I have to complete an Excel assignment but I don't know the relevant formula that I have to use in my question! It goes like this:
In the gambling game of heads or tails, a coin is tossed. You win if it is heads and lose if it is tails. A win means you keep the bet plus and additional bet amount given to you by the banker, and a loss means the banker takes your bet.
In this case, the probability of winning,p, is 0.5 and therefore the total return (inclusive of the bet) to the winner is two times the bet. After a few rounds, your net balance or win is the amount you currently have minus the amount you initially had.
a. A simple strategy is to bet the same amount each time until money runs out or completing round 40, whichever comes first. Note the last bet, depending on what is available, may not be equal to the first bet amount. Using this strategy, with an initial fund of $1000 and $10 bet size, what are the average and standard deviation of the last net balance? Do the same for $50 and $100 bets.
b. A "better" strategy, supposedly a sure win, goes like this: You first bet a fixed amount. If you lose, you double the bet and keep doing that until you win. Once you win, you quit the first round and begin again from the start if there is still time. Again with an initial $1000 and start bet sizes of $10, $50, $100, evaluate the average and standard deviation of the last net balance.
I have written columns and formulas for part (a) of the question: Heads/Tails, Outcome(used lookup table), bet returns(first value obtained by "total initial fund + bet return" obtained from using index and match from a table and later on, using the "first value + bet return" to find subsequent bet balance.
for part (b) however, it is much trickier because the Bet sizes do not stay the same. This gives me a headache because my bet returns formula initially depended on having a one formula taking the bet size of 10 and filling the formula for the rest of the trials (rows). How do edit my part (a) working to double the bet size after losing the bet?
Also, is the inputting of the column/row number in index and lookup functions, Eg. INDEX($G$3:$H$4,MATCH(D11,$G$3:$G$4,0),2) , considered hardcoding? Because hardcoding is not allowed in my assignment?
In the gambling game of heads or tails, a coin is tossed. You win if it is heads and lose if it is tails. A win means you keep the bet plus and additional bet amount given to you by the banker, and a loss means the banker takes your bet.
In this case, the probability of winning,p, is 0.5 and therefore the total return (inclusive of the bet) to the winner is two times the bet. After a few rounds, your net balance or win is the amount you currently have minus the amount you initially had.
a. A simple strategy is to bet the same amount each time until money runs out or completing round 40, whichever comes first. Note the last bet, depending on what is available, may not be equal to the first bet amount. Using this strategy, with an initial fund of $1000 and $10 bet size, what are the average and standard deviation of the last net balance? Do the same for $50 and $100 bets.
b. A "better" strategy, supposedly a sure win, goes like this: You first bet a fixed amount. If you lose, you double the bet and keep doing that until you win. Once you win, you quit the first round and begin again from the start if there is still time. Again with an initial $1000 and start bet sizes of $10, $50, $100, evaluate the average and standard deviation of the last net balance.
I have written columns and formulas for part (a) of the question: Heads/Tails, Outcome(used lookup table), bet returns(first value obtained by "total initial fund + bet return" obtained from using index and match from a table and later on, using the "first value + bet return" to find subsequent bet balance.
for part (b) however, it is much trickier because the Bet sizes do not stay the same. This gives me a headache because my bet returns formula initially depended on having a one formula taking the bet size of 10 and filling the formula for the rest of the trials (rows). How do edit my part (a) working to double the bet size after losing the bet?
Also, is the inputting of the column/row number in index and lookup functions, Eg. INDEX($G$3:$H$4,MATCH(D11,$G$3:$G$4,0),2) , considered hardcoding? Because hardcoding is not allowed in my assignment?
