Deal or No Deal Strategy - Expected Value
HTML-код
- Опубликовано: 25 янв 2025
- The Perfect Strategy for Deal or No Deal Games. This is a mathematically perfect strategy, including a discussion of probability and expected value, not a video of someone getting extremely lucky. They are two very different things. Produced by @riskoriented and www.riskoriente...
Игры
As a viewer and when I play computer game, my strategy is if I can get at least $100,000 AFTER taxes, then I take the deal. That's how I would play it if I was on the show.
How does this approach account for risk? For example, a player with only 10k, 25k, 50k, 75k, and 100k remaining would have an expected value of 52,000. Yet, a player who have not opened up a single case on the left side, but has nothing but the 750k on the right, would have an expected value that is similar to the first player's. Is there a way we can supplement this by adding some sort of risk factor to this value?
You could introduce the median value and use that as the equity instead.
It's called Fair Deal and a version of it was used for the banker's offers in the UK version. You take the square root of all the boxes/cases remaining individually, sum them, average that, and then square it back out.
The banker never gives an offer above EV...that's the 'house edge' in this game
actually they do , I have seen 130% on one show
@@oldconspiracydude236 then thats just stupid
@@mrmarkius4855 Well it's not a casino, it's a game show. The math is different.
They never have a house edge, they're giving money away for free.
Lol, I have no idea what's going on! I just need the formula for my ACNH deal or no deal game I'm hosting
In the end when you are asked to switch the cases it actually does really matter what you do.
How? It’s a random selection during the reveals so 50/50 at the end.
ruclips.net/video/r6qg4NaUvfI/видео.html it doesnt. Its not an example of the monty hall problem
@@morbideddie no its not. The fact all the other cases have been revealed increases the odds that the the case at the end is not $1
@@bigbeefe yes, increases it to 50%. Exactly the same as with the 1mil, there is no bias in the reveals to no bias between the final boxes. 50/50 chance of containing the 1$ or 1mil for both boxes.
@@bigbeefeif you're thinking of the Monty hall problem, it doesn't apply here
1st of all why are you basing it on an equity and where does that equity amount come from don't you want to base it on the odds the game is based on luck but the only factor you can play is on the odds
If you want to reduce the standard deviation of winnings. Could setting a percentage of equity help with that.
how do you amke this table
Can you talk about incorporating kelly criterion into this game? I would rather use that than try to assess my own utility curve.
bobtheguy Kelly only matters if you're going to get to play DOND an unlimited number of times and there's a wager attached to playing the game. If this was ever offered in a casino, it's likely that it would be offered at a negative EV level overall. In this case, we get $131k just by playing due to our equity -- if we were charged $100k to play it, we'd jump on the chance. If we were charged $150k, we'd never play.
This was a terrible strategy for the game. First of all, the game host particularly mentions that the banker will always try to buy the case for as cheap as possible, meaning that his offer will always be lower than the average value of the chosen case. This strategy essentially tells the player to never make the deal. Secondly, and most importantly, the actual odds at the end (the switch of the cases) were never mentioned. The odds there are highly stacked up against the player's case; they are not 50 - 50 %. From the moment someone picks a case, they have a 1/26 chance of getting the million dollars and a 25/26 chance of getting anything else. If all the cases except for the million dollar one are revealed, switching would be the absolute best choice, because your case never leaves the 1/26 odds of containing the million; therefore it is much more likely that the leftover case contains the money (Monty Hall Problem).
@alexandra delliou This is not the Monty Hall problem, as the Monty Hall problem only increases your odds because the host knows which door has a goat, and he opens that one for you. Once you've opened every case but one, that remaining case is still just as likely as yours to be a big winner. Misapplication of statistics you don't understand makes you look dumb.
As far as "buying the case as cheap as possible," no, there are times where the banker has offered slightly more than the EV of the case. I believe the premise is the "banker" has no insider knowledge of what a case is worth - of course, if we believe there's behind-the-scenes scamming going on, then the statistical analysis of this falls short of giving you a good strategy, and the best strategy would be to go to the "banker" and offer to split your winnings after the show if he tells you the best case.
Monty hall does not apply here since the case selection is random and not targeted. This is closer to the monty fall problem and is 50/50 at the end.
Monty has the information of the outcomes behind the doors. This is not a Monty hall problem.
I’m pretty sure the banker won’t give you a good price
It actually does matter if swap or don't swap at the end. You always swap because that is a 1/2 chance of getting the higher price; where as when you first picked your case that was a 1/26 chance of getting the highest price. It's called the Monty Hall problem... Look it up, Numberphile did a video explaining it with math.
