Monday, November 28, 2016 Game Recap & Discussion [SPOILERS]

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Re: Monday, November 28, 2016 Game Recap & Discussion [SPOILERS]

Post by xxaaaxx » Wed Nov 30, 2016 2:12 pm

1stlvlthinker wrote:For the noobs here (like me) can you ELI5 why their wagering strategy was so wrong?
Assume Justin wagers to cover a double-up by Hobie (the standard wager from the lead). If he gets it wrong, he'll only be left with 799 (in the actual game, he under-wagered, but it didn't matter in the end).

Ideally, while also wagering to give themselves the best chance to win if they got FJ right, both challengers should've wagered to stay above that 799 total, if they got FJ wrong. Specifically:

Hobie only needed to bet 9801 to cover Allison and, most importantly, stay ahead of Justin if they all got it wrong (a triple stumper). This would've left him with 6799 and, the way the other wagers turned out, given him the win.

Allison could've bet 3801 to top a 0 wager from Justin. Most importantly, a small wager would've kept her ahead of Justin and Hobie in the case of a triple stumper. This would've left her with 9199, and given her the win.

Instead, they both bet nearly everything, and let Justin escape with a piddly 1199. These kinds of over-wagers happen...a lot.

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Re: Monday, November 28, 2016 Game Recap & Discussion [SPOILERS]

Post by opusthepenguin » Wed Nov 30, 2016 2:41 pm

1stlvlthinker wrote:
opusthepenguin wrote:Lots of people here can, but it will make your eyes glaze over UNLESS you're willing to put in a little work. And I really mean a little. Not much. You ready?

Here were the scores going into FJ:

Justin Bender: 17000
Hobie Barnes: 16600
Allison Totura: 13200

It's easiest to take things one player at a time. Start with Justin. What would you wager in his position and why?
If I'm Justin, I want to make sure I win if Hobie gets it right and wagers everything, so Hobie can get to 33200, I want to wager 16,201.
Perfect! That's the standard shutout bet (sometimes called minimum shutout bet or msb). Justin wagered $15,801. Just to review, what's wrong with that bet?
SpoilerShow
If Hobie wagers everything (or close to it) and gets FJ right, Justin will LOSE. Justin didn't bet to shut Hobie out.
So now we know what's wrong with Justin's bet. I don't know if Justin made a math error or was just too rattled to do math or what. This is a bet that most players get right. Justin's in the minority here.

Now, let's put ourselves in Hobie's shoes. He doesn't KNOW what Justin's going to bet. But he does know what most players would bet in Justin's situation. Most players will make the shutout bet of $16,201. You explained why above.

So ASSUMING Justin makes the shutout bet, can Hobie win the game if Justin gets FJ right?
SpoilerShow
No.
That means Hobie needs to focus on the scenario where Justin gets FJ wrong. How much will Justin have if Justin makes the shutout bet and gets FJ wrong? Do the math and then check my work to see if I got it right. (These conversations are almost impossible to follow unless you do the math yourself before looking at the answer.)
SpoilerShow
$799
Was I right? I hope so. Otherwise this conversation starts making a lot less sense. Ok, this means it is VERY unlikely that Justin will dip down below $799 when he misses FJ. So Hobie would be foolish to leave himself with less than $799 on a miss, right? So what is the absolute maximum Hobie should bet?
SpoilerShow
$15,800.
If he bets more than that, he almost certainly can't win if he misses FJ. What did Hobie bet? $16,000. He missed and left himself with $600. Foolish, right? He basically threw away the opportunity to win if he missed FJ. He didn't have to.

So what SHOULD Hobie bet?

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Re: Monday, November 28, 2016 Game Recap & Discussion [SPOILERS]

Post by 1stlvlthinker » Wed Nov 30, 2016 3:06 pm

opusthepenguin wrote:? So what is the absolute maximum Hobie should bet?
SpoilerShow
$15,800.
If he bets more than that, he almost certainly can't win if he misses FJ. What did Hobie bet? $16,000. He missed and left himself with $600. Foolish, right? He basically threw away the opportunity to win if he missed FJ. He didn't have to.

