bernoulli 1738).
@ancyjohn7750
4 жыл бұрын
Thankyou
@shanejohns7901
4 жыл бұрын
Never play a game where there are potentially infinite winnings for the simple fact that the loser could never pay up!
Пікірлер: 28