Added first implementation.

pom.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project xmlns="http://maven.apache.org/POM/4.0.0"
+         xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
+         xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd">
+    <modelVersion>4.0.0</modelVersion>
+
+    <groupId>nl.andrewl.</groupId>
+    <artifactId>randomhotbar</artifactId>
+    <version>1.0.0</version>
+
+    <properties>
+        <maven.compiler.source>17</maven.compiler.source>
+        <maven.compiler.target>17</maven.compiler.target>
+    </properties>
+
+    <dependencies>
+        <dependency>
+            <groupId>com.formdev</groupId>
+            <artifactId>flatlaf</artifactId>
+            <version>2.0.2</version>
+        </dependency>
+        <dependency>
+            <groupId>com.github.kwhat</groupId>
+            <artifactId>jnativehook</artifactId>
+            <version>2.2.1</version>
+        </dependency>
+    </dependencies>
+
+    <build>
+        <plugins>
+            <plugin>
+                <artifactId>maven-assembly-plugin</artifactId>
+                <configuration>
+                    <archive>
+                        <manifest>
+                            <mainClass>nl.andrewl.randomhotbar.RandomHotbar</mainClass>
+                        </manifest>
+                    </archive>
+                    <descriptorRefs>
+                        <descriptorRef>jar-with-dependencies</descriptorRef>
+                    </descriptorRefs>
+                </configuration>
+                <executions>
+                    <execution>
+                        <id>make-assembly</id>
+                        <phase>package</phase>
+                        <goals>
+                            <goal>single</goal>
+                        </goals>
+                    </execution>
+                </executions>
+            </plugin>
+        </plugins>
+    </build>
+
+</project>

src/main/java/nl/andrewl/randomhotbar/BlockPlaceListener.java

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+package nl.andrewl.randomhotbar;
+
+import com.github.kwhat.jnativehook.GlobalScreen;
+import com.github.kwhat.jnativehook.mouse.NativeMouseEvent;
+import com.github.kwhat.jnativehook.mouse.NativeMouseInputListener;
+import com.github.kwhat.jnativehook.mouse.NativeMouseWheelEvent;
+
+import java.util.List;
+import java.util.Random;
+import java.util.concurrent.Executors;
+import java.util.concurrent.ScheduledExecutorService;
+import java.util.concurrent.TimeUnit;
+
+public class BlockPlaceListener implements NativeMouseInputListener {
+	private final Random rand = new Random();
+	private final ScheduledExecutorService executor = Executors.newSingleThreadScheduledExecutor();
+	private final List<SlotSetting> settings;
+	private float randSum;
+	private int currentSlot = 1;
+
+	public BlockPlaceListener(List<SlotSetting> settings) {
+		randSum = 0;
+		for (var v : settings) {
+			randSum += v.chance();
+		}
+		this.settings = settings;
+		for (var v : settings) {
+			float percent = (v.chance() / randSum) * 100.0f;
+			System.out.printf("Will use slot %d, %.1f%% of the time.\n", v.slot(), percent);
+		}
+		System.out.printf("Starting at slot %d. Please select this slot if it is not selected already, then start right-clicking. Do not hold right-click.\n", currentSlot);
+	}
+
+	private int getNextSlot() {
+		float idx = rand.nextFloat(randSum);
+		float sum = 0;
+		int i = 0;
+		while (sum < idx) {
+			sum += settings.get(i++).chance();
+		}
+		return settings.get(Math.max(0, i - 1)).slot();
+	}
+
+	private void moveToSlot(int slot) {
+		final int dir = slot < currentSlot ? 1 : -1;
+		int n = Math.abs(currentSlot - slot);
+		for (int i = 0; i < n; i++) {
+			executor.schedule(() -> {
+				GlobalScreen.postNativeEvent(new NativeMouseWheelEvent(
+						2505,
+						0,
+						500,
+						500,
+						1,
+						NativeMouseWheelEvent.WHEEL_UNIT_SCROLL,
+						1,
+						dir,
+						NativeMouseWheelEvent.WHEEL_VERTICAL_DIRECTION
+				));
+			}, i * 50L, TimeUnit.MILLISECONDS);
+		}
+		currentSlot = slot;
+	}
+
+	@Override
+	public void nativeMouseClicked(NativeMouseEvent nativeEvent) {
+		if (nativeEvent.getButton() == 2) {
+			int newSlot = getNextSlot();
+			moveToSlot(newSlot);
+		}
+	}
+}

src/main/java/nl/andrewl/randomhotbar/RandomHotbar.java

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+package nl.andrewl.randomhotbar;
+
+import com.github.kwhat.jnativehook.GlobalScreen;
+import com.github.kwhat.jnativehook.NativeHookException;
+
+import java.util.*;
+import java.util.regex.Matcher;
+import java.util.regex.Pattern;
+
+public class RandomHotbar {
+	public static void main(String[] args) {
+		try {
+			GlobalScreen.registerNativeHook();
+		} catch (NativeHookException e) {
+			e.printStackTrace();
+		}
+		var settings = parseSettings(String.join(",", args));
+		var listener = new BlockPlaceListener(settings);
+		GlobalScreen.addNativeMouseListener(listener);
+	}
+
+	public static final Pattern SETTINGS_PATTERN = Pattern.compile("([1-9])\\s*:\\s*(\\d*\\.\\d+|\\d+)%?");
+
+	public static List<SlotSetting> parseSettings(String s) {
+		List<SlotSetting> settings = new ArrayList<>(9);
+		Matcher m = SETTINGS_PATTERN.matcher(s);
+		while (m.find()) {
+			int slot = Integer.parseInt(m.group(1));
+			float value = Float.parseFloat(m.group(2));
+			for (var setting : settings) {
+				if (setting.slot() == slot) {
+					throw new IllegalArgumentException("A setting for slot " + slot + " is already defined.");
+				}
+			}
+			settings.add(new SlotSetting(slot, value));
+		}
+		settings.sort(Comparator.comparing(SlotSetting::slot));
+		if (settings.isEmpty()) {
+			for (int i = 1; i <= 9; i++) {
+				settings.add(new SlotSetting(i, 1));
+			}
+		}
+		return settings;
+	}
+}

src/main/java/nl/andrewl/randomhotbar/SlotSetting.java

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+package nl.andrewl.randomhotbar;
+
+public record SlotSetting(int slot, float chance) {
+}