I need someone to calculate and then explain a very simple (in terms of rules), but who know with things like maths, gameshow type situation. In terms of the likelihood of outcome of multiple repeated (though altered events).
Also to explain the maths briefly, so I can use it myself going forward with different values or number of sets etc.
It’s much clearer if I just explain the game;
It’s a game show, or casino game etc, however you like to visualise it.
There are to start 9 envelopes on a pin board, hidden inside 8 of them is the value £1. Inside the 9th is the value £25. The £25 is considered the winning prize. The £1 is considered a lose. The envelopes are arranged randomly and no one knows where the prize is.
A single person, pays an entry fee of £X. I get to keep that entry fee. They then choose an envelope freely. If they pick the prize envelope then they keep the £25, (but I still have their £X), and the game is over.
It can then be reset in the exact same way as it was before, but with a new random envelope containing the prize. A complete restart of all parameters, no information carries forward.
However, if the first person picks an envelope with £1 in, (I keep their £X, as is always the case), they get to keep their £1 prize. BUT as they chose a losing envelope, the envelope they chose is removed leaving the same 8 envelopes on the pin board that were there before.
Another person can now pay their £X (it is always the same entry fee), and choose from the remaining 8 envelopes. The same rules apply, if they choose the winning prize, they keep the prize, and the game is over, or if the chosen a lossing envelope they get their £1, their envelope is removed, in this case leaving 7 and another player can have a turn.
This is always repeated until the prize is found at which point the game is over.
Obviously the game could end on round 1, and I’d have £X, but the player would have £25. Or it could run until the 9th envelope in which case I’d have (£X x9) and would have paid (£25 + £1x8) in prizes. Or it could end in any round in between with the appropriate fees paid and prizes paid etc.
The question is;
How much should X be set at to ensure a profit over multiple instances of running the game. And over how many instances of the game would you need to run to realistically to be able to avoid a crazy run of luck making you lose just from a string of flukes.
My assumption is this will fall under some kind of distribution curve as in theory all results are possible, ie winning envelope chosen first time every time for ever, but it gets less likely of course, so although guarantees can be made I guess, ther must be a point where likely holds hold up enough for real life situations, as casinos have that same risk surely, and they seem to do pretty well?
I’m perhaps going to code this into excel or something once I get the mathematics of it confirmed and explained.
Hopefully I would then understand it enough to calculate it with different values for the prizes, and entry fees and number of envelopes. And perhaps even for say prizes in two envelopes with the game running until both are found.
Also, I know I posted this in computing, but there was no section for mathematics. I don’t need anything building, just a min explanation of the maths above.
Also, this is a fun project, not a business, the budget here is low I’m afraid, but equally all I really want is a well worded, complete explanation etc, if this stuff is your jam then that may only be a few minutes if work. I don’t expect more than I pay for.
Thanks
Richard |
