This one is convoluted, and I’m not sure if there actually is an answer. For a character in a story.

You have magic and want to rig a sporting event. However sometimes the spell will backfire. The backfire is intelligent. What is a spell you could cast in a basketball game that would enable you to still win a sports bet? The backfire's purpose is to be your enemy and to keep you stuck where you are.

Examples. Say you cast a spell to make Team A win. It will work, but the backfire kicks in if you start to win consistently or you get larger amounts of money. In that case if it kicks in then Team B will win.

If the backfire consistently kicks in and you notice and instead try to bet against the team you spelled to win, the backfire will notice and stop itself from kicking in, letting your spell take affect as intended.

Sometimes the backfire will not activate on purpose just to trick you to bet larger amounts.

For this question, we are assuming the backfire has to kick in or the spell will work as intended. There is no situation where neither occur.

Let’s also assume spell and backfire will take priority with what the exact wording of the spell says. Say you wish for Team A to win, it’s smart enough to know to activate or not to in order to screw you up. So the spell plus bets needs to be for something you want to happen, but if the opposite occurs, you still win. The spell can be in plain English and as simple or complex as it needs to be.

What is a spell and a bet, or combination of bets, that would ensure you always make a profit regardless of if the backfire kicks in or not? Is this possible? Let’s assume the types of bets are any kind of bet you can make on an average basketball game. You can also cast multiple spells, though each operate independently of another.

  • $\begingroup$ So essentially you're playing rock-paper-scissor against an intelligent spell, trying to guess whether it will decide to backfire or not in the next match? $\endgroup$
    – Stef
    Commented Jan 26 at 12:16
  • $\begingroup$ Are "prop bets" in scope? (Someone will score 50 points, someone will miss 4 free throws...) These have big odds, so betting two of them and making a spell/backfire that ensures one or the other will happen should get you big returns $\endgroup$ Commented Jan 26 at 13:23

3 Answers 3


This "spell" is equivalent to any sports fan's totally ineffective superstition. It is the equivalent of a "lucky hat" - sometimes wearing it makes your team win, but sometimes it doesn't, and whether or not it will work is totally unpredictable from your perspective. An occasionally-lucky hat cannot make you a better gambler. To guarantee a win, we must assume the worst possible outcome - all outcomes must be profitable, since if any are not, we can't guarantee a win.

To profit, what you need is arbitrage betting or a Dutch book, which means there is a combination of bets with odds set in such a way that you can win money regardless of the outcome. The "spell" is totally irrelevant to the question, whether or not you can make a bet that is guaranteed to win depends only on the odds and payouts.

If the bookie is offering 3:1 on one team and 1:1 on the other, you can bet \$50 to win \$150 on the first team and \$100 to win \$100 on the second - regardless of which team wins, you walk away with \$200 despite having spent only \$150 on the bet. For obvious reasons, real-life bookies do not offer odds like this unless they've made a mistake.

If there is any possibility that you'll lose money on the bet (which is always the case with odds that are properly set by a real odds-maker), you obviously cannot guarantee that the losing outcome will not occur.

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    $\begingroup$ This completely ignored the most important part of the question. Regardless if the person is within a fantasy setting, the “spell” is a highly important part of this question. This isn’t a situation where the user thinks it works. It’s a fact of the setting that it does. $\endgroup$
    – rclev
    Commented Jan 25 at 16:45
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    $\begingroup$ @rclev But sometimes it doesn't work, and you don't know when it will or won't. How, exactly, is the spell different from a lucky hat? The overall point is that to guarantee a win, all outcomes must win, and the only way to do that is with a Dutch book. If there are any possible losing outcomes of the game, the spell can backfire and make that one happen, making your win not guaranteed. $\endgroup$ Commented Jan 25 at 16:48
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    $\begingroup$ @rclev Whether it works matters to the probabilities of different outcomes, but not to which outcomes are possible. You haven't asked "what's the best way to maximize expected reward", but "what's a way to guarantee a positive reward". $\endgroup$
    – Sneftel
    Commented Jan 25 at 16:48
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    $\begingroup$ @rclev What you wish for is totally irrelevant, as the spell is free to choose to grant your wish or not. You must assume the worst possible outcome to see if your win is guaranteed. If your worst possible outcome is a loss, you can't guarantee a win. Unless you have a Dutch book, there cannot be only winning outcomes, therefore, it's always possible you'll lose with properly set odds. $\endgroup$ Commented Jan 25 at 16:55
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    $\begingroup$ @NuclearHoagie I figure that may be correct too, thank you. Though one note difference, the spell has the option to grant my wish or do the opposite. It doesn’t have the option of just doing nothing and letting things play out. I was hoping the magic user could come up with a clever play on words and bets that would result in him still getting a payout in the green. $\endgroup$
    – rclev
    Commented Jan 25 at 17:04

