Plinko
Rules
The contestant is given a Plinko chip for free. Four small prizes are then shown, each of which has a wrong price. The contestant must decide if the first digit in the wrong price is the first digit in the actual price or if the last digit in the wrong price is the last digit in the actual price. If they are correct, they get another Plinko chip. They then take their Plinko chips to the board and drop them one at a time. They win whatever money their chips land in.
Random fact
For the game's 30th anniversary, the show had an episode where they played Plinko 6 times. Buzzfeed wrote a behind the scenes article about it here:
Win-loss record
- Actual (seasons 29-47): 0-564 (0%)
- What it would be by random chance: 35/958579 (0.0037%)
(That assumes the contestant drops every chip from the center slot.)
Hey, I don't make the rules. According to the show's staff, a game is considered to be won if and only if its main announced prize is won. In Plinko's case, that means the full $50,000 must be won for the game to be won.
Yeah, but...
But what?
Can we consider it to be a win if the contestant hits the center slot at least once? Please?
OK, fine. Here are the stats for that...
Win-loss record if a win means the center slot was hit at least once
- Actual (seasons 29-47): 257-307 (45.57%)
- What it would be by random chance: 1456/2799 (52.02%)
(That assumes the contestant drops every chip from the center slot.)
Correct choice for the small prizes... (seasons 40-47)
Last digit of % of time first % of time last
wrong price digit was right digit was right
0 2.90 97.10
1 94.20 5.80
2 57.89 42.11
3 71.79 28.21
4 82.76 17.24
5 7.03 92.97
6 73.97 26.03
7 50.77 49.23
8 65.79 34.21
9 18.67 81.33
Strategy
Part 1: Small Prizes
Simply put, if the last digit is 0, 5, or 9, your guess should be that the last digit is the correct one, unless you have strong reason to believe otherwise. If the last digit is 1, 3, 4, 6, or 8, your guess should be that the first digit is the correct one. If it's 2 or 7, you need to know the price. That said, to simplify this, if you want to think of it as "0, 5, or 9 means last, otherwise choose first," I won't object to that.
Part 2: Where to drop the chip from
Drop every chip from the center slot. I repeat, drop every chip from the center slot. One more time:
DROP EVERY CHIP FROM THE CENTER SLOT!!!!
Your expected winnings are highest if you drop the chip from the center slot. This makes sense--the chip is equally likely to bounce left or right. If you drop the chip from the center slot, you need an equal number of left and right bounces to get the $10,000. If you drop the chip from one slot left of the center slot, you need seven bounces to the right and five to the left to get the $10,000. Which do you think is more likely--six bounces to the right and six bounces to the left or seven bounces to the right and five to the left? Yup, the first one. One thing this means is that you should NOT correct for a previous bad bounce. In other words, if you drop your first chip from the center slot and it goes into the left $0, do NOT move one spot to the right for your next drop. You should drop every chip from the center slot no matter what the previous results were!
Let me back this up with some data from a simulation I created where I "released" 10 million chips over each slot.
Where the chip % of time center Avg. winnings
was dropped from slot was hit of each chip
Left- or right- 3.21 $779.54
most slot
Second slot from 5.67 $1,009.77
the left or right
Third slot from 12.11 $1,606.17
the left or right
Slot adjacent to 19.37 $2,269.45
the center slot
Center slot 22.58* $2,559.93
* The theoretical rate of the chip hitting $10,000 if you drop it from the center slot is 924/4096, or 22.56%. So my simulation gets pretty close to that rate.
No comments:
Post a Comment