# Price is Right Spinoff Strategy

One of my interests besides gambling is game shows. I love watching them and analyzing them. The flip side of that coin is I can be heard screaming at my television as math-challenged players make awful decisions. A case and point is when they played through the Monty Hall problem on the last season of Survivor, but let’s not get into that. I still haven’t recovered.

One game I find especially interesting, as a mathematician, is The Price is Right (TPIR). I wrote about the strategy of the Then and Now game in the June 25, 2020 newsletter. This time, I will write about something I analyzed a long time ago, the spin-off. This is a game played twice every one-hour show.

Here I am spinning the spinoff wheel at the old Price is Right show in Las Vegas. This was not for real prizes, but was the actual wheel that was used on the show at one time. You can watch the full video on YouTube.

Here are the rules to win:

1. A wheel has 20 stops, numbered from 5 from 100, which represent cent 5 cents to \$1.
2. Three players play with the goal to get closest to \$1, without going over.
3. The first player spins the wheel.
4. That first player may either accept his result from the first spin, or spin again. If the player spins again, his score will be the sum of his two spins.
5. The second player, knowing the first player’s score, will go next. He too has the same option as the first player, to take one or two spins.
6. The third player, knowing the high score of the first two players, also has the same choice to spin once or twice.
7. In the event of a tie, those players involved in the tie will have a tie-breaking single spin. If the result of a tie-breaking spin is still a tie, they will repeat the tie-breaking spins until somebody wins.
8. There are special prizes for achieving a score of exactly \$1 (which is why I’m so excited in the video), but I won’t get into those rules here.

“What is the optimal strategy?” you may ask.

### First player Strategy

Spin again if the first spin is 65 cents or less. Stand with 70 cents or more.

### Second Player Strategy

The second player should spin again if any of the following conditions are true, otherwise stand.

• Lower score than first player.
• First spin is 50 cents or less.
• First spin is 65 cents or less and is tied with the first player.

### Third Player Strategy

If there is NOT a tie between the first and second players, then the player should spin again if either:

• Lower score than winner of first two players.
• Score of 45 cents or less and ties the winner of first two players.

If the third player gets 50 cents on the first spin, which ties the winner of the first two players, then he should be indifferent to spinning again and standing.

If there IS a tie between the first and second players, then the player should spin again if either:

• Lower score than that of the first two players.
• Score of 65 cents or less and ties the first two players.

There is obviously a positional advantage to going last in this game. Assuming all three players follow optimal strategy, here is the probability of each player winning:

• Player 1: 30.82%
• Player 2: 32.96%
• Player 3: 36.22%

I hope you enjoyed this analysis of the spin-off game. Until next week, may the odds be ever in your favor.