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Bad bets should NEVER be made, especially if they are being made to massage your fragile ego!
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Never is a long time.
To say that negative expectation bets should never be made would be an incorrect assumption, even mathematically.
If you are a believer in the Kelly Criterion, this comes rather easy. It was first illustrated (to my knowledge) in Alan Wilson's
Casino Gambler's Guide, back in like 1959. In that book he gave a theoretical example of how it could work.
Suppose you have a system which produces a 20/1 play in every race and that each such horse wins 1-time-in-10. Thus, you win 10% at $42 = $4.20 $net, an advantage of +110%.
Optimum bet would be 5.5% (advantage divided by odds).
Suppose you also bet an equal amount on the favorite in every race which loses 10% on each bet but wins 30% of the time at $6.00. Thus, out of 100 bets, you now have:
100 bets @ $4 each = $400
10 wins @ $42 each = $420
30 wins @ $ 6 each = $180
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40 wins = $600 (avg mutuel = $15 or 6.5:1 odds)
$Net has dropped to $3.00, a 50% advantage but now you are winning
4 times as often!
Optimum bet is now 50% / 6.5% = 7.7%.
In other words, you can now safely wager more money.
While the example is a bit rigid and the loss on the favorite inaccurate, it is a perfect example of how a hedge helps you play a
better game.
Regards,
Dave Schwartz
