Optimal Betting

[partsnut]

"Recently I posted a winning ticket, where I bet 2 horses to win
My bankroll was $50 I bet $5 per horse. The odds on each horse
were 3.10 and 3.30 to one
A poster criticized me for making the bet
I want to see if you can tell me if the bet was okay
Thanks
Bill"

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It is not my intention to insult anyone. I merely want to express what I believe to be true. If I'm wrong, which I don't believe I am, I stand corrected.

Assuming that you can maintain a 55% win percentage picking two horses in a race in the long term (100 races minimum), it would be necessary for one to maintain a minimum of a 5% edge to show a meager profit which would hardly be worth ones time.
The following formula can be used to calculate this “edge”

Winning Edge = Win% X Average Odds - Loss%

In the above scenario, you were wiling to accept an $8.00+ payout on $4.00 bet which relates to an even money bet on average possibly 6-5 at most.
Using the above formula which I believe is mathematically credible, this is what you have achieved and what you have to look forward to over the long run.
As per your example race:


Horse 1 (which you conceded as a loss in your two horse bet ) taking into consideration a possible Dead Heat to win.
1% X 1.2 -99% = -97.8 negative edge

Horse 2 (which is your winning horse)
55% X 1.2-45% = +21 positive edge

Total edge on a 2 horse bet at the above odds = -66.8% negative edge.
Over the long run you will deplete your bankroll on these type of bets and at the aforementioned odds.