Check-Out Stats Observation

[TPIRfan#9821]

Based on the previous two threads by Ton80.

I decided to do stats for Check-Out to see what value should you bid in total in order to maximize winnings. I used stats for the previous two seasons in order to justify my work.

RLB- Range Lower Bound
RUB- Range Upper Bound
Date          Center Range   RLB           RUB          ARP of Prize Offered
1/19/2017.........$15.95    $13.95    $17.95    $9,230
12/28/2016.......$18.95    $16.95    $20.95    $12,381
12/21/2016.......$20.25    $18.25    $22.25    $8,296
11/22/2016.......$17.85    $15.85    $19.85    $16,721
10/31/2016.......$20.06    $18.06    $22.06    $6,879
10/7/2016.........$21.31    $19.31    $23.31    $22,655
6/13/2016.........$18.75    $16.75    $20.75    $10,109
5/27/2016.........$15.95    $13.95    $17.95    $11,765
5/3/2016...........$16.45    $14.45    $18.45    $6,000
4/14/2016.........$20.25    $18.25    $22.25    $6,800
3/2/2016...........$15.25    $13.25    $17.25    $6,337
2/8/2016...........$15.55    $13.55    $17.55    $6,301
1/4/2016...........$17.45    $15.45    $19.45    $10,787
12/18/2015.......$20.45    $18.45    $22.45    $13,158
11/13/2015.......$19.83    $17.83    $21.83    $17,020
10/6/2015.........$18.45    $16.45    $20.45    $9,057

Running through the numbers, just on these alone, you should go either $18.45 or anywhere in between $19.31 to $19.45 to win 11/16 times. Not as sturdy as I hoped, but only 7/16 of these games were won, so you do better than the actual outcome if you went in this range.

I decided to split the data up to 4 digit prizes and 5 digit prizes. For 5 digit prizes, you get a 7/8 shot of winning if you guess in between $19.31-$19.45. For 4 digit prizes, you can't do much better than a 5/8 chance with either $14.45-$17.25 or $18.25-18.45.

EDIT: Added periods to make the graph look better.

[TPIRfan#9821]

Stray observation I forgot to mention. Out of those 16 games, only one time it repeated. 4/14/2016 and 12/21/2016 both had the same Check-Out total: $20.25. Coincidence? Probably. Both of them were played for a 4 digit prize, so I am not that concerned about that.

[Ton80]

The only problem with applying this theory to Check Out is that, unlike Check Game or Magic #, the contestant isn't being asked to submit a single price or number as an answer.  Rather, they are being asked to price 5 items individually.  Unless they go the Army route of guessing 1¢, 1¢, 1¢, 1¢, then $19.40 for the final item, it'll be hard to mentally keep a running tally in order to reach the desired total.

It is interesting to see that there is a general consistency in the grocery item totals - most are in the $17 to $20 range.

There doesn't seem to be a pattern with the ARP of the prize as compared to the total of the grocery items.  One might speculate that more expensive prize packages might correspond to a higher than normal grocery item total, on the theory that more expensive items are more difficult to price, but that's really not the case.

Still quite interesting to view the numbers.

[TPIRfan#9821]

The only problem with applying this theory to Check Out is that, unlike Check Game or Magic #, the contestant isn't being asked to submit a single price or number as an answer.  Rather, they are being asked to price 5 items individually.  Unless they go the Army route of guessing 1¢, 1¢, 1¢, 1¢, then $19.40 for the final item, it'll be hard to mentally keep a running tally in order to reach the desired total.

That is legitimately what I do when I play my TPIR video game, and probably what I would do on this game. I know that would change the long term effects (producers getting suspicious), but if I was down to do that for a $15k car, I would probably do that. Or you could go $3.87 for each prize, but  unless you are keeping count(Oh, I will do 5 bucks for this one, 4 for this, 4 for this, and $3.20 for the other two), there is no easy way to not awaken the producers.

And on the issue that a higher prize causes a higher Check Out total, I have to agree. Using Excel, I got a linear R² value of about 0.21, which just sucks. (For those of you who haven't taken Statistics, a lower R² value usually means there is no pattern. .21 explains about 11% of the standard deviation.)

Still, there is a sweet spot. However, once someone uses it, the sweet spot will probably change. And yeah, still interesting to view the numbers.

EDIT: Follow-Up question: Are you allowed to ask what is your total so far for Check Out? If so, maybe you could ask that after your third pricing and get about in the range.

[TPIRighteous]

Could the Check-Out distribution be bimodal? I haven't looked at the numbers, but it seems to me like setups are usually designed to make the contestant either overshoot (ARPs unexpectedly low) or undershoot (ARPs unexpectedly high).

[TPIRfan#9821]

Could the Check-Out distribution be bimodal? I haven't looked at the numbers, but it seems to me like setups are usually designed to make the contestant either overshoot (ARPs unexpectedly low) or undershoot (ARPs unexpectedly high).

I can start to see a trend, but not a great one. Give me a few hours, and I will probably reevaluate with a couple more seasons.