Thread by @PopCultureMath

Contestant’s Row Bidding, a Long Thread (4)

So how to bid in Contestant’s Row? Let’s discuss what to do, and what not to do, based on whether you bid 1st, 2nd, 3rd, or last (Bidder 1, Bidder 2, Bidder 3, Bidder 4).

Please pick up the book in ~1 year’s time to learn more. 🧵👇

1. Let’s start off and define the goal: To maximize one’s odds of being closest to the actual retail price without going over? This does not mean having the best point estimate, but rather capturing the largest probability of winning across reasonable price ranges.

2. Bidding $1,000 as Bidder 1 for an item you think is worth about $1,100 does not do you much good if one of the subsequent bidders bids $1,001 (“clips” you). As an early bidder, the better your bid is, the more likely it is to be clipped.

3. Being overly concerned about going over as Bidder 1 is foolish because Bidder 1 only won 18% of bidding rounds in Seasons 47-48, with Bidder 4 winning 41% of the time. As the first bidder, you should be willing to go over a lot if it ups your chance of winning above 18%.

4. Recall that underbidding was egregious. The highest bid won 53% of bidding rounds, and the last bidder, who has the benefit of being able to bid $1 over the highest bid or bid $1, won 64% of the time with the highest bid.

5. Last Bidder: Most fans realize Bidder 4 should bid $1 over the best prior bid or bid $1 if the chance of Bidders 1-3 having gone over is high. But Bidder 4 also gets to bid 4th in a re-bid, so a $1 bid is only practical if odds of winning are better than winning on a re-bid

6. Underbidding and strategic play by Bidder 4 meant that the most frequent pattern was for Bidders 1-3 to come in low and somewhat clustered, with Bidder 4 topping the highest prior bid by $1, as seen in the examples below.

7. Now for Bidders 1-3: Things get a bit advanced. Consider a simplified game where 4 bidders are choosing a random number between 1 and 100, as if in Contestant’s Row. Bidder 1 should bid 77.78, Bidder 2 should bid 55.56, Bidder 3 should bid 33.34, and Bidder 4 should bid 0.01

8. In this game, with these strategies, Bidder 1, 2, and 3 will each win 2/9 of the time, and Bidder 4 will win 1/3 of the time. But Contestant’s Row bidding is a lot more complex than choosing a random number between 1 and 100. Or is it?

9. Turns out that Bidder 1 should mostly bid towards the high end of the range of values he/she feels are realistic. That move “self-limits” the range of values over which he/she can win but prevents others from clipping his/her bid or coming in slightly above.

10. Of course, this Bidder 1 strategy does not work as cleanly as it does in the Simplified Game. It works better for known prizes like electronics where contestants are likely to agree on the likely range of values for that prize.

11. Without going into to detail, Bidder 2 has a couple different best actions depending on how Bidder 1 bids, and Bidder 3 has a few best actions depending on how Bidder 1 and Bidder 2 bids.

12. If Bidder 1 goes high, Bidders 2 and 3 should come in progressively lower, as in the Simplified Game. But if Bidder 1 instead delivers his best estimate (i.e. in the middle of the likely range), Bidder 2 should go high, as Bidder 1 should have done.

13. Broadening one’s bid has relevance in real life. In applying for college, good grades make for a good point estimate bid. But how can you broaden your bid to include athletics, extracurriculars, and volunteer activities, so that you have a greater chance of gaining admission?

14. In case you are skeptical that Bidder 1 should always bid high, the evidence on underbidding may convince you otherwise. My next thread.

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