In my last blog " Gamblers Ruin", I mentioned about the gambling game I posed to my class. A quick recap of that:
It turns out that a few in the class wanted to play the game, but did not know the best strategy to win. They were risk takers and willing to bet their money with a 50-50 chance. Much of the class was conservative and didn't want to play. It is worth mentioning that there were a handful who think gambling is bad (I guess there is some sanity still left in the universe).
There is a winning strategy in this game and if you have enough money to bet, there is a high chance that you will double your initial bet.
I start with a bet of $x. If I win in the first toss, I will take my $2x and leave. If I lose in the first toss, I will double my bet to $2x and play again. If I win, I get $4x. Since my investment was $x + $2x, I make an additional $x. You can keep doing this till you win, but the first time you win, you should stop.
The game follows a geometric distribution, with a
probability of first win on the kth try. Since winning probability is 0.5 for a fair coin, the chance of winning it in the first try is 0.5; the chance of winning it in the second try is (0.5)(0.5), the chance of winning in the third try is (0.5)(0.5)(0.5) and so on...So, you will have a high chance of winning (more than 90% chance) within the first 5 trails. Just stop playing it the first time you win..and take your money.
Now, I know, it is easy to throw numbers and show that I can win... but will I bet my bucks on it?
I can perhaps bet a $100 and win back my $100 plus an additional $100, because i can rise the bets up to a limit..
... am I willing to bet $1000 or more ??? ...
"I have a coin toss game where I give you 2 times your bet if you win and
nothing if you lose. Assume we have a fair coin, would you play the
game with me and bet your money? If you will, then what is your
strategy, assuming you are in it to win."
It turns out that a few in the class wanted to play the game, but did not know the best strategy to win. They were risk takers and willing to bet their money with a 50-50 chance. Much of the class was conservative and didn't want to play. It is worth mentioning that there were a handful who think gambling is bad (I guess there is some sanity still left in the universe).
There is a winning strategy in this game and if you have enough money to bet, there is a high chance that you will double your initial bet.
I start with a bet of $x. If I win in the first toss, I will take my $2x and leave. If I lose in the first toss, I will double my bet to $2x and play again. If I win, I get $4x. Since my investment was $x + $2x, I make an additional $x. You can keep doing this till you win, but the first time you win, you should stop.
The game follows a geometric distribution, with a
probability of first win on the kth try. Since winning probability is 0.5 for a fair coin, the chance of winning it in the first try is 0.5; the chance of winning it in the second try is (0.5)(0.5), the chance of winning in the third try is (0.5)(0.5)(0.5) and so on...So, you will have a high chance of winning (more than 90% chance) within the first 5 trails. Just stop playing it the first time you win..and take your money. Now, I know, it is easy to throw numbers and show that I can win... but will I bet my bucks on it?
I can perhaps bet a $100 and win back my $100 plus an additional $100, because i can rise the bets up to a limit..
... am I willing to bet $1000 or more ??? ...
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