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February 22nd, 2019 at 2:04:29 AM permalink
Say you pick a number from 1 to 100 randomly, and are awarded the number picked in coins. You can take the price or reject it and pick again (with replacement). You have a maximum of 2 rejections. However, whenever you pick a number from 1-10 your rejections are renewed to 2 but without being awarded any coins. What is the mathematical expression for the optimal strategy for each pick?
Wizard
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February 22nd, 2019 at 2:40:27 AM permalink
This would be easy if it weren't for the 1 to 10 rule. I think the answer could be closely approximated by just having numbers 11 to 100, as getting 1 to 10 is like starting over.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
avianrandy
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February 22nd, 2019 at 7:46:57 AM permalink
At first I thought this thrread was about the deal or no deal tv show or slot machine. Not trying to hijack this thread,but the other day I was flipping through the channels and seen a new version I believe on CNBC where once during the game you can make a counter-offer and either the banker accepts it and the game is over or if they don't you have to continue that round anyways. Has anybody else seen this and what are your thoughts on the counter-offer gimmick?
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February 22nd, 2019 at 9:30:55 AM permalink
Quote: avianrandy

At first I thought this thrread was about the deal or no deal tv show or slot machine. Not trying to hijack this thread,but the other day I was flipping through the channels and seen a new version I believe on CNBC where once during the game you can make a counter-offer and either the banker accepts it and the game is over or if they don't you have to continue that round anyways. Has anybody else seen this and what are your thoughts on the counter-offer gimmick?



That is a new rule for this season. It doesn't change the dynamic much. I've seen some counter-offers accepted and some denied. I think if the player counters for no more than about 10% more, the bank will take it. You sometimes see greedy players countering for more than expected value, which I'm always happy to see the banker deny.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
charliepatrick
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February 22nd, 2019 at 11:15:18 AM permalink

I worked this out various ways to work out when you should redraw. Here is a summary once the strategy had been established.
Draws in various roundsPermsAverageContribution
1st (100 to 69)
320 000
84.5
27 040 000
1st (68 to 11), 2nd (100 to 58)
249 400
79.0
19 702 600
1st (68 to 11), 2nd (57 to 11), 3rd (100 to 11)
245 340
55.5
13 616 370
TOTALS
814 740
60 358 970
Starting Average
74.083 720

Nathan
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February 22nd, 2019 at 2:43:42 PM permalink
Quote: Wizard

That is a new rule for this season. It doesn't change the dynamic much. I've seen some counter-offers accepted and some denied. I think if the player counters for no more than about 10% more, the bank will take it. You sometimes see greedy players countering for more than expected value, which I'm always happy to see the banker deny.



Is this similar to the guy who claimed he had a chance of making 500 times his bet but there was still a 1,000 times his bet box still left unopened, so he rejected the 500 times box, and he ended up with only 15 times his bet and was understandably pissed off at himself for doing that?
In both The Hunger Games and in gambling, may the odds be ever in your favor. :D "Man Babes" #AxelFabulous "Olive oil is processed but it only has one ingredient, olive oil."-Even Bob, March 27/28th. :D The 2 year war is over! Woo-hoo! :D I sometimes speak in metaphors. ;) Remember this. ;) Crack the code. :D 8.9.13.25.14.1.13.5.9.19.14.1.20.8.1.14! :D "For about the 4096th time, let me offer a radical idea to those of you who don't like Nathan -- block her and don't visit Nathan's Corner. What is so complicated about it?" Wizard, August 21st. :D
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February 22nd, 2019 at 3:06:49 PM permalink
Quote: Nathan

Is this similar to the guy who claimed he had a chance of making 500 times his bet but there was still a 1,000 times his bet box still left unopened, so he rejected the 500 times box, and he ended up with only 15 times his bet and was understandably pissed off at himself for doing that?



I don't think I saw that one.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Nathan
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February 22nd, 2019 at 3:29:37 PM permalink
Quote: Wizard

I don't think I saw that one.



Oh my God! I should have clarified that I was talking about Deal Or No Deal Slot Machine Game! Not the TV Show! ;)
In both The Hunger Games and in gambling, may the odds be ever in your favor. :D "Man Babes" #AxelFabulous "Olive oil is processed but it only has one ingredient, olive oil."-Even Bob, March 27/28th. :D The 2 year war is over! Woo-hoo! :D I sometimes speak in metaphors. ;) Remember this. ;) Crack the code. :D 8.9.13.25.14.1.13.5.9.19.14.1.20.8.1.14! :D "For about the 4096th time, let me offer a radical idea to those of you who don't like Nathan -- block her and don't visit Nathan's Corner. What is so complicated about it?" Wizard, August 21st. :D
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February 24th, 2019 at 3:37:17 PM permalink
Nathan, you would be the perfect contestant on Deal or No Deal.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Nathan
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February 24th, 2019 at 7:18:01 PM permalink
Quote: Wizard

Nathan, you would be the perfect contestant on Deal or No Deal.



I'd have a panic attack in a bad way if I held out for the big box only to get a kiddie box so to speak. O.O I'd have a panic attack in a good way if I got the Parent box so to speak. ;)
In both The Hunger Games and in gambling, may the odds be ever in your favor. :D "Man Babes" #AxelFabulous "Olive oil is processed but it only has one ingredient, olive oil."-Even Bob, March 27/28th. :D The 2 year war is over! Woo-hoo! :D I sometimes speak in metaphors. ;) Remember this. ;) Crack the code. :D 8.9.13.25.14.1.13.5.9.19.14.1.20.8.1.14! :D "For about the 4096th time, let me offer a radical idea to those of you who don't like Nathan -- block her and don't visit Nathan's Corner. What is so complicated about it?" Wizard, August 21st. :D
Bowler377
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January 25th, 2024 at 6:50:26 PM permalink
The network seems much more concerned about entertainment value, as opposed to making mathematically sound deals for the network.

They have literally turned down mathematically good counter offers, only to offer more than fair value a round or 2 later.

The American version loves to push people beyond their comfort zone, and then "award" them, with a bank offer worth up to 10% above fair value, and sometimes more.

Other versions, like the UK version, are so stingy, that they have a large number of top and bottom prize winners, even having their own "1p club."

No 1 penny club here in the US. Only 1 person, a pig farmer, won the penny (the brown dresses indicate her game went to s*), and we had only 2 million dollar winners, in due part because American bank offers are much more generous mathematically speaking.
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