I know this is an old post but Im gonna reply to it anyways, maybe there are others who dont yet grasp why the percentage of doubles in boxed form is so much higher than the percentage of the doubles in straight form.
They key to understanding the odds and frequencies of Pick 3 is to relize that no matter how you play (straight or boxed) there is ALWAYS 1000 possible outcomes for each game. Playing a Double in boxed form just means that when any one of the 3 versions of it is drawn that you will win. For example, we all know that if you play the number 122 boxed that 221 or 212 can come up to make you a winner.
Remember there are 1000 numbers that could be drawn for that game, so we take the 1000 possibilities and divide by the 3 that we hope to see drawn and come up with odds of 1 in 333.33.
When looking at a list of all 220 boxed numbers you would see exactly 90 different doubles, but you have to remember that each one of those 90 doubles only represents ONE version (or arrangement) of the THREE that are possible for each. This means that each of those 90 numbers can be played or arranged 3 ways for the straight game - 90 X 3 = 270.
Out of 1000 different numbers (or possibilities) you can see that 270 of them are doubles. 270 is 27% of 1000. Since there is always going to be 1000 outcomes that can occur the doubles should be drawn about 27% of the time.
So why then - if there are 220 boxed numbers and 90 of them are doubles (and 90 is 40.9% of the 220) - do doubles NOT fall 40+% of the time?
You have to look at the remaining 130 boxed numbers for your answer. Actually 10 of those 130 are Triples and cannot be played boxed so you are now left with 120 boxed numbers. All of the 120 numbers that are left are all No-Match numbers. No-Match numbers have 3 different digits in them. For example 123, 472 and 059 are all No-Match numbers. When playing a No-Match number boxed you must relize that each No-Match number can come up (or be arranged) SIX different ways. The number 123 boxed could also be drawn 132, 213, 231, 312, or 321 to make you a winner.
Since every one of those 120 No-Match boxed numbers can be drawn (or arranged) in SIX different ways this means that there are 720 total straight No-Match numbers (120 X 6 = 720). 720 is 72% of 1000 and thus No-Match numbers will be drawn about 72% of the time.
To calculate your odds of winning with a single No-Match number in boxed form - (remeber that it can be drawn 6 different ways) - take the 1000 possible outcomes and divide it by your six hopefuls to get your odds of 1 in 166.66 or round it up to 1 in 167.
720 No-Match numbers + 270 Double Digit numbers = 990 out of the total 1000 numbers. The remaining 10 are obviously the Triples, which only occur about 1% of the time (10 is 1% of 1000).
Hope this helps anyone new to the game.