So what SHOULD Hobie bet?
So in this case, Hobie should bet $15,800 right? (not counting Allison yet).

However, if Hobie bets 15,800 and Justin knows he's going to bet that, can't he adjust his own bet? It seems like a never ending level-fest here.
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Re: Monday, November 28, 2016 Game Recap & Discussion [SPOILERS]

Post by This Is Kirk! » Wed Nov 30, 2016 3:17 pm

1stlvlthinker wrote:However, if Hobie bets 15,800 and Justin knows he's going to bet that, can't he adjust his own bet? It seems like a never ending level-fest here.
He could, but that would expose himself to losing even if he got FJ correct, and he wouldn't want that to happen. That's why the leader usually makes the shutout wager.

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Re: Monday, November 28, 2016 Game Recap & Discussion [SPOILERS]

Post by opusthepenguin » Wed Nov 30, 2016 3:23 pm

1stlvlthinker wrote:
opusthepenguin wrote:? So what is the absolute maximum Hobie should bet?
SpoilerShow
$15,800.
If he bets more than that, he almost certainly can't win if he misses FJ. What did Hobie bet? $16,000. He missed and left himself with $600. Foolish, right? He basically threw away the opportunity to win if he missed FJ. He didn't have to.

So what SHOULD Hobie bet?
So in this case, Hobie should bet $15,800 right? (not counting Allison yet).

However, if Hobie bets 15,800 and Justin knows he's going to bet that, can't he adjust his own bet? It seems like a never ending level-fest here.
To a certain extent that's true, BUT: a) Not always. Often one contestant can make a wager that puts them in an objectively better position and there's nothing the other one can do about it. More importantly in this case, b) Other contestants almost never engage in this sort of second order thinking. Until they start, there's tremendous leverage available to the contestant who does some basic analysis. If this were to change, we'd definitely see some some Vizzini vs The Man in Black wagers. But that hasn't been the norm for 30 years of Trebek-era Jeopardy! So our best bet (by FAR) is to assume this isn't the game where all three contestants get savvy.

So, yes, Hobie should bet NO MORE THAN $15,800. As you shrewdly point out, we haven't dealt with his position vis-à-vis Allison yet. Let's factor that in. Hobie's max (reasonably) safe bet is $15,800. With Allison in the picture, what's the minimum Hobie should bet?

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Re: Monday, November 28, 2016 Game Recap & Discussion [SPOILERS]

Post by 1stlvlthinker » Wed Nov 30, 2016 3:36 pm

opusthepenguin wrote:
1stlvlthinker wrote:
opusthepenguin wrote:? So what is the absolute maximum Hobie should bet?
SpoilerShow
$15,800.
If he bets more than that, he almost certainly can't win if he misses FJ. What did Hobie bet? $16,000. He missed and left himself with $600. Foolish, right? He basically threw away the opportunity to win if he missed FJ. He didn't have to.

So what SHOULD Hobie bet?
So in this case, Hobie should bet $15,800 right? (not counting Allison yet).

However, if Hobie bets 15,800 and Justin knows he's going to bet that, can't he adjust his own bet? It seems like a never ending level-fest here.
To a certain extent that's true, BUT: a) Not always. Often one contestant can make a wager that puts them in an objectively better position and there's nothing the other one can do about it. More importantly in this case, b) Other contestants almost never engage in this sort of second order thinking. Until they start, there's tremendous leverage available to the contestant who does some basic analysis. If this were to change, we'd definitely see some some Vizzini vs The Man in Black wagers. But that hasn't been the norm for 30 years of Trebek-era Jeopardy! So our best bet (by FAR) is to assume this isn't the game where all three contestants get savvy.