Oops not a 1/2 chance a 25/26 chance... I think.
It doesn't matter whether you swap or not because Deal or No Deal is slightly different to the Monty Hall problem. In the classic Monty Hall problem, "Monty" knows which door has the car and which doors have the goat and so he always chooses a door with a goat in order to give you a choice. This means that you should swap in the Monty Hall problem as Numberphile explained (although personally I think the singingbanana explained it more clearly for people who are not as experienced in mathematics). However, in Deal or No Deal, the contestant doesn't know what is in each box and so it is completely random as to whether or not the higher value is in the "swap box". I hope this makes sense.
Furthermore, this video is false in saying that this is the "perfect" mathematical strategy. In fact, a better strategy would by to find the average of the utilities of each sum of money and compare that to the utility of the banker's offer. You should obviously take whatever has higher utility to you. Unfortunately, the utility of different sums of money is different for every individual who plays so it is impossible to give a specific "optimal strategy". For example if Bill Gates played then the sums of money would all have low utility to him but to someone who was not as rich as he was (I mean a normal person lol because no one in the world is a rich as he is according to Forbes) then the sums of money would have much higher utility but would also go up very quickly at the start and then gradually slow down. I don't feel I have explained this very well at all so I advise you to read the book which I will leave in the bottom of my comment if you do not understand already despite my incredibly poor explanation.
If you don't already understand the Monty Hall problem or why it is important that the host knows which door has the goat, I advise visiting singingbanana who did a video on it. It is Dr James Grime's channel and Dr James Grime is the most frequent expert on Numberphile anyway. If you don't understand the idea of utilities of different sums of money there is a great maths book called "How Long is a piece of String" (which is the sequel to "Why do Buses Always Come in threes" which is also a great book but not relevant to this comment as far as I can remember) and there is a section in there about Who Wants to be a Millionaire which explains are very similar idea but obviously in the context of a different game show. I hope this is a helpful comment.
Matthew Barber Agreed on all counts. This isn't intended to be a video discussing utility theory -- but expected value. Personally, I'd take the first offer, if given the chance, even though it's hugely negative EV. $58k means no more student loans! I wouldn't flip a coin on that kind of bet.
THATS NOT HOW IT WORKS LOL SO STUPID
It is a Monty hall problem. Hundreds of professors couldn't get the reality of the Monty hall. In the last 2 cases, if you swap. You have a 66% chance of winning. This test has been done a recorded a million times.
Where can we play deal or no deal online by the way?
Well, there is a Deal or No Deal app that has a very small chance of rewarding you a prize.
I would disagree, I think it would matter which case you choose. Wouldn’t the Monty hall problem conclude that you should switch?
No, the Monty Hall problem only works because the host gives information by removing a door that is guaranteed to be a goat thus changing the conditional probability compared to if he chose a door at random. You could wittle all the briefcases down to $100,000,000 and $1 prize and the probabilty of you choosing the correct case or switching would be the same because the information revealed is random. Monty Hall would only apply if you were guaranteed to never pick the highest value briefcase remaining.
The probability of choosing the each value is the same in this game, so the Monty Hall does not work.
How does the equity change each round depending on your choices
The expected value of your box is the mean of the values left in play. The reason is because the box has an even chance of being any of the values and so we can assess the average value of the box based on what’s left in play.
The best strategy would actually be to write down what each case you open contains, and let us say you open a case number 9 with 100 000 USD, which is a relatively high amount I would try to open number 8 and 10 immediately as i would consider it less likely that 3 cases in a row contain high sums of money and i must also admit i fear number 1, 10, 20 and 26, but of these i think number 10 and 20 is the most scary ones and 1 the least scary one. And i do not agree on the strategy as I would have a very high focus on stopping in the right time, and that is the round before you feel you have to, let us say you have only 3 huge amounts, and have a round you have to choose 3 cases and 2 of them contain the huge amounts, then the offer drops significantly and you are practically done. Anyone playing will always compare their bid with the highest amount possible to win, usually 1 million dollar, and then of the offer is upto 200 000 USD they do not want to stop because they fear they lose the opportunity to hit the right case with 1 million dollar, so it is like og no, i lost 800k usd rather than yes, i just won 4-5 years of income.. and taxfree!. It is quite insane how greedy even families have acted on this show and some lost 200k USD by beeing greedy and one of the parents did not even have a job, and these people were not rich at all. I think the show likes to choose people with no real understanding of big money and that they should have professional guidance as they play.
