Real life Scrabble puzzle

[Pablo]

My wife and I play Scrabble almost every day. A while back I noticed that she seemed to get the blank tiles at a much higher frequency than I did. After I noticed that, I started keeping track.

In the last 87 games, I have drawn 52 blanks. That means that in those games she has drawn 122. Can someone help me figure the odds against drawing 70% of the blanks over an 87 game span? I figure it's the same as flipping a coin 174 times and getting 122 heads. I'm assuming we each use the same number of letters per game. I have won roughly 80% of the games, so in reality, I've probably drawn more letters than she, but can't say for sure.
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All religions are the same - Guilt....just with different holidays.

[Persona]

The odds of a particular number of coin flips aren't that useful, it'll just tell you that it's hard to predict the exact number of coin flips that turn up one way or the other. Specifically, the odds of 122 heads in 174 flips is about 1 in 30 million What you want is probably the odds against drawing 122 or more of the blanks, basically asking 'How likely am I to see something at least this surprising?' That's given lower on that page as 5.758*10 ^-8 , or about 1 in 18 million.

I don't know a delicate way to bring this up, but I will anyways: it's possible to fish for blank tiles by feeling both sides before pulling them from the bag. A fair coin makes for a poor model in this case.

[Chuck]

As I said in another thread, a weaker player might play more tiles due to not saving good letter combinations for future opportunities and being less concerned about creating opportunities for opponents. If she's getting about 70% of the blanks maybe she's drawing 70% of the tiles. That seems kind of high but it's starting to seem more likely now.

[Antrax]

You best bet is to assume the number of games is large enough that a normal distribution approximates it. Then you can use that phi function thing to approximate the odds your wife will stray so far from the average, in terms of blanks drawn.
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After years of disappointment with get rich quick schemes, I know I'm gonna get rich with this scheme. And quick!

[PuzzleScot]

I would suggest an alternative method of drawing tiles! (I agree with Wolfram Alpha)

1) Place all unused tiles face down inside the scrabble box lid. This is what we used to do in the 'olden days' before bags were invented. Make sure the tiles aren't marked in any way. or...

2) Draw tiles from the bag for each other.

It would be interesting to see how the statistics added up over the next 50 games using the latter method:

- If she is subconsciously choosing the blanks, you will get more than her.
- If she is still getting most of them, then she is cheating by not letting you have any of the blanks she finds!
- If the distribution becomes even again, then perhaps it was a statistical anomoly, or she's started behaving...

I'm impressed she still plays you if she's consistently losing. Perhaps she feels the blanks give her an edge to make it fairer. I got the game 'Boggle' a few years ago. We played 20-30 times, and I won every time, so she won't play against me any more.

[Zag]

I like the idea that you draw each other's tiles. That way, at least, if there is evil karma going on, you can transfer it!

You also should start keeping track of how many tiles you each play over the course of a game. I'll bet that she is drawing more than you.

PuzzleScot, I had the same problem, but we solved it somewhat. We used to play fairly often as a family, when my kids were 10 and 12 until they were 12 and 14. We adjusted the rules in this way, to try to make it even.

1. Our younger child could count a word unless EVERYONE else had it.
2. I could count a word only if no one else had it.
3. Our older child could count a word unless the younger child had it, but the parents having it did not exclude him from counting it.
4. My wife could count a word as long as neither child had it. If she and I were the only ones to have a word, she counted it and I didn't.

With these rules, games were pretty close, and everyone won occasionally. Mostly, though, the older child and I won.

[Pablo]

We never draw out of the bag. In every game I lay the tiles out face down in the lid of the box. Neither of us looks when we choose our own tiles. I watch her, and it's very obvious she's drawing quickly and randomly.

After playing all these games, I would estimate that neither of us has drawn a majority of tiles that exceeds 52%.

In those 80+ games, I have had both blanks maybe 5 times. She usually has both of them before half the tiles are played.

Maybe the law of averages has a few exceptions....like most other laws.
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All religions are the same - Guilt....just with different holidays.

[Trojan Horse]

Then maybe you better count the tiles once they are all laid out. Make sure they are all there.

There's always the "hide the blank tile up the sleeve" trick, after all...

On second thought, maybe you shouldn't investigate too closely. Perhaps the best strategy is "let the wookie win".

[Pablo]

[Forrest Gump]

This being the Grey Labyrinth and all, I'm surprised no one has thought outside of the box on this. Consider:

> Hundreds of games have been played with (I presume) the same set of tiles.

> The tiles are clearly visible during draws.

> Pablo wins 80% of the games despite the fact that

> His opponent draws 70% of the blanks.

> His opponent is also his wife.

Given these facts, has anyone considered that it might actually be that Pablo is subconsciously avoiding drawing the blanks in order to give his opponent a sporting chance?

[Antrax]

And his psychic powers could also explain his success in the fast-moving world of PVC pipes.
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After years of disappointment with get rich quick schemes, I know I'm gonna get rich with this scheme. And quick!

[Pablo*]

[Pablo]

Just in case anyone is still interested (1 chance in 18 million?), I have now drawn 73 blanks in the last 113 games, which means it's getting better. I've had 21 blanks in 26 games since I opened this thread.

However, I'm on a "cold" streak at the moment. One blank in the last four games, none in the last three.
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All religions are the same - Guilt....just with different holidays.

[MatthewV]

You should get another scrabble set and replace your blank tiles with the ones from the new set.
If your tiles are now slightly worn from usage, the new blanks should be easy to spot. Have no mercy!