Ok, so I counted the squares on the board, and there are 133, including 4 that make you stop dead in your tracks when you land on them. (meaning that if it’s 2 spaces away, and you spin 8, you just stop on that space that’s 2 away.)
The spinner goes from 1-10. Stocks you buy for 50k, and when anyone spins that number, you get 10k. The stocks go from 1-9.
So my question is, how would I figure out whether or not it’s worth it to buy stocks with how many people in the game? I figure that if the average spin is a 5 (in the middle of 1-10), that’s about 26 spins per person, which means that each person will spin each number 2.6 times. So I figure that with 2 people, each number is spun 5.2 times, for an average of 52k money, when I only put 50k in, meaning that as long as I’m not playing with myself (heh), it’s always worth my money to buy them.
I think it’s more complicated that that, 2nd grade jokes aside.
You should tally up the number of possible moves and look at their distribution. For example, if the first stopper is at spot #12, then the first two squares permit all ten moves, and then the third square permits 1-9, and the fourth 1-8 (with 9 and 10 spins yielding only 8 moves). You could even write a short script to simulate a bunch of games with different players, where the only thing you track would be the outcome of a stock.
If the stoppers are at 13, 21, and 44, for example, you would spin until you reached or exceeded 13, then spin again until you reached or exceeded 8, then spin again until you reached or exceeded 23 – keeping track of total number of spins made. The output would be easy: which numbers were “winners” and which ones were “losers” over the course of the game.
I’m betting that the stocks almost always pay off with four players, break even or make very little with three, and are a risk with only two players.
I’m not up to the heavy math, but I always buy stock on “1” in Life, figuring that while my opponents may spin any number, spinning 1’s will result in the need of making more spins, which gives the opportunity of yet more 1’s being spun. Or am I totally out in left field…
You also need to figure out what else that 50k could have been put to if you didn’t buy stock. If your money could be used more profitably somewhere else, then buying stock, even with a positive expected return would not be a good idea.
This principle is known as oppurtunity cost in economics.
There’s also the question of when you buy it. In the version I remember as a kid, you didn’t get to buy stock until some way down the board. It’s only the rolls (and therefore the board squares) after the stock-buying squares which would matter for this calculation.
But then, this game seems to change radically every few years, and my memory’s not all that anyway, so this may not be accurate.
Well, that is an issue. The thing is, we don’t use the right amount of money to start out… we just get 2 of each bill and leave it at that, meaning that as long as no one else buys any, I could buy 7 of them.