Some Thoughts on the Pick-3

by Dick Mitchell

My good pal James Quinn has improved his profits dramatically because of this wonderful addition to exotic wagering. In Southern California, every race is a Pick-3 race because of the rolling Pick-3's. Quinn has devised a powerful strategy that works beautifully. Basically, it's to make a line on the contenders in each race, then bet each combination in proportion to the probability of success. (This is really the correct way to bet any exotic.) A simple example would be as follows:

Let's convert Jim's odds line to a probability line:

Leg 1 Leg 2 Leg 3
A .333 A .385 A .286
B .250 B .222 B .200

The probability of Jim's AAA ticket hitting is the product of .333, .385 and .286 or 3.67%. Jim can win the Pick-3 in eight possible ways. Let's compute the probability of each possible winning combination and total his chances of winning the Pick-3:

AAA .0367
AAB .0256
ABA .0211
ABB .0148
BAA .0275
BAB .0193
BBA .0159
BBB .0111

Quinn has a 17.2% chance to hit this Pick-3. This checks out with fact that he had a .583 probability of winning the first leg, a .607 win probability of winning the second leg, and a .486 win probability of winning the last leg. When you multiply .583 times .607 times .486, the product is .1720. Therefore, he needs at least 6-to-1 on his bet to guarantee a positive edge.

(AAA is three times more likely than BBB, yet most players will bet the same amount on each of these combinations. Too many horseplayers make the mistake of betting the same amount of money on each combination even when there is a great disparity in possible outcomes.) 

Suppose Quinn's betting a total of $100 on this particular Pick-3. The way he would bet this Pick-3 is to wager the following amounts on each combination:

AAA $21
AAB 15
ABA 12
BAA 16
BAB 11

The way each bet was calculated was to divide each winning probability by his total probability of winning the bet (.172), then multiply by the bet size of $100. The result is then rounded-off to the nearest dollar. The probability of AAA was .0367. This divided by .172 equals .213. Multiplying by 100 and rounding-off to the nearest dollar yields $21. The balance of this table was calculated in the very same way.

Quinn won't have too many problems getting over $600 back because he has each possible winning bet multiple times.

Notice that Quinn's strategy says nothing about favorites. This may be a big mistake. My research into the Pick-3 proves beyond a shadow of a doubt that you shouldn't include public favorites on your ticket. The worst case allows only one public favorite. It's a mathematical fact that zero public favorites appearing on a winning Pick-3 ticket is more probable than two or more winning favorites appearing on the same winning ticket! Which leads to my cardinal rule for playing the Pick-3:

Never Purchase A Pick-3 Ticket Which Contains More Than One Public Favorite. It's A Negative Expectation Bet. Let The Suckers Do It. It's Not For You.

Quinn advises that two favorites can be used in a very special case. It's when some "zongo" horse at double-digit odds is your stand-out top pick in one of the three legs. I reluctantly agree.

See you on the short line, and hopefully the special IRS line.