Re: current trades
This is the ultimate example: http://en.wikipedia.org/wiki/St._Petersburg_paradox
Both you and Litodude have pretty much explained this, but I just felt the need to throw some math in here.
In this game, you begin with a pot of $2. You flip a coin. If it lands tails, the game ends and you take the pot. If it lands heads, the pot doubles and you continue / repeat the process again. What's the expected value of this game? (1/2)*2 + (1/4)*4 + (1/8)*8 + ... and so on. This reduces to 1 + 1 + 1 + 1 + ..., which implies an infinite expected value.
In other words, you should be willing to pay *anything* to play this game. And yet, in practice, you would go bankrupt playing this if it required a nontrivial participation / transaction cost relative to your wealth. Why? Because hitting the huge payouts takes a long, long time. In the meantime, you would burn through a ton of money.
If you have "infinite" (or crazy insane huge) wealth, this game is fine because you can continue to play and eventually win all your money back and then some. But of course, this calls into question practical concerns, like why you'd be gambling in the first place if you had that much wealth, or why you'd be participating in such an inefficient game.
Here's a Python program I slapped together to illustrate. You can play around with the cost and initial wealth parameters:
In real life, of course, this sort of thing operates on much smaller scales, but the underlying point is similar. If you have a lot of starting wealth relative to your costs, you can afford to screw up a lot because through sheer brute force alone, you'll hit a winner eventually.
This is the ultimate example: http://en.wikipedia.org/wiki/St._Petersburg_paradox
Both you and Litodude have pretty much explained this, but I just felt the need to throw some math in here.
In this game, you begin with a pot of $2. You flip a coin. If it lands tails, the game ends and you take the pot. If it lands heads, the pot doubles and you continue / repeat the process again. What's the expected value of this game? (1/2)*2 + (1/4)*4 + (1/8)*8 + ... and so on. This reduces to 1 + 1 + 1 + 1 + ..., which implies an infinite expected value.
In other words, you should be willing to pay *anything* to play this game. And yet, in practice, you would go bankrupt playing this if it required a nontrivial participation / transaction cost relative to your wealth. Why? Because hitting the huge payouts takes a long, long time. In the meantime, you would burn through a ton of money.
If you have "infinite" (or crazy insane huge) wealth, this game is fine because you can continue to play and eventually win all your money back and then some. But of course, this calls into question practical concerns, like why you'd be gambling in the first place if you had that much wealth, or why you'd be participating in such an inefficient game.
Here's a Python program I slapped together to illustrate. You can play around with the cost and initial wealth parameters:
Code:
from random import randint
costPerGame = 20
wealth = 1000
#------------------------------------
trial = 0 #to track how many games we play
print "starting wealth =", wealth
while 1: #play as long as we can
pot = 2 #initial pot
numHeads = 0 #to track how many heads we've flipped in this single game
while 1: #play the game
coin = randint(1,2) #flip the coin
if coin == 1: #heads
numHeads += 1
pot *= 2 #double the pot
elif coin == 2: #tails
break #we cash out, break the while loop
wealth += (pot-costPerGame) #profit = revenue - cost
trial += 1
print "trial =", trial, ", numHeads =", numHeads, ", cost =", costPerGame, ", payout =", pot, ", wealth =", wealth
if wealth < costPerGame:
print "You can no longer play!"
break
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