So, yes, Hobie should bet NO MORE THAN $15,800. As you shrewdly point out, we haven't dealt with his position vis-à-vis Allison yet. Let's factor that in. Hobie's max (reasonably) safe bet is $15,800. With Allison in the picture, what's the minimum Hobie should bet?
Hobie should be able to cover Allison, because he's now "the leader" in this scenario, so 9801 with my quick math. Knowing this, Allison might wager 6400 to stay above Hobie should he get it wrong?

- One of the reasons I ask about the wager of wits is because when playing the game, I might have no confidence in myself and would wager 0 as the leader.
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Re: Monday, November 28, 2016 Game Recap & Discussion [SPOILERS]

Post by opusthepenguin » Wed Nov 30, 2016 5:06 pm

1stlvlthinker wrote:Hobie should be able to cover Allison, because he's now "the leader" in this scenario, so 9801 with my quick math. Knowing this, Allison might wager 6400 to stay above Hobie should he get it wrong?

- One of the reasons I ask about the wager of wits is because when playing the game, I might have no confidence in myself and would wager 0 as the leader.
So we don't have to keep scrolling up to check, here again were the scores going into FJ. This time I've included the actual wagers made:

Justin Bender: 17000-15801=1199
Hobie Barnes: 16600-16000=600
Allison Totura: 13200-12800=400

Correct on Hobie. Had he made the wager you suggest, he would have won if he got FJ right OR if he got it wrong! His overwager cost him the game.

Allison's got a range of decent wagers. You suggest $6,400 which is good. As you say, that keeps her ahead of Hobie if Hobie takes our wagering advice and both he and Allison miss. Hobie loses $9,801 and drops to $6,799. Allison loses $6,400 and drops to $6,800. She wins by a buck.

But that makes $6,400 the MAXIMUM Allison should wager. She's probably safer going smaller if she can. Second place contestants like Hobie tend not to make the subtle calculations we've just made. They are more likely to bet (almost) everything, especially if they are male. Or they'll bet (almost) nothing. I think females are more likely than males to go this route, but I suspect they're still more likely to go big than small in Hobie's position. If that makes sense. But I could be wrong. This might just be my inner sexist talking, buttressed by some confirmation bias selectively remembering the results. I hate this possibility because a) I don't want to have an inner sexist, and b) I don't want to be wrong. But honesty compels me to admit that I have unconscious biases that I consciously reject but don't always succeed in identifying and suppressing.

What a drag. Where were we? Oh yeah.

Our suggested maximum wager of $6,400 helps Allison guard against a shrewd wager by Hobie AND ALSO against any overwagering by Hobie. This is good since the overwager is the most likely mistake for Hobie to make.

But what about the underwager? As you note, your own tendency is to freak out and bet nothing. That's definitely worth considering. (You're having all the right thoughts about this. They're just getting tangled up in your head because you're trying to think them all at once.) What if Hobie bets $0? Then Allison should bet...
SpoilerShow
$3,401. If she gets it right, she's a buck ahead of Hobie. If she gets it wrong, she's still way ahead of where Justin and Hobie will likely end up on a triple stumper.
But wait! you say. What if JUSTIN bets $0? Good point. And since Justin is only $400 ahead of Hobie, it won't cost Allison much more to hedge against Justin as well. So Allison should bet...
SpoilerShow
$3,801.
That way, Allison is protected against a $0 bet by either competitor, and she still leaves herself with $9,399 if she misses. That's a lot more than Justin and Hobie will have on a triple stumper if they make shrewd bets OR if they overwager.

Others might argue for something a little higher or lower. I don't know. But unless I'm missing something, we'll all agree that this bet is in the right range.

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Re: Monday, November 28, 2016 Game Recap & Discussion [SPOILERS]

Post by opusthepenguin » Wed Nov 30, 2016 5:06 pm

So let's sum up.

