This was interesting. I parallel played yours and my strategy 10 times. My average win was 126K. Once I had the 1 million in my box, so I ended up with the big prize using your strategy, but that only happens 4% of the time. The last offer was 700K and the other box had 400K in it. But if I take out that game and average just the 9 other games, the average of your strategy was pretty much the same 126K. The only difference was that my strategy had a more even result, 9 times I ended up over 100K (102-173) the smallest win being 68K, and yours had 3 smaller wins (32,52,81) but a few bigger wins (225,231). My strategy was this: take the first offer above 100K or always take the 3rd offer...
Don't really have time to follow up on this. But a simple optimization is possible (hybrid between yours and mine?) But this would involve some math. After first 3 offers, compute the max potential loss (ie the highest dollar box left/# of boxes left), and if it exceeds 20% (30% or whatever) of the offer, then deal. Otherwise continue. You can optimize the threshold percentage.
It's a pretty simple probability problem. Figure the expectation of the game (sum of all prob. * payoffs)/26 = 39,600 Take any offer above 39,600... refuse any below. Playing any other way is gambling...something traders never do....lol.
This is not a correct analysis. The payoff changes with the boxes you choose. You also need to consider future possibilities, just like in poker. Unless you say playing poker is gambling (it's not for people who know how to play it).
Yours won. I did another 10 sets of parallel games, and this time it wasn't so lucky. My average was win was 87K, yours surprizingly the same, 126K. Averaging all 20 games my win average is 106K, yours without the 1 million prize winner 126K counting it lifts the average up to 169K. I call your strategy the "follow through", because about 10-20% of the time it goes all the way, and wins a pretty decent amount, while mine most of the time usually stops in the 100-200K range. In this second set of 10 you had 350,300,294K wins, and I only had a 231K big one. There were 5-6 under 100K wins.... So congratulations, your strategy is better over the long run...
Can't stand the show... The times I've seen it, my favorite scenario is as folows. Say, 5 cases left, only one case above 100K, say 750K, remainder of cases are under 10K, gets an offer in the low 6 figures (100-125K) and turns it down... Ummmm OK!
I don't like the show, either. The game show is the equivalent of the Jerry Springer show. That said, I would sometimes see 5-10 min of the show while channel surfing and laugh at the mathematics of the show. I've always thought that the 'right' way to play the game was simply to take any 'good' deal where the offer was greater than the mathematical expectation of your box. For example, to begin the game, there are 26 boxes containing a total of $3,418,416, therefore, the 'average' box contains $131,477. You should look at this as being the minimum you should expect for a long term average playing this game, as this is what you would average over 1000 games if you just held you box and took what was in it. However, with 'smart' play, you should expect to improve upon this number. After each grouping of boxes are opened, simply divide the total dollar values left on the board with the total number of remaining boxes to determine the expectation of your box. Any offer above this amount should be taken, to ensure your average profit playing this game is above $131,477. In practice (after ten runs myself), the banker always gives pathetically low offers until you have six or fewer boxes remaining. Once you get an offer above the average value of the remaining boxes, you take the offer. For what it's worth, I tried ten times. Best was $389k, worst was 13k and the average was $159.4k. Seemed like ~8 of the 10 times through the game, the first 'fair' offer was made with 5 boxes remaining. While the above is a simple way to 'beat' the 131k expectation that you initially have after choosing your box, it might be improved upon by reviewing whether even more attractive offers are made (larger percentage above the average expectation of the remaining boxes) once you get down to less than 5 boxes.
When the show first aired, the expectation was very close to the offers. Now the house offers much lower than the expectation