I won the football pool a couple times and thought: “Wouldn’t it be fun to win more?” It’s a one-dollar pool. There is no limit to the number of entries. What if I submitted more than one sheet? I would have a greater chance of winning. My one in twenty chance could be a two in twenty-one chance. What if I really wanted to mess with people one week and guarantee I’d win just for fun; submit enough entries to cover every possible combination? Fifteen games in a week, excluding Monday night. How much would it cost to just bet every game? There are only two possible outcomes on the betting sheet for each game. There couldn’t be *that* many possibilities altogether. I did the math. Actually I tried to do the math, but lost the thread. If there is only one game, there are two possible outcomes (discounting ties); one team wins or the other one does. If there are two games, there are four possible outcomes. It gets a little harder after that. Three games, eight possibilities. Now I’m confused. I need a formula. It’s not simple multiplication; it’s something more sophisticated. I remember “factorial” from a statistics class a gazillion years ago. That’s a number times every whole integer number below it in sequence. That applies to some statistical situations, and almost to this one, but not quite. We turned to our grandson Tony for the math. He said the answer would be the number of possible outcomes, to the power of the number of games played. I tested that out on the lower numbers. One game, two possible outcomes, two to the power of one equals two. That works. Two games. Two to the power of two. Four. That works. Four games, sixteen possibilities. That’s sixteen dollars to dominate a four game pool. It’s starting to get a little scary. Okay, so what’ my out-of-pocket cost to guarantee the football pool? No more bye-weeks at this point in the season, so each pool is fifteen games. Two to the power of fifteen. Ooh, that’s a lot of doublings to win a $20 pool. For a mere $32,768, I can guarantee that no one will beat me; but I can’t guarantee that no-one will tie me! If one person tied me once, I’d be out $16,000! Not a good bet.
Judy and I each got the gift of hearing for Christmas at our house this year
Judy opened hers early; her hearing aid. I waited until Christmas to open mine. My hearing assist has more to do with birding than just regular hearing.
It’s a headset with a digital processor that picks out the higher frequencies that I can’t hear, and cuts them in half (or by three or by four), to bring them down to my hearing range. Here is the processing unit. It can just drop in a shirt pocket and the controls are still accessible from the top.
Here is a link to the demo of how it can bring high-pitched bird sounds into hearing range: http://hearbirdsagain.com/sound-samples/ We were going to test it out today, do a little bird listening, but there is a front blowing through. We didn’t think a roaring windstorm was the best time to check out our new listening device, so we stayed home for a calmer day.
It’s a headset with a digital processor that picks out the higher frequencies that I can’t hear, and cuts them in half (or by three or by four), to bring them down to my hearing range. Here is the processing unit. It can just drop in a shirt pocket and the controls are still accessible from the top. Here is a link to the demo of how it can bring high-pitched bird sounds into hearing range: http://hearbirdsagain.com/sound-samples/ We were going to test it out today, do a little bird listening, but there is a front blowing through. We didn’t think a roaring windstorm was the best time to check out our new listening device, so we stayed home for a calmer day. Merry Christmas everybody
Or as we say at our house, Merry Skype Christmas. We started our day with coffee and fresh cinnamon rolls for breakfast at Becky and Brian’s house in Colorado. (They didn’t actually eat hot cinnamon rolls, but we did. I did hear something about fresh Monkey Bread on the agenda at their house a little later.)
Then we moved on to Matt and Lindsay’s house about fifty miles south of Becky’s.
Both houses had a cold snow-on-the-ground, crunchy-ice-on-the-streets Christmas Day. Arie colored really really close to the computer screen without actually coloring on it (we think).
And we finished up the day with dinner at Tom and Kathy’s thirty-five miles south of us here in the Valley.
Smoked ham. Yum. They got us fed and gone by five so we could make it home by dark. Judy can’t see to drive after dark, and I’m not turning my head yet. A darn good day. (And 80 degrees too.) Happy Holidays.
Then we moved on to Matt and Lindsay’s house about fifty miles south of Becky’s. Both houses had a cold snow-on-the-ground, crunchy-ice-on-the-streets Christmas Day. Arie colored really really close to the computer screen without actually coloring on it (we think). And we finished up the day with dinner at Tom and Kathy’s thirty-five miles south of us here in the Valley. Smoked ham. Yum. They got us fed and gone by five so we could make it home by dark. Judy can’t see to drive after dark, and I’m not turning my head yet. A darn good day. (And 80 degrees too.) Happy Holidays. Happy Christmas Eve
From Henry.
…and us.
…and us. Has anyone noticed?
Has anyone noticed Donald Trump’s campaign claim that he’s the only candidate who is not beholden to special interests? He’s self-financed so he’s not beholden to any billionaire. That’s one of the knocks against one of his rivals, Marco Rubio; that he is backed by one billionaire so big, that if we elect Rubio we’ll just be electing the conservative billionaire Paul Singer’s proxy. Do we think Singer would have direct access to a Rubio presidency? Well, yeah! Trump’s claim that he is independent of any special interests has some appeal on the face of it, but if we think about it a little, we realize that he actually does represent the interests of a major donor. He has his own billionaire; himself. Does Trump strike us as an impartial man who will put the interests of every citizen ahead of his own? His claim is disingenuous, but I haven’t heard anyone call him on that. Just saying…., not that it would make any difference. It would be fruitless to campaign against him, at least in the primaries. Donald Trump is the face of the Republican Party.