Scandinavian wrote:For example, say we flip just two times. There's four possible outcomes: heads-heads, heads-tails, tails-heads, tails-tails. If heads is the winning side, we would have the results: $729, $81, $81, $9 AVERAGE: $225
2retire wrote:No. This example is meant to teach you how losing a percent of your money is not equal to gaining that same percentage back. In order to recover from a 70% loss, you need to gain 233.33%. 170% won't cut it; you are guaranteed to lose money.
tadamsmar wrote:I ran across a discussion of this question in a paper by Paul Samuelson on investment management.
You have the opportunity to bet on repeated flips of a fair coin. For heads, you get a 170% gain (for instance, $100 becomes $270), for tails, you have a 70% loss (for instance, $100 becomes $30).
Would you take the bet?
nisiprius wrote:If what is being offered is a one-time opportunity to do this with as many coin-flips as I like, with results of each flip being parlayed as the start for the next bet, then things get much trickier.
2retire wrote:No. This example is meant to teach you how losing a percent of your money is not equal to gaining that same percentage back. In order to recover from a 70% loss, you need to gain 233.33%. 170% won't cut it; you are guaranteed to lose money.Scandinavian wrote:For example, say we flip just two times. There's four possible outcomes: heads-heads, heads-tails, tails-heads, tails-tails. If heads is the winning side, we would have the results: $729, $81, $81, $9 AVERAGE: $225
Another way to look at it is 75% of the time you lose money, 25% of the time you make money. Now, would you still take that bet?
inbox788 wrote:nisiprius wrote:If what is being offered is a one-time opportunity to do this with as many coin-flips as I like, with results of each flip being parlayed as the start for the next bet, then things get much trickier.
So, in this instance, how many flips would be sane? 1 flip, expect 1.5, 2 flips 2.25, etc, but win loss ratio goes to zero quickly, so 100 flips is basically guaranteed loser. Infinite flips expect infinite return, but zero chance. Even 5 is probably too many, so I'd guess somewhere between 1 to 3 flips maximizes something.
Scandinavian wrote:I'd definitely take the bet, but only with a very small piece of my net worth. The bet has a positive expected value, but you're going to lose more often than you win.
For example, say we flip just two times. There's four possible outcomes: heads-heads, heads-tails, tails-heads, tails-tails. If heads is the winning side, we would have the results: $729, $81, $81, $9 AVERAGE: $225
So, good expected value, but don't bet the farm!
Mister Whale wrote:No way!
I'd be curious to see the context of the question and the subsequent discussion.
staythecourse wrote:I'm sorry I must not be bright enough to understand all the threads regarding bets and there implied relation to the stock market. The difference is that investing in the market is not some random bet. If so then it would be up and down randomly 50% of the time. That, of course, is not true as it is positive in 2/3+ of the time. The other thing is that even though every bet is independent of the other they are LINKED together to give you a CAGR. That is why one year is MUTIPLIED to the next which is done to the next and so on. That CAGR with stock investing does go up with time. I believe the data is 50/50 in one day to 66-70% in 1 yr. to near 100% in 10 yr. periods.
I'm hoping someone who is smarter then me will explain this constant analogy.
Good luck.
Wagnerjb wrote:Scandinavian wrote:I'd definitely take the bet, but only with a very small piece of my net worth. The bet has a positive expected value, but you're going to lose more often than you win.
For example, say we flip just two times. There's four possible outcomes: heads-heads, heads-tails, tails-heads, tails-tails. If heads is the winning side, we would have the results: $729, $81, $81, $9 AVERAGE: $225
So, good expected value, but don't bet the farm!
If you do this enough times, you end up with something that looks like the lottery (but with better odds). You will have an exceedingly high likelihood of losing money, and an extremely tiny chance of a big payoff. Once you put the opportunity into that light, I suspect the psychological factors (utility of gains and losses) may overwhelm the purely economical aspects of the opportunity.
Best wishes.
tadamsmar wrote:I ran across a discussion of this question in a paper by Paul Samuelson on investment management.
You have the opportunity to bet on repeated flips of a fair coin. For heads, you get a 170% gain (for instance, $100 becomes $270), for tails, you have a 70% loss (for instance, $100 becomes $30).
Would you take the bet?
Code: Select all
import random
total_flips = 100
# flips = 0
# money = 100
# current_flip = 0
total_runs = 100
run = 0
while (run < total_runs):
run += 1
flip = 0
money = 100
current_flip = 0
max_this_run = (0, 100)
while (flip < total_flips):
flip += 1
current_flip = random.randrange(2)
if current_flip == 0:
money = money * 0.3
else:
money = money * 2.7
if max_this_run[1] < money:
max_this_run = (flip, money)
print "Run %s completed. Terminal value is $%s. Max value was $%s at flip %s." % (run, int(money), int(max_this_run[1]), max_this_run[0])
Epsilon Delta wrote:inbox788 wrote:nisiprius wrote:If what is being offered is a one-time opportunity to do this with as many coin-flips as I like, with results of each flip being parlayed as the start for the next bet, then things get much trickier.
So, in this instance, how many flips would be sane? 1 flip, expect 1.5, 2 flips 2.25, etc, but win loss ratio goes to zero quickly, so 100 flips is basically guaranteed loser. Infinite flips expect infinite return, but zero chance. Even 5 is probably too many, so I'd guess somewhere between 1 to 3 flips maximizes something.
Not true. If you do 100 flips you have a 24% chance of winning money, and a better than 13% of multiplying it by more than 127. The real problem with a lot of flips is you have a real chance of breaking the house and not getting paid (1% chance of winning by a factor of 7,500,000). At a guess as you increase the number of flips the chance of winning is asymptotic to about 25% and the chance of winning by at least any particular amount is also asymptotic to the same 25%
Epsilon Delta wrote:Not true. If you do 100 flips you have a 24% chance of winning money, and a better than 13% of multiplying it by more than 127.
amoeba wrote:I still don't see the downside of taking my entire networth, whatever that may be, dividing it in to the smallest allowable betsize possible, say 1 penny, make (networth/0.01) number of bets, and choosing to flip once for each bet (networth/0.01 number of total flips).
Code: Select all
import random
networth = 100000
pennies = networth * 100 # net worth in pennies
flip = 0
new_networth = 0
heads = 0
tails = 0
while (flip < pennies):
flip += 1
current_flip = random.randrange(2)
if current_flip == 0:
new_networth = new_networth + (0.01 * 0.3)
heads += 1
else:
new_networth = new_networth + (0.01 * 2.7)
tails += 1
print "%s flips completed. New net worth is $%s. Heads: %s, Tails: %s" % (flip, int(new_networth), heads, tails)
bigred77 wrote:Cant I just not "let it ride" and repeatedly bet $100 exactly on every flip?
In that case I do it untill they eventually run out of money to pay me...
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