so I bought a pinball machine: bagatelle notes: pin bagatelles / French bagatelle / Klondike Pool

Here we have the innovation that truly scratches the gambler's itch: the entire table is slanted, ensuring the balls always roll down towards the player, and introduces a strong element of chance.

These designs would be imitated by the toy bagatelles of the 1800s, which would eventually include a spring plunger in the 2nd half of the 19th century. (citations needed!)

Previous entries in this series include bagatelle notes, and carombolette notes.

These slanted tables tend to also get called bagatelle interchangeably with the flat billiard-style ones, which is why I like say "pin bagatelle" as the overarching category. AFAIK there was never any steadfast naming convention, which mirrors billiards whole convoluted history, rife with variants of design and rules.

According to Bueschel's Encyclopedia of Pinball, it was "cockamaroo" that added the left channel and the scoring pockets along the bottom, but it's quite rare to find tables that don't have them.

CHEVROT & LE BON
F 101, Avenue Montaigne Paris Très belle table de Billard chinois Placage de palissandre vernis, métal et bronze doré France, Paris, fin du XXème siècle Nous y joignons une queue de billard et des billes en bois (restaurations à la partie recevant les billes) Haut.: 103 cm - Larg.: 86 cm - Prof.: 105 cm Inventaire de la collection n°686 Modèle similaire à celui livré en 1862 pour le Salon des Cartes au château de Compiègne. Un autre exemplaire est conservé au château de Fontainebleau. Ce jeux à l'origine de salon sera par la suite exploité par les forains Very beautiful Chinese Billiards table - Varnished rosewood veneer, gold metal and bronze - Billiard queues and balls included (restoration for recipient) - H: 40" W: 33" D: 22" DM
cornettedesaintcyr

Oh will you look at that ornamental gate with the ball and drawbridge! Incredibly cute. Also a rather expensive table.

CHEVROT & LE BON F 101, avenue Montaigne Paris.
Rare Chinese pool table.
Rosewood veneer, wood stained in the manner of rosewood, metal and gilded bronze.
End of the 20th century.
Model similar to the one delivered in 1862 for the Salon des Cartes at the Château de Compiègne.
Another copy is kept at the Château de Fontainebleau.
A copy sold at auction in the Marchal collection, Paris September 28, 2011.
H_103 cm L_164 cm P_84 cm.
Small accidents and losses.
metayer-auction

A very similar table to the one above, except without the extra ornamental gate in the center of the playfield. These photos allow us to see the adorable bell mechanism at the top very well, and show where a ball would be placed to get knocked into that bell-loaded center gate!

BILLARD CHINOIS EN PLACAGE DE PALISSANDRE MARQUETÉ D'UN FILET À ARCEAUX MUNIS DE CLOCHETTES EN
Billard chinois en placage de palissandre marqueté d'un filet à arceaux munis de clochettes en bronze doré et pointes en os, reposant sur un piétement pliant en bois naturel à cannelures en relief. XIXe siècle. Accidents et manques. H. 105, L. 71, P. 150 cm Note : Notre billard est à rapprocher du modèle livré en 1862 pour le Salon des Cartes au château de Compiègne. Un autre exemplaire est conservé au château de Fontainebleau. Expert : Cabinet AUTHENTICITÉ PARTNERSHIP A French 19th century rosewood Chinese pool table. AUTHENTICITE PARTNERSHIP
the-saleroom

A much cheaper table given the woodwork, this table features the cue lane on the right and the plunger on the left

JOST & Cie
Chinese billiard Table with folding legs Natural varnished wood, felt, gilded metal France, Paris, late 19th century We include a billiard cue and wooden balls Height: 96 cm - Width: 80 cm - Depth: 150 cm Inventory of collection n ° 562 The balls are launched either using the pusher (left lane) or using a billiard cue (right lane). Points are scored on the game. Chinese Billiard - Table with three folding legs - Natural wood, varnished, felt, gilded metal - Includes a pool cue and wooden balls - H: 38 "W: 31" D: 59 "'
cornettedesaintcyr

Another less expensive table with a plunger on the left channel.

This game is a variant of Bagatelle, which used pins that could be knocked down, whereas these metal pins are fixed and are closer to a game called Billiards Japonaise, all precursors to pachinko. The spring loaded plungers used to launch wooden balls into the pin field started showing up in games in the late 1700's. This 1848 model is a rare purely mechanical pinball, the first with plungers. Case is mahogany with fruit wood banding, metal pins, and bronze gates. The diamond shaped mother of pearl inlay reads "Chevrot Ft De Jeux / Lebon Sr / Avenue Montainge 103 Paris". Some evidence of repairs, one ball is included. Condition: (Good - Very Good). Dimensions: 65"L x 33-1/4"W x 41-3/4"T.
liveauctioneers

I am unsure about the plungers on this one! They certainly look cool. One thing to note is that the plungers are activated within the shooter channel, and have no external plunger control.

There are no scoring pockets along the bottom. Almost all other tables I've seen have scoring slots at the bottom, but for this table no points are awarded along the bottom.

A fruitwood campaign Bagatelle board, 19th century, on turned tapered legs, 75cm high, the board 80cm x 39.5cm
liveauctioneers

Another one that is slightly less extravagant but it has a visible plunger on the left-hand side!

For sale is an antique bagatelle table.
It is made from wood with steel pins and brass hinges.
The playing surface is baize, rather faded. There is a small repair patch, also faded, on one of the cueing channels. The table is backed with baize.
There are seven, numbered, wooden scoring cups and seven numbered channels at the bottom.
There are scoring holes down each side.
The table comes with a small, antique cue.
There is a wooden bar underneath which raises the table to a playing pisition. This pivots on two, brass hinges.
The table measures 38 x 84 x 5cm.
ebay

Klondike Pool

1898 Brunswick-Balke-Collender Co. catalog

Klondike Pool takes pin bagatelle and adds a trough. The shallow pockets on the playfield are replaced with holes in the playfield, which feed a trough that delivers the balls to the front of the table.

Perhaps this is what is referred to when they say "American Bagatelle"?

Oak Bagatelle / Bar Table Mid-19th C Saloon Pinball
Mid-19th century saloon floor model "Bagatelle Table or Bar Billiards Table" an early pinball game - a hybrid between a pinball table and pool table. Table built on an oak slanted case, pressed scroll and egg and dart moldings, large turned legs, 4 ball-drop holes each with a score amount on metal plate, numerous rubber pins to deflect balls, front end with 9 half round holes each with score amount on metal plate, probably original green felt cover, 6 white balls, 2 later cue sticks, manufactured by R. B. Salter Builder (prominent owner of a saw mill), Colby Wisconsin. Game object - players hit balls with cue sticks on either side of a slotted trough aiming at targeted pockets, 84" long (slanted for ball returns), highest end 42 1/2" H, lowest end 36 1/2" H x 36" W, condition - good, no holes, stains or tears in felt.
liveauctioneers

This one is slanted, has pins on the playfield, and presents scoring cups along the bottom. Very similar to the earliest of pinball tables. It appears the playfield has 4 holes which feed balls to a trough at the front.

Another one from IPDB, this one states that a red cue ball is to be placed at the tiny top center hole. You would shoot for it up either lane, and if you could knock it from it's place then you could collect points with BOTH falling balls.