This answer is derived from the comment thread under Nuclear Hoagie's answer; I figured that the findings of the discussion there was significant enough to warrant being restated as an answer.

This is impossible

It seemed from that discussion that the intended answer was probably something similar to

The wizard should cast a spell to make one team win, and then bet that the game will not be a tie.

This (and other constructions like it) do not work because

The opposite of the Blue Team winning is not that the Blue Team loses; it's that the Blue Team does not win. Since the spell misfire behaves in a way is maximally bad for the caster, the misfire will cause a tie.

This is true in all possible constructions. Suppose that you bet on outcome $p$ and cast a spell to cause outcome $q$ to happen.

If $p = q$, then any backfire causes you to lose your bet.
Example: You bet that the blue team will win, cast a spell to make the blue team win, the spell backfires and the red team wins.
If $q \subset p$, then the backfire can pick an outcome in $\neg q$ such that you lose your bet.
Example: You bet that the game will not be a draw and cast a spell such that the blue team will win. Your spell backfires, blue team does not win and the game ends in a draw.
If $p \subset q$, then it is possible that your spell will succeed but you still lose your bet.
Example: You bet that the blue team will win and cast a spell such that the game will not be a draw. Your spell succeeds, but the red team wins.
If $q \not \subseteq p$ and $p \not \subseteq q$, then your spell can make no guarantees about the outcome of your bet.
Example: You bet that blue team will win and cast a spell such that the weather is sunny. Your spell can succeed or fail, but either way the red team might win.

This covers all possible cases.

Multiple spells also don't make a difference

For any set of multiple spells, consider the single spell which combines all the effects of those spells into a single spell.
*Example: If you were going to cast two spells, "The blue team wins" and "It is sunny on the game day," then consider the combined spell "It is sunny on the game day and the blue team wins."

The negation of a conjunction is a negated disjunction, so a misfire can cause one or more of the original statements to fail.
*Example: The spell above's misfire means, "It is not sunny on the game day or the blue team does not win."

This negated disjunction covers all possible outcomes of any non-empty subset of spells in the original set backfiring. Therefore, for any set of multiple spells, there is a single spell such that every outcome that is possible under the set of spells is also possible under the combined spell and vice-versa.

We're all wizards

While writing this answer, I discovered that I can cast this spell in real life! In fact, if I know the probability of $x$ happening, I can even calculate the probability of my spell backfiring (because it is the same probability).

Given a randomized deck of 52 playing cards, I can cast a spell to summon the Ace of Spades to the top of the deck, with a $\frac{51}{52}$ chance of it backfiring and sending the Ace of Spades somewhere else in the deck.

Every human on earth has this power, and it seemingly hasn't helped us develop betting strategies to always win - at least not against competent bookies.


Given you say this is for a character in a story, the Worldbuilding StackExchange might be a better venue for this question. I answer as if it was posted there.

The spell is intelligent. What does it want?

It's not entirely clear what the spell wants; but if it's consistent, then it's potentially abusable.

If it always tries to lose you money, make small bets against your favourite sports team and watch them trounce the opposition.

If it always tries to make sure you never make net money from gambling, giving away your winnings to good causes might make it consider those as deductable losses.

If the spell only watches you and your actions, a friend might be outside the scope of the spell and be able to make greater opposite bets. Or simply someone who notices that you have terrible, terrible luck and always bets against you.

Only if the spell is omniscient and perfectly malevolent is there no chance that something might be wrought from it.


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