Code: Select all

                                   RESULT ON                      RESULT ON
                   ACTUAL BET      MISS/GET     RECOMMENDED       MISS/GET
----------------------------------------------------------------------------------------------
Justin:  17,000      15,801      1,199/32,801     16,201          799/33,201
Hobie:   16,600      16,000        600/32,600      9,801        6,799/26,401
Allison: 13,200      12,800        400/26,000      3,801        9,399/17,001
(I hope everything lines up on your screen the way it does on mine.)

Justin: Underwagered by $400. If Hobie had wagered everything (or at least $16,202) and they both got FJ, Justin would have been one unhappy camper. To be in first place going into FJ, get FJ right, and STILL lose is pretty sad. With the actual wagers, Justin would've lucked out if he and Hobie had both gotten FJ. Hobie's wager wasn't quite enough to get him past Justin if they both got it right. But hang on. Justin's about to have some more luck break his way.

Hobie: Overwagered by quite a lot. He should have had much more than Justin if both he and Justin missed FJ. Justin should have gone home today. But Hobie wagered so much that he ended up with less than Justin. He threw away the lead when he didn't have to. But hang on (part 2, the hang onnening). Justin needs even more luck than this.

Allison: Overwagered by even more than quite a lot. She should have beat Hobie (who should have beat Justin) EVEN IF HOBIE HAD WAGERED CORRECTLY. And Hobie's overwager gave her an even bigger chance at coming out ahead. But she out-overwagered him. Hobie threw the game away to Allison who picked it up and threw it away to Justin.

Summary: Justin's underwager could have cost him the game if he and Hobie had both gotten FJ. Instead it was a triple stumper. Allison should have won on a triple stumper but she overwagered. Hobie should have won on a triple stumper in which Allison overwagered but he ALSO overwagered and handed the game to Justin.

Conclusion: Justin just dodged so many bullets it was like the climactic scene in The Matrix. He tried to throw the game away, but BOTH his opponents threw it even harder right back at him. And that's why we say this is the worst set of FJ wagers we've seen in quite a while.

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Re: Monday, November 28, 2016 Game Recap & Discussion [SPOILERS]

Post by 1stlvlthinker » Wed Nov 30, 2016 5:23 pm

opusthepenguin wrote:So let's sum up.

Code: Select all

                                   RESULT ON                      RESULT ON
                   ACTUAL BET      MISS/GET     RECOMMENDED       MISS/GET
----------------------------------------------------------------------------------------------
Justin:  17,000      15,801      1,199/32,801     16,201          799/33,201
Hobie:   16,600      16,000        600/32,600      9,801        6,799/26,401
Allison: 13,200      12,800        400/26,000      3,801        9,399/17,001
(I hope everything lines up on your screen the way it does on mine.)

Justin: Underwagered by $400. If Hobie had wagered everything (or at least $16,202) and they both got FJ, Justin would have been one unhappy camper. To be in first place going into FJ, get FJ right, and STILL lose is pretty sad. With the actual wagers, Justin would've lucked out if he and Hobie had both gotten FJ. Hobie's wager wasn't quite enough to get him past Justin if they both got it right. But hang on. Justin's about to have some more luck break his way.

Hobie: Overwagered by quite a lot. He should have had much more than Justin if both he and Justin missed FJ. Justin should have gone home today. But Hobie wagered so much that he ended up with less than Justin. He threw away the lead when he didn't have to. But hang on (part 2, the hang onnening). Justin needs even more luck than this.

Allison: Overwagered by even more than quite a lot. She should have beat Hobie (who should have beat Justin) EVEN IF HOBIE HAD WAGERED CORRECTLY. And Hobie's overwager gave her an even bigger chance at coming out ahead. But she out-overwagered him. Hobie threw the game away to Allison who picked it up and threw it away to Justin.

Summary: Justin's underwager could have cost him the game if he and Hobie had both gotten FJ. Instead it was a triple stumper. Allison should have won on a triple stumper but she overwagered. Hobie should have won on a triple stumper in which Allison overwagered but he ALSO overwagered and handed the game to Justin.