That's the gamblers fallacy.
Every sequence of cases is equally likely.
They're just as likely to be clumped together as they are to be spread apart.
Any link for this
Geez, talk about trying to act smart. Bro, have you ever heard of a median? If you have 3 cases left, 1 penny, $1 and $1,000,000, and the banker offers me anything over $150-200k, you bet your damn life I'm taking that, despite the "equity" (AKA the mean) being "higher", because the median is a dollar. Only an idiot wouldn't take that.
As another point, how much more could $1,000,000 change your life that $200,000 couldn't, especially if you are smart with your money. I suppose it depends on what you value, but to compare a simple average against the banker's offer as grounds for decision making is ludicrous.
This is where the limitations of EV begin to show themselves. Money does not have linear value, it has diminishing returns. 200,000 dollars is not worth twice as much 100,000 dollars to most people. Life changing money values have their own intrinsic value beside the pure worth of the currency, once that point is reached there are diminishing returns on how life changing the money is.
@@arandombard1197🤨huh?
Incorrect. This only works if you get to play multiple times. In a single game with real world implications this isn't the correct strategy.
Then what is?
@@nrknice I have a good general idea, but it's very complicated. The first thing we need to do is look at it as an investment instrument as opposed to a game show. Then we ask ourselves based on.our current financial situation how much are we comfortable losing on our current offer? If the amount is more than we are comfortable with we stop. If not we keep playing. Generally for a normal middle-class person about 50k is the max you'll be able to shrug off. It be nice, but it won't change your life. Generally once your offer hits 80%+ of the average or 150k you should stop. The reason for both of them is at 80% you're getting a good return and losing the risk of continuing to play. You can push your luck if it's a low amount but generally taking the sure money and investing it for a year is better than risking it. Also once you hit 150k even with a very good board you should generally stop. The reason being that generally you never play to the end in any case. And to get more money requires not only getting the right cases out, but getting them out in a certain general order. Imagine this. You have 1M 500k 300k 50k 100 and 1 dollar. Even if you were going to keep the million in for the final 2 cases, it doesn't matter if you don't get 4 of those cases out in the right order. For instance if you get out 100, 1 then 500k then 300k. You can walk with 500k at rhe end. If however the order is reversed, you would never know you would have that final 2 cause youd be forced to stop due to no safety net. So even in the reality where you were going to get a solid final two, it didn't matter due to the order. The game is designed for you to like your odds if you have a good game, only to walk on a bad offer when left with only 1 good case. The vast majority of people leave on a decreased rather than increased offer due to this. There is a lot more, but it gets super involved.
Everything was OK but at the end statistically you always switch the case
Not in Deal or no Deal. It’s 50/50 since the reveals are random and not deliberate. Without a bias in the game there cannot be a bias between the doors.
@@morbideddie When there are two briefcases left, it must be switched based on probabilities change of variables.
.
In other words, the probability that the new random variable Y will be in an interval [c, d] is defined to be the probability that the old random variable X will be in the transformed interval [g(c),g(d)] = [a, b]. To begin with, Equation (1) is just a rule for assiging a real number to each interval [c, d].
.
If you do the math at the beginning of the game the probability of choosing the right briefcase is around 3.85% But at the end of the game the probability of choosing the current briefcase increase to 96.16% by just switching the briefcase.
.
By the way I'm not a mathematician just a numbers enthusiastic maybe a mathematician can explain it better or correct any errors in my calculations in the comments.
@@theendoffaith5903 I have done the maths, your position is simply incorrect. You could equally argue that you had a 3.85% chance of picking the 1$ so switching gives you a 96.15% chance of winning.
If there are n boxes then in 1/n games you pick a certain value and 1/n games you leave a certain value. There is no weighting or distinction between them. When you reach the final round with $x and $1,000,000 the odds that you picked the 1m originally and the odds you didn’t and managed to avoid it for n-2 picks are exactly the same.
@@morbideddie You making me work on this on a Sunday 😂 I did a little more digging and you’re probably right at the end it’s about 50/50 chance 👍
@@theendoffaith5903 yeah, Sunday isn’t the best time for maths conundrums lol.
While DOND superficially resembles the Monty Hall problem it is actually analogous to the Monty Fall problem where the host trips over and reveals a door. Same action but the probability is entirely different because the intent and behaviour of the host also gives us information.
Sabi SA deal or no deal ang regulations sabi mo deal pindutin kung no deal isara