In the same vein as steel shot, would a single-shot handgun firing steel shot have any chance of that many ricochets?
A steel bullet or even something like a solid copper FMJ should have some high potential.
Pretty much everything listed on the federal prohibited list of what creates an illegal 'armor' piercing handgun material, with some they missed.
Another big factor is the angles of the ricochet. Just like you can skip a rock on water at one angle, but just have it splash into the water at another, the bullet will retain different amounts of energy after ricochets at different angles.
I don't recomend it because of the clear danger to you and anyone else around, but you can get quite accurate with intentional ricochets (of course if the surface chips, breaks etc it can give erratic results) having them go where you want.
A round ball, especialy one that is plated will be easier to ricochet in a desired direction because it won't start tumbling and impacting at different random points on the bullet giving more erratic results like other bullets. A sphere that holds its shape gives much more repeatable and predictable results.
As for a bullet in common use, a .22 is exempt from the regulation of how much of the jacket can legaly be the total weight of the bullet (no more than 25% for rounds above .22) which means some can consist of mainly jacket. Such a .22 should ricochet on hard surfaces very well. They might not be really common anymore though because the lead inside is cheaper than the copper jacket, so there is probably not many manufacturers adding more jacket material than necessary.
Think about a bullet trap. It is essentialy forcing a ricochet. You could even design one to richochet the rounds in a half circle right back at the shooter with all internal flat surfaces if you were inclined, causing them to do a 180. If each ricochet was a gradual change from the previous angle, much of the energy would be retained.
The greater the angle a round impacts a surface at the more of the energy is generaly lost. Several slight angles would preserve most of the energy of the round.
In a circular room with sheet metal lined walls you could fire the round along the wall and be hit in the back.
In fact if you setup a gun to fire by itself in such a room along the wall it would be interesting to see just how many revolutions around the room the projectile took before coming to a stop. The harder the surface and harder the bullet the more ricochets possible with more energy retention. One of the reasons lead is actualy much safer at a range than something like steel. It takes a bigger error with lead projectiles fired downrange to put people in danger than with steel projectiles.
You could ricochet something like steel shot all over the place by impacting a hard surface at an angle, whether a rock in the ground or a piece of metal etc
