(http://wiki.dominionstrategy.com/images/thumb/7/7c/Chariot_Race.jpg/375px-Chariot_Race.jpg)
Chariot Race was the card that proved the long-standing fan card guideline "don't do cantrip VP tokens" wrong. But is it any good?
The Gist
Chariot Race is bad as an opener. The best time to get it is usually around the third shuffle onwards. It behaves a lot like some other $3 cantrips (Harbinger, Scheme, Sage etc.) in that it hardly ever hurts to add it, so the main question becomes "could I do something better"? Chariot Race likes a high-value deck and thus encourages heavy trashing. You usually want maybe 3 of them, on boards where you want them. When buying them late-game, you should ask yourself whether you expect to activate them twice before the game ends. Chariot Race especially likes cards that give you control over your opponent's draw pile.
In general, it is good to keep in mind that you get Chariot Races for the VP and not so much for economy.
Diminishing returns
This section is devoted to just a bit of simple math that helps us understand Chariot Races a bit better. Let us for a moment assume a hypothetical situation in which your opponent and have decks consisting of 5 $3-costs and 5 $5-costs each. If you add a Chariot Race here, the chance that it fires is 25%: You need to flip a $5 and your opponent needs to flip a $3. So the expected output is 0.25 VP, 0.25$.
Now what if you add second Chariot race? The chance that one of them fires decreases, since you now have an additional $3 in your deck. The output drops to 0.23 VP, 0.23$. But of course you now have two, so the total expected output is 0.46 VP, 0.46$, a plus of 0.21 from the single Chariot Race case. (I am dismissing some technical details on conditional probability that would have some impact here.)
Now let us say you add n Chariot Races. The chance of firing for each will be 5/(2*(9 + n)). But of course you have n of them, so the total output is 5n/(18 + 2n). As n tends to infinity, this expression approaches 2.5. That means that no matter how many Chariot Races you add, you will not make more than 2.5 VP per turn on average.
What this shows is that the more Chariot Races you have, the less benefit you receive from each new one you add. This is bad. Generally speaking, if you build a deck you'd want the benefit-per-turn of each new card you add to be at least as high as the one of the cards you already bought. This is the reason why on most boards, you do not want to gain more than maybe 3 Chariot Races - at that point, there is usually something better you could do for your deck.
What makes Chariot Races better
The first thing to notice is that when the game starts, you have a lot of $0 cost cards in your deck. These will never provide any benefit to Chariot Race, so a key ingredient for a Chariot Race deck is trashing.
With the same reasoning, Chariot Races of course want expensive cards in your deck, and cheap ones in your opponent's. Since you don't normally go for Chariot Race straight away, by the time you would get them you can usually tell which of you has the higher-value deck. If that is you, then grab the Chariot Races. If not, then you better have a plan to end the game quickly before your opponent grabs lots of VP tokens. The expected outcome however is that there is not much of a difference to speak of. In that case, Chariot Races are available as a gain when you have nothing better to do.
A cute trick you can do to improve your Chariot Races is deck inspection and manipulation. If you know just which cards are on your - or your opponent's - deck, then you can choose the best moment to play the Chariot Race. It is good to keep some things in mind however.- generally speaking, manipulating your opponent's deck is much better than manipulating your own, since your opponent's card stays on top for the rest of your turn while yours will be in your hand after you play one Chariot Race.
- you will still be forced to play your Chariot Races without prior inspection a good amount of the time, so don't overrate the effect that deck manipulation has.
- for your own deck, inspection beats manipulation: cards that let you look at the top of your deck (Mystic, Herald, Ironmonger, Doctor etc) usually have a much lower opportunity cost than cards that specifically put certain cards on top of your deck (Mandarin, Count, Secret Passage etc.)
A final, if a bit niche, situation that benefits Chariot Races is discard + overdraw. With overdrawing, you can draw your deck while holding on to most of your Races. Then you can use a discarder to discard your expensive cards, and draw them back up with your Chariot Races.
Pitfalls
Generally speaking, when none of the options discussed above is applicable, then you should not go out of your way to get Chariot Races. But there are some noteworthy cases that can make it particularly bad.
One such case are non-standard costs. A City Quarter on either of your decks will almost always mean that there will be no VP to be gotten. Potion-costs have the same issue. A game where either debt cards or Potion cards feature prominently will make Chariot Race next to useless.
Some attacks - most notably Ghost Ship - can actively help your opponent block your Races.
Finally, if you build a thin deck, then you need to ensure that your Races still have things left to draw by the time you play them. Cards like Scrying Pool can lead to problematic situations; in such cases you usually want to play your Races as early as possible.
Some notes on deck tracking
Finally, it should be pointed out that you can get more value from your Races if you track your deck. Also, once you have already played a Chariot Race, remember what card is on top of your opponent's deck. Sometimes you can guarantee that you flip a higher card if you know what's left in your draw pile. Or there may be an opportunity to let a well-timed Swindler remove that troublesome Province from the top of your opponent's deck.