Engineering

Feeding & Breeding

Our observation about the superfecta earnings correlating with the placement of horses in positions 10, 11, and 12 is intriguing. It seems you’re identifying a pattern where the earnings scale based on how many of these specific horses are included. Here’s my take:

Breakdown of Earnings Patterns:

1. None of 10, 11, 12 in the superfecta: Earnings remain around $1,000 or less.

   • This suggests the payout is more typical or aligned with a low-risk bet when these longer-shot horses are excluded.

2. One of 10, 11, 12 in the superfecta: Earnings hover around $5,000.

   • This payout implies a modest risk-reward ratio, as only one long-shot horse features.

3. Two of 10, 11, 12 in the superfecta: Earnings jump to $40,000.

   • Now you’re entering higher-risk territory with longer-shot horses. This greater risk results in a significantly larger payout.

4. Three of 10, 11, 12 in the superfecta: Earnings skyrocket to $200,000.

   • Including three long-shot horses in the top four places is an extremely rare event. The earnings reflect the improbable nature of this scenario.

What Might Be Happening:

This pattern is likely tied to the odds and probabilities of long-shot horses finishing in top positions:

• Long-shots (positions 10, 11, 12) are generally expected to perform poorly due to weaker form, experience, or other factors.

• Including long-shots significantly decreases the probability of correctly predicting the superfecta. Fewer people bet on such combinations, so when they hit, the pool is distributed among fewer winners.

Why the Jump in Earnings Isn’t Linear:

• Adding the first long-shot (10, 11, or 12) doesn’t shift probabilities much, as it’s still plausible for one to break into the top four.

• Adding the second and third long-shots shifts the bet into the realm of highly improbable outcomes, leading to a disproportionately larger payout.

Strategic Implications:

1. Higher Rewards for Unlikely Outcomes: Betting on combinations that include multiple long-shot horses (e.g., two or three of 10, 11, 12) might be worth the risk, especially in larger pools.

2. Consideration of Pool Sizes: Larger pools may amplify the payouts further, particularly for rare outcomes.

3. Pattern Exploitation: If this earnings trend holds consistently, you could strategically target superfecta bets with specific combinations of long-shots to optimize risk versus reward.

From the military school of life.—That which does not kill me, makes me stronger.
– No. 8, Maxims & Missiles, Twilight of Idols

Show code cell source Hide code cell source

import numpy as np
import matplotlib.pyplot as plt
import networkx as nx

# Define the neural network structure
def define_layers():
    return {
        'Pre-Input': ['Life', 'Earth', 'Cosmos', 'Sound', 'Tactful', 'Firm'],
        'Yellowstone': ['G1 & G2'],
        'Input': ['N4, N5', 'N1, N2, N3'],
        'Hidden': ['Sympathetic', 'G3', 'Parasympathetic'],
        'Output': ['Ecosystem', 'Vulnerabilities', 'AChR', 'Strengths', 'Neurons']
    }

# Assign colors to nodes
def assign_colors(node, layer):
    if node == 'G1 & G2':
        return 'yellow'
    if layer == 'Pre-Input' and node in ['Tactful']:
        return 'lightgreen'
    if layer == 'Pre-Input' and node in ['Firm']:
        return 'paleturquoise'
    elif layer == 'Input' and node == 'N1, N2, N3':
        return 'paleturquoise'
    elif layer == 'Hidden':
        if node == 'Parasympathetic':
            return 'paleturquoise'
        elif node == 'G3':
            return 'lightgreen'
        elif node == 'Sympathetic':
            return 'lightsalmon'
    elif layer == 'Output':
        if node == 'Neurons':
            return 'paleturquoise'
        elif node in ['Strengths', 'AChR', 'Vulnerabilities']:
            return 'lightgreen'
        elif node == 'Ecosystem':
            return 'lightsalmon'
    return 'lightsalmon'  # Default color

# Calculate positions for nodes
def calculate_positions(layer, center_x, offset):
    layer_size = len(layer)
    start_y = -(layer_size - 1) / 2  # Center the layer vertically
    return [(center_x + offset, start_y + i) for i in range(layer_size)]

# Create and visualize the neural network graph
def visualize_nn():
    layers = define_layers()
    G = nx.DiGraph()
    pos = {}
    node_colors = []
    center_x = 0  # Align nodes horizontally

    # Add nodes and assign positions
    for i, (layer_name, nodes) in enumerate(layers.items()):
        y_positions = calculate_positions(nodes, center_x, offset=-len(layers) + i + 1)
        for node, position in zip(nodes, y_positions):
            G.add_node(node, layer=layer_name)
            pos[node] = position
            node_colors.append(assign_colors(node, layer_name))

    # Add edges (without weights)
    for layer_pair in [
        ('Pre-Input', 'Yellowstone'), ('Yellowstone', 'Input'), ('Input', 'Hidden'), ('Hidden', 'Output')
    ]:
        source_layer, target_layer = layer_pair
        for source in layers[source_layer]:
            for target in layers[target_layer]:
                G.add_edge(source, target)

    # Draw the graph
    plt.figure(figsize=(12, 8))
    nx.draw(
        G, pos, with_labels=True, node_color=node_colors, edge_color='gray',
        node_size=3000, font_size=10, connectionstyle="arc3,rad=0.1"
    )
    plt.title("Red Queen Hypothesis", fontsize=15)
    plt.show()