Conclusion: Justin just dodged so many bullets it was like the climactic scene in The Matrix. He tried to throw the game away, but BOTH his opponents threw it even harder right back at him. And that's why we say this is the worst set of FJ wagers we've seen in quite a while.
Ahh, I see now. Thanks for clarifying.
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Re: Monday, November 28, 2016 Game Recap & Discussion [SPOILERS]

Post by SavoyGirl » Thu Dec 01, 2016 1:11 am

Guess I'm the only one aware of the comic opera "Zar und Zimmerman" wherein Peter the Great goes to work incognito in a shipyard. Was fairly sure it was in Holland. Tricolor was obviously negbait for France. Ironically, the category seemed likely to be a triple stumper and I would have probably bet zero.

https://en.wikipedia.org/wiki/Zar_und_Zimmermann

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Re: Monday, November 28, 2016 Game Recap & Discussion [SPOILERS]

Post by seaborgium » Mon Dec 19, 2016 8:51 pm

This story was posted by David Madden on Facebook over a year ago, and the post resurfaced today because the ambassador in it was just assassinated:
On November 20th the Turks summoned Russia’s ambassador; a spokesman for the Turkish foreign ministry said the Russians “were bombing civilian Turkmen villages, not fighting terror”. Nationalist activists have rallied in support of the Turkmen. Last week some attempted to pelt the Russian consulate in Istanbul with eggs, but instead accidentally egged the nearby consulate of the Netherlands, which has a similar flag.
I don't wish he had been assassinated sooner, but I do wish I had remembered this story.

edit: it's from The Economist. http://www.economist.com/news/europe/21 ... needed-was

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Re: Monday, November 28, 2016 Game Recap & Discussion [SPOILERS]

Post by marethyu » Thu Jan 05, 2017 11:17 pm

That was a great discussion of the wagering, which absolutely drove me crazy as I was watching my backlog of Jeopardy episodes on my Tivo. After the teen tournament where the second place contestant was somehow unable to figure out that he was going to lose when the kid in the lead got his FJ correct, I was glad to return to a couple of episodes of correct wagering by contestants. However, this episode made my head explode and drove me to sign up for an account on this forum.

It's helpful to have it explained so clearly, but quite honestly, I don't see why it's so complicated. If you are in second place, you can only beat the leader (assuming they bet reasonably) if the leader gets FJ wrong. In that case, you have to protect against two things: the leader betting between $0 and the third place person betting everything. You bet enough to double the score of the third place contestant and be $1 ahead of the first place contestant. In this case that was $9801.

For the third place contestant, if you have enough, which Allison did, you bet to get ahead of the starting scores of the other two contestants, which was $3801, because you have almost zero chance of beating either of them if they get it correct (unless they bet $0.) You need to them both to get it wrong. Also, in this case, you are in the best position to actually have quite a bit of money left even if you get it wrong as well, because the other two are going to have to wager a lot more. I guess there is probably some odd scenario where the other contestants make too small of a wager and you might be able to pass them if you bet a little more, but that seems very unlikely to me. The more likely scenario is that they will either bet to beat you if they get it correct or they will bet as little as possible ($0 for 1st place, and initial first place+$1 for 2nd place.) The only one of those where getting FJ correct matters for the 3rd place contestant is if the other two make the minimum bet, so you should bet to beat the minimum bet if you can, leaving you the best chance to get second or possibly first if they both get it wrong.

Also, I thought the flags category sounded difficult, so I actually assumed that this would be a perfect scenario for Allison, given how close Hobie and Justin were and that she was within reasonable striking distance if they got it wrong.

So frustrating to watch!

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Re: Monday, November 28, 2016 Game Recap & Discussion [SPOILERS]

Post by seaborgium » Fri Jan 06, 2017 12:30 am

marethyu wrote:That was a great discussion of the wagering, which absolutely drove me crazy as I was watching my backlog of Jeopardy episodes on my Tivo. After the teen tournament where the second place contestant was somehow unable to figure out that he was going to lose when the kid in the lead got his FJ correct, I was glad to return to a couple of episodes of correct wagering by contestants. However, this episode made my head explode and drove me to sign up for an account on this forum.

