Winning underlay or losing overlay? The Players Pool conundrum

You are offered two games of chance with fixed odds. In the first game, you flip a coin and get 4-to-5 odds on your choice (heads or tails). In the second game, you roll a standard six-sided die and get 6-to-1 odds on your choice (1, 2, 3, 4, 5, or 6).

Which game do you choose if...

A) You get one chance and must bet 100% of your bankroll?
B) You get 100 chances but can only bet 1% of your bankroll on each chance?


The coin offers underlaid odds but a much higher chance of success. The die offers better value, but you fail 83.3% of the time.

So if I only get one chance for all of my bankroll I'm flipping the coin. My expected value is lower, but so is my risk of ruin. Sort of a one in the hand is worth two in the bush situation. Under the "B" scenario I'm rolling the die. I'll win less often, but getting 6-to-1 instead of the fair value 5-to-1 on each successful roll makes it far more likely that I will profit.

Balancing these probabilities is at the heart of multi-race wagering for me. Giving yourself a chance not only at success from a "hitting it" standpoint but also financially rewarded for the risk taken.

The Pick 6 on Wednesday at Belmont featured a $248,140 carryover and a coin flip paying 1-to-2 in the form of Crackerjack Jones in race 5 (leg 2). 3-to-5 on the morning line, Crackerjack Jones paid $2.90 after winning by 4 3/4 lengths. He was never threatened, and in retrospect  was probably fair odds to win considering it's tough to see him losing that race more than a third of the time.

The Players Pool took a stand against him, however, using him on "only" 42.82% of our tickets, which indicates odds of about 4-to-3. The thinking was that there was far more value in beating him than trying to hit it multiple times at the expense of not using longshots we liked later in the sequence. As it turns out, Crackerjack Jones won and none of the potential $20+ horses we liked ran a step.

We correctly leaned on Strapping Groom, who won race eight (leg five) at odds of 23-to-5. We used him on 22.7% of our tickets (17-to-5), but made our biggest mistake in the first leg where Cay To Pomeroy faltered as the 1.55-to-1 second choice but as the top choice on our tickets with 48.9% (nearly even money) of our action.

All that adds up to we backed the wrong side of the coin and was wrong about the die. We took the calculated risk to play the ticket to give us the best chance at a $500,000 score. We don't always play it that way. Sometimes I agree with the public that a horse like Crackerhead Jones can't lose, and we ask, "what can we do to hit this thing 10 times?"

Even with all the dead money in the pool from the two-day carryover, a horse like Crackerhead Jones winning is never going to produce the watershed payoff, and that's OK. If you choose to flip the coin then make the most of the opportunity. But having $48,315 to put into the Pick 6 and not loving a 1-to-2 favorite put us in a unique position to make a really nice score otherwise.

Here's to next time.