03/31/2005 1:00AM

A complex bet made affordable

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NEW YORK - Hawthorne Park's website was carrying the following message Thursday afternoon:

10 cent Superfecta begins at Hawthorne!

Box 6 horses for only $12.00!

Bet a little and win A Lot!

The math was wrong (even for a dime, a six-horse superfecta box costs $36, not $12), but the enthusiasm was forgivable. When Hawthorne takes its first 10-cent superfecta bets on Saturday, following the lead of Hinsdale Greyhound Park and Sam Houston Race Park, it will become the first major-market Thoroughbred signal to offer super-exotic bets at deep discounts.

Fractional betting, as it is known in other countries that long ago embraced the concept, offers a majority of racetrack customers their first real chance to play racing's most complex bets the way that only the well-heeled previously could afford. That six-horse box, which would cost $720 for a $2 unit or $360 at the common $1 minimum, can now be made for $36, and a five-horse box goes for $12 instead of $240 or $120.

"The superfecta has been considered a wager for the big hitters with deep pockets," said Thomas F. Carey, Hawthorne's general manager. "Hawthorne has made the superfecta affordable for all horseplayers."

In addition to basic affordability, dime supers offer two advantages that even those big hitters can enjoy. First, they allow bettors to play some combinations in heavier increments than others, rather than having $1 units on each combination and rooting for the most chaotic result. Second, they will shelter many a superfecta payoff from the illogical Internal Revenue Service reporting and withholding requirements, allowing horseplayers to preserve capital for reinvestment rather than extending interest-free loans to the government while their cash is drained.

Given the confusion over the cost of even a simple six-horse box, horseplayers may want to start doing some scratchpad math at home before tackling the discounted wager. They probably will find that the bets are even cheaper than they imagined, though calculating the cost can sometimes be tricky.

The key to figuring out how much your box or part-wheel will cost is remembering that the same horse can finish in only one position. This is why the cost of a four-horse box is not 4x4x4x4(256 combinations) but 4x3x2x1 (24 combinations). For each additional finish position, you subtract 1 from the number of horses you're using, so a four-horse box is 4x(4-1)x(4-2)x(4-3), or 4x3x2x1. So a six-horse box is 6x5x4x3, or 360 combinations, and an eight-horse box is 8x7x6x5, or 1,680 combinations.

The eight-horse box, even at a bargain $168 for dime bets, is not necessarily a savvy play, given that the $2 payoff has to be $3,360 just for you to get your $168 back. Just as with exactas and trifectas, boxes tend to be wasteful by giving equal emphasis to every horse used. Players may instead want to consider part-wheels, using fewer contenders in the top one or two spots while widening the net below.

Suppose that instead of boxing five horses for 120 combinations, or $12, you instead decreed that only two of them can finish first but as many as eight of them can finish fourth. You might construct a 2x4x6x8 partwheel, which, after you remember to subtract one from the second position, two from the third position and three from the fourth position, works out to a cost of 2x3x4x5 - the same 120 combinations, or $12 at a dime, as the five-horse box.

The math works a little bit differently if you're keying just one horse to win the race over a bunch of them in the other positions, a reasonable approach if you're trying to improve the price of a short-priced favorite in a race where you think a longshot or two could sneak in underneath. If you were keying one horse over six others, a 1x6x6x6 part-wheel, you would start your subtraction one slot later and the cost would be 1x6x5x4, another 120 combos or $12 for a dime.

Plenty of readers including some track executives may already be shaking their heads at what sounds like a lot of intimidating calculation, but the American betting public has repeatedly proven itself more than smart enough to understand exotic bets. Bettors do the same kind of calculations already with trifectas, and even more difficult ones with pick sixes. Even slots players understand that there are eight payout-line possibilities on the tic-tac-toe grid (three up, three down, two diagonal) after they pull the handle. This isn't a lot tougher.

Hinsdale, Sam Houston, and Hawthorne deserve three cheers for trying something new and different that may help bridge the widening gap between the game's most intriguing bets and the reality of most customers' bankrolls. The best way to applaud them, and perhaps to encourage more and bigger tracks to follow suit, is by dropping some dimes into their superfecta pools.