It's helpful to have it explained so clearly, but quite honestly, I don't see why it's so complicated. If you are in second place, you can only beat the leader (assuming they bet reasonably) if the leader gets FJ wrong. In that case, you have to protect against two things: the leader betting between $0 and the third place person betting everything. You bet enough to double the score of the third place contestant and be $1 ahead of the first place contestant. In this case that was $9801.

For the third place contestant, if you have enough, which Allison did, you bet to get ahead of the starting scores of the other two contestants, which was $3801, because you have almost zero chance of beating either of them if they get it correct (unless they bet $0.) You need to them both to get it wrong. Also, in this case, you are in the best position to actually have quite a bit of money left even if you get it wrong as well, because the other two are going to have to wager a lot more. I guess there is probably some odd scenario where the other contestants make too small of a wager and you might be able to pass them if you bet a little more, but that seems very unlikely to me. The more likely scenario is that they will either bet to beat you if they get it correct or they will bet as little as possible ($0 for 1st place, and initial first place+$1 for 2nd place.) The only one of those where getting FJ correct matters for the 3rd place contestant is if the other two make the minimum bet, so you should bet to beat the minimum bet if you can, leaving you the best chance to get second or possibly first if they both get it wrong.

Also, I thought the flags category sounded difficult, so I actually assumed that this would be a perfect scenario for Allison, given how close Hobie and Justin were and that she was within reasonable striking distance if they got it wrong.

So frustrating to watch!
You've got mostly the right idea, but wagering to catch up to first place is a bad idea if they lead you by an amount at least half your score but more than a third of your score. In that situation, the standard wager from first place is enough to drop them behind you if they're wrong, but if you wager to catch up, you'll drop below where they fall. If you're in second place, attempting to catch up on your FJ wager is only advisable if first place leads you by less than a third of your score. Consider the following:

Leader: $24,000
You: $18,200

According to your strategy, you bet $5,801. The leader, as can be expected, wagers $12,401. You're both wrong, and the (former) leader falls to $11,599, just below your $12,399. Good!
However, change your score slightly, and...

Leader: $24,000
You: $17,400

According to your strategy, you bet $6,601. The leader, predictably enough, wagers $10,801. You're both wrong, and the leader falls to $13,199, while you fall to $10,799. Bad!

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Re: Monday, November 28, 2016 Game Recap & Discussion [SPOILERS]

Post by marethyu » Sat Jan 07, 2017 12:20 am

You've got mostly the right idea, but wagering to catch up to first place is a bad idea if they lead you by an amount at least half your score but more than a third of your score. In that situation, the standard wager from first place is enough to drop them behind you if they're wrong, but if you wager to catch up, you'll drop below where they fall. If you're in second place, attempting to catch up on your FJ wager is only advisable if first place leads you by less than a third of your score. Consider the following:

Leader: $24,000
You: $18,200

According to your strategy, you bet $5,801. The leader, as can be expected, wagers $12,401. You're both wrong, and the (former) leader falls to $11,599, just below your $12,399. Good!
However, change your score slightly, and...

Leader: $24,000
You: $17,400

According to your strategy, you bet $6,601. The leader, predictably enough, wagers $10,801. You're both wrong, and the leader falls to $13,199, while you fall to $10,799. Bad!
Good point. I was over generalizing. It did seem like there were a string of episodes in December where people lost because of bad wagering strategy and others won because of good strategy. It doesn't seem that complicated, except I don't know how much time and what resources (e.g. paper and pencil, calculator) they are given to make their wager. I could see that you might make a mistaken calculation under the pressure of being on the show, but it seems like some people ignore strategy completely, which I find odd for such otherwise intelligent people.

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