To solve this problem, we can simulate the bidding process based on the assumptions provided. Here's how to approach each part of the problem:

(a) Probability of Winning with a Bid of $123,000

To estimate the probability that Strassel will win with a bid of $123,000, we need to simulate the bids of the two competitors, which are uniformly distributed between $100,000 and $143,000. The probability that Strassel wins is the proportion of trials where both competitors bid less than $123,000.

1. Simulate the bids:

   • Generate two random bids from a uniform distribution between $100,000 and $143,000.
   • Count the number of trials where both bids are less than $123,000.

2. Calculate the probability:

   • Divide the count of successful trials by the total number of trials (5,000).

(b) Bid Needed to Ensure Winning

To ensure that Strassel wins the property, he must bid higher than both competitors. Since their bids can go up to $143,000, bidding at least $143,000 ensures a win.

(c) Expected Profit Calculation

To compute the expected profit for each bid alternative, follow these steps:

1. Simulate for each bid ($123,000, $133,000, $143,000):

   • For each bid, generate two competitor bids.
   • If Strassel's bid is higher than both competitors, calculate his profit as: $\text{Profit} = \text{Sale Price} - \text{Bid Amount}$
   • If he does not win, profit is $0.

2. Calculate expected profits:

   • Sum the profits from all trials and divide by the number of trials (5,000) for each bid amount.

Simulation Results

Assuming we simulate this with the appropriate random number generation, here are the expected outputs you should find:

1. Expected Profit for Each Bid:
   • Bid of $123,000: Expected profit might be around $x (calculate this).
   • Bid of $133,000: Expected profit might be around $y (calculate this).
   • Bid of $143,000: Expected profit will likely be higher due to guaranteed win, $z (calculate this).

Recommendation

Based on expected profits from the simulations, the bid that yields the highest expected profit would be recommended.

If you need assistance with the simulation coding or specific calculations, please let me know! Would you like to go through the calculations in more detail, or do you have any other questions? Here are some related questions:

1. What is the formula for calculating expected profit in scenarios like this?
2. How does uniform distribution affect bidding strategies?
3. What are the potential risks associated with bidding strategies in real estate?
4. How can Strassel Investors use this simulation for future property bids?
5. What other factors should be considered when placing a bid besides the competitor's bids?

Tip: Always consider running multiple simulations to account for variance in outcomes and ensure robustness in decision-making.