For most racing fans, the dead heat between Alpha and Golden Ticket in last month’s Travers Stakes was a charming oddity, the first such outcome in a Travers in more than a century. For those (and I was not among them) who had the acumen to include 33-1 Golden Ticket in their pick four and pick six tickets that day, however, they will remember the race for exposing a flawed and unfair parimutuel rule that deprived them of their rightful winnings on the race.

It is a completely unjustifiable error in the rules that has come up before and prompted calls for change that were quickly ignored or forgotten. Perhaps now that a dead heat occurred in Saratoga’s signature race, regulators will take the few minutes it would require to change the rules.

Without getting too bogged down in the math, here is what happens in most pools when there is a dead heat: The pool is cut in half and ticketholders receive roughly half of what they would have received had their horse been the sole winner. (It’s a rough rather than precise halving of payouts because of rounding and breakage and the inclusion of the $2 wager standard in the way we conventionally express payoffs. The point is that the people who bet on the longer-priced horse get bigger payoffs than those with the shorter-priced horse, as it should be.)

Here’s how it worked on Travers Day:

Those who had an exacta of 5-2 Alpha over 33-1 Golden Ticket got $133.50 for $2, while a ticket of Golden Ticket over Alpha paid $230.00. An Alpha-Golden Ticket-Fast Falcon trifecta paid $2,696, while a Golden Ticket-Alpha-Fast Falcon combo paid $5,296. The superfecta payouts were $20,676 with Alpha on top and $38,545 the other way. The payouts look odd but are mathematically correct if you do the math – the differences are not as big as you would expect because so many bettors box and wheel in intrarace bets, a topic for another day.

The same thing happened in the double and pick three and better illustrated the difference in odds between the dead-heat winners. The double from Willy Beamin in the Woody Stephens paid $68 to Alpha and $579 to Golden Ticket. The pick three ending with Alpha paid $141.50, while the one to Golden Ticket paid $1,907.

When it came to the pick four ending with the Travers, however, an entirely different procedure was dictated by the rules. Instead of splitting the pool in half, and giving higher payouts to the fewer number of tickets alive to Golden Tickets, the entire pool was divided by the total number of winning tickets on both horses. The pick four paid $990.00 regardless of whether you had used Alpha or Golden Ticket.

This is completely unfair and completely different from the way the other pools were paid out. If you get more than 13 times as much for a pick three ending with Golden Ticket than you do for a pick three ending with Alpha, why should you get the exact same payout with either horse in the pick four? Had the pick four payouts been calculated in the same manner as the win, exacta, trifecta, superfecta, double, and pick three payouts, it would have paid something more like $500 to Alpha and $7,500 to Golden Ticket. Instead, everyone got the same $990 payoff, an undeserved boost for those who bet Alpha and a devastating reduction for those who deserved so much more with Golden Ticket.

Here’s the real irony: The pick four still would have paid $990 to Golden Ticket had he been scratched at the gate – the tickets live to him would have been transferred to the post-time favorite, who happened to be Alpha. So bettors in effect got zero credit for Golden Ticket’s performance.

In the pick six, the same unjust rule applied and those who picked 6 out of 6 (the Travers was the fifth leg) got $11,497 regardless of whether they used Alpha or Golden Ticket. It’s impossible to know how many live tickets ran through each horse, but the payoffs should have been more like $5,000 to $10,000 if you used Alpha and $50,000 or more if you used Golden Ticket.

It gets a little more complicated with the pick six, with some side issues such as what to do about consolation payoffs, but there are solutions to those problems. There is no complexity, however, to changing the rules for the pick four: Simply make them the same as the pick three and every other bet and have two payouts. It’s a simple software rewrite for the tote system, and all it requires is a rule change from the State Racing and Wagering Board.

Saratoga officials met and endorsed a change in the pick four rules within days of the race. Now regulators should act quickly to implement it.