Startling bowling result

[BruceZ]

Where I bowl there is a jackpot which you win by making 9 strikes in 9 particular frames. My friend was considering entering the jackpot, so I asked him how many strikes he averages per game. He said 6. This would be out of 11 tries since you average 2 tries in the final frame. So his probability of striking is 6/11, and his chance of winning the jackpot is (6/11)^9 = 235-1. Since it costs $5 to enter the jackpot, it would need to be over $1175 to enter, and it is sometimes over this amount.

Then I calculated how big it needed to be for me to enter. I average 4 strikes per game, so the odds of me winning the jackpot are (4/11)^9 = 8996 to 1! The jackpot would have to be over 45 grand for me to enter as opposed to just $1175 for my friend, and that's just with a difference of 2 strikes per game.

bruce, a difference of "just" two strikes per game is still a 1.5 fold advantage for your friend. this advantage starts big; of course it's going to get huge after 9 trials.

we know from games like blackjack that even tiny edges are devastating in the long run, so it shouldn't come as a shock that the relatively large 3-2 advantage you describe here is also devastating.

so, perhaps taking side bets on strikes is better than counting cards.

[BruceZ]

There's no question he will have a big advantage over me in 9 frames, but when it came up that he was a 235-1 dog and I was almost a 9 THOUSAND-1 dog, I initally assumed I had too many beers and typed the numbers into my calculator wrong.

[irchans]

Bruce, I often wonder whether we can really assume independence in these sport game estimates. Can we forecast the record number of strikes for a person given his average number of strikes?

For your friend, assuming he plays 150 games a year for 10 years, it is more or less likely that he will have a 300 game. Did he ever get one?

[BruceZ]

I've heard about a study of professional athletes that disproved the concept of hot and cold games. For example, a basketball player would not have an exceptionally good shooting night any more frequently than his overall shooting statistics would dictate. I suppose this may suggest a sort of independence depending on what statistics were used.

On the other hand, I definitely feel that I am a fundamentally better bowler on some days than on others. If I start off striking, I am more likely to keep striking. Some of this may be an illusion too. Often a player will bowl a top game followed immediately by a mediocre game. He will say he "lost the recipie". Much of this may be that he never really had the recipie, but just got lucky. Since we are constantly making mental and physical adjustments, we tend to credit a success to our last adjustment. We can make the same adjustment the next day or even the next game with poor results.

As for my friend, he has only been bowling a couple years but has already bowled a 290 game with 11 strikes in a row. Many amateurs have been bowling all their lives without a 300 game, while some have had several.

[lorinda]

Assuming independence is very tough in these situations.
We used to take advantage of the "bowl all day" offers at our local bowling alley (Bowling in England is so expensive that you guys would cringe)
A regular pattern (we would bowl 40 games in a day) would be to start of around 120. The scores would increase to around 160 and then drop off again.
After concentration had been regained, the scores would build up again and we could bowl several 180s in a row.
On almost every occasion that I have bowled a 200 (At my level this is like a 300 to a good player) my next game has been hideous.
Also bowling with an opponent is harder if they are having a terrible game.
When my friend got our first ever 200 game, I beat him in that game!!!!

[BruceZ]

The lane conditions play a big factor, and the oil patterns change as play goes on. At times there is a hard wall worn into the oil which tends to keep balls online into the pocket. Shots inside do not drift too far inside, and shots outside come hooking back into play. If it's severe enough (and you are a good bowler) you almost have to try to miss. Lanes start out with a certain oil pattern (which also varies with the house), and then dry out in certain areas causing greater hook. Sometimes oil carries further down the lane causing a delayed hook for balls thrown in that region. Depending on your style, you will get better or worse as conditions change. This also depends on the line your opponent is using, and even on the type of balls being used. A large part of bowling is figuring out how to adapt quickly to the oil patterns as they are changing. As you tire, you tend to change your timing and throw the ball slower. This results in greater hook.

How much is bowling in England? 40 games per person??? That's nuts, 8 games at a stretch is alot. Do you have alot of 10-pin bowling there, not lawn bowling? [img]/forums/images/icons/smile.gif[/img]

[lorinda]

Typically you would pay around $12-15 for three games.
If you play the all day offer it is about $12 for 9 hours [img]/forums/images/icons/laugh.gif[/img]

I bowl straight, so I can never get a 300 game, I have calculated long ago that my highest of 214 is about as good as I can get without learning to hook [img]/forums/images/icons/frown.gif[/img]

A city over here would have one or two bowling alleys, but it is considered an unusual night out,most people probably go no more than twice a year.

[BruceZ]

lorinda - I sent you a pm about becoming a hooker....er, someone who throws hooks.

[chaos]

The only way to bowl a 290 is 11 strikes followed by a gutterball. Not a very believable claim!