# Run the visualization
visualize_nn()

Fig. 9 Horse Racing Against the Red Queen. The generations on generations of horse-breeding fit this narrative. In philosophy we might be sympathetic to Karl Marx (School of Resentment), parasympathetic to Plato (School of Athens), but we surely have gotta be delighted by Nietzsche (School of Life). We might also consider The Schools of ART: athens (plato), resentment (marx), transactions (nietzsche)

Worthy & Adversarial

Horse Racing Against the Red Queen: Evolution in the Endless Race

The Red Queen Hypothesis, born from evolutionary biology, captures the ceaseless contest of adaptation in a competitive world. Borrowing its name from Lewis Carroll’s Through the Looking-Glass, where the Red Queen remarks that one must run as fast as possible just to stay in place, this concept finds its embodiment in the meticulously cultivated lineage of thoroughbred horses. Across generations, horse racing has evolved into a literal and metaphorical race against the Red Queen, as breeders, trainers, and competitors strive not just for triumph but for survival in a landscape defined by relentless change.

In the high-stakes world of horse racing, the Red Queen’s shadow looms large. Each horse represents the culmination of genetic refinement—speed, stamina, and physical resilience honed through selective breeding. However, this process does not yield a static advantage; rather, it creates a dynamic equilibrium. A faster horse begets faster competitors. A stronger lineage inspires counter-lineages that are equally determined to redefine the boundaries of equine capability. The result is a perpetual arms race, an echo of the predator-prey dynamics seen in ecosystems where a gazelle’s speed fuels a cheetah’s swiftness, and vice versa.

The Red Queen Hypothesis becomes even more striking when viewed through the lens of human intervention. Unlike natural ecosystems, where the forces of adaptation operate without explicit intention, horse racing is a deliberately engineered contest. Generations of breeders have utilized meticulous record-keeping, advanced genetic knowledge, and an acute understanding of animal physiology to refine equine lineages. This deliberate pressure accelerates the evolutionary race, crafting horses that are marvels of speed and endurance but are also finely tuned to the point of fragility. The very act of adaptation introduces vulnerabilities: a horse bred for unparalleled speed may sacrifice bone density, while one built for stamina may lose explosive power. These trade-offs exemplify the core tension of the Red Queen Hypothesis—progress and vulnerability intertwined.

Beyond the biological, horse racing illuminates the Red Queen dynamics in human society. The sport is not merely about horses; it is a grand theatre of human ambition, strategy, and rivalry. Owners and trainers, like adversarial agents in an evolutionary contest, continually innovate in training methods, dietary regimens, and race strategies. Advances in veterinary medicine, biomechanics, and data analytics mirror the broader societal Red Queen races, where technological leaps beget new challenges, and success demands perpetual reinvention. Yet even as horse racing embodies progress, it is also haunted by its inherent fragility. A misstep, an injury, or an unforeseen competitor can undo years of meticulous preparation, underscoring the precarious balance of this evolutionary game.

At the heart of this contest lies the nervous system—a biological mirror of the Red Queen dynamics. The interplay of sympathetic and parasympathetic systems reflects the balance between adversarial and cooperative pressures. In the horse, as in humans, this equilibrium governs the capacity for explosive action, recovery, and sustained effort. Acetylcholine (ACh), a neurotransmitter with a vast combinatorial space, stands as the nexus of this balance. It is the signal that compresses the myriad inputs of the autonomic nervous system into actionable outputs, enabling the horse to transition seamlessly from rest to the thundering charge of a race. Yet this very versatility introduces a point of vulnerability. Like the horses bred for speed, ACh’s expansive capacity makes it a potential target for disruption—a pressure point in the endless race against entropy and adversaries.

Fig. 10 Queen Elizabeth II watches the racing as she attends the “Derby Day” of the Investec Derby Festival at Epsom Race course on June 1, 2019, in Epsom, England. Source: Max Mumby / Getty Images

The metaphor of horse racing against the Red Queen extends beyond biology into culture and history. It reflects humanity’s own relentless pursuit of progress, a race that mirrors the ecological arms race seen in nature. In this context, horse racing becomes an allegory for the human condition: an unyielding drive to innovate, adapt, and excel, even as each step forward necessitates new defenses against emerging challenges. The thoroughbred, with its lineage of calculated risks and hard-earned triumphs, symbolizes both the heights of human ingenuity and the precariousness of our creations.

Yet, amidst this ceaseless contest, there is also beauty. The sight of a horse at full gallop, muscles rippling with precision and power, captures the paradox of the Red Queen Hypothesis. It is a moment of transcendence—a fleeting equilibrium achieved through countless iterations of effort, competition, and adaptation. It reminds us that even in a world defined by struggle, there is room for awe and admiration. The Red Queen’s race is not just a tale of survival but a celebration of resilience and creativity, played out on a stage as old as time and as immediate as the thunder of hooves on a racetrack.

In horse racing, we see the Red Queen not as a distant myth but as a living reality. It is a race without a finish line, where progress is perpetual and equilibrium is dynamic. The thoroughbred, bred to perfection and poised on the edge of fragility, stands as a testament to the power and cost of adaptation. And so, the race goes on, a vivid embodiment of the Red Queen Hypothesis, reminding us that to stand still is to fall behind, and to move forward is to embrace both the triumphs and vulnerabilities of life in an ever-changing world.