Revised land count analysis for Magic: The Gathering

bin.rs

use num_bigint::BigUint;
use num_traits::ToPrimitive;

// calculate the binomial coefficient `n choose k`
fn binomial_coefficient(n: u32, k: u32) -> u64 {
    let mut result = BigUint::from(1u32);
    for i in 0..k {
        result = (result * (n - i)) / (i + 1);
    }
    result.to_u64().unwrap()
}

// calculates the probability of getting `sample_successes` in a sample
// without replacement of size `sample_size` from a population of size
// `population_size` containing `population_successes` successes.
fn hypergeometric_pmf(
    sample_successes: u32,
    sample_size: u32,
    population_successes: u32,
    population_size: u32,
) -> f64 {
    assert!(population_successes <= population_size);
    assert!(sample_size <= population_size);
    assert!(sample_successes <= sample_size);

    let num0 = binomial_coefficient(population_successes, sample_successes);
    let num1 = binomial_coefficient(population_size - population_successes, sample_size - sample_successes);
    let denominator = binomial_coefficient(population_size, sample_size);
    
    (num0 * num1) as f64 / denominator as f64
}

fn analyze(deck_size: u32) {
    println!("# {}-card Decks\n", deck_size);

    let min_land_count = deck_size / 4;
    let max_land_count = deck_size / 2;

    {
        print!("|         ");
        for i in 0..=6 {
            print!(" | P(S = {})", i);
        }
        println!(" | max. range |");
        print!("|---------");
        for _ in 0..=6 {
            print!("-|---------");
        }
        println!("-|------------|");
    
        for land_count in min_land_count..=max_land_count {
            print!("| {} lands", land_count);
            
            let mut p_prev = 0.0;
            let mut max_interval_lo = -2;
            let mut p_max_interval = 0.0;
            
            for lands_in_hand in 0..=6 {
                let p = hypergeometric_pmf(lands_in_hand, 7, land_count, deck_size);
                let p_interval = p_prev + p;
                if p_interval > p_max_interval {
                    max_interval_lo = lands_in_hand as i32 - 1;
                    p_max_interval = p_interval;
                }
                
                print!(" |  {:6.3}%", 100.0 * p);
                p_prev = p;
            }
            println!(" | {}-{}: {:4.1}% |", max_interval_lo, max_interval_lo + 1, 100.0 * p_max_interval);
        }
        
        println!();
    }
    
    for lands_kept in 1..=4 {
        print!("|          | P(S = {})", lands_kept);
        for target_land_drop in (lands_kept + 1)..=(lands_kept + 4) {
            print!(" | P({} lands on T{0})", target_land_drop);
        }
        println!(" |");
        print!("|----------|---------");
        for _ in (lands_kept + 1)..=(lands_kept + 4) {
            print!("-|-----------------");
        }
        println!("-|");
        
        for land_count in min_land_count..=max_land_count {
            print!("| {} lands", land_count);
            print!(" |   {:5.2}%", 100.0 * hypergeometric_pmf(lands_kept, 7, land_count, deck_size));
            
            for target_land_drop in (lands_kept + 1)..=(lands_kept + 4) {
                let lands_needed = target_land_drop - lands_kept;
                let p_on_play = 1.0 - (0..lands_needed)
                    .map(|i| hypergeometric_pmf(i, target_land_drop - 1, land_count - lands_kept, deck_size - 7))
                    .sum::<f64>();
                let p_on_draw = 1.0 - (0..lands_needed)
                    .map(|i| hypergeometric_pmf(i, target_land_drop, land_count - lands_kept, deck_size - 7))
                    .sum::<f64>();
                
                print!(" |  {:5.2}% / {:5.2}%", 100.0 * p_on_play, 100.0 * p_on_draw);
            }
            
            println!(" |");
        }
        
        println!();
    }
}

fn main() {
    analyze(40);
    analyze(60);
    analyze(80);
    analyze(99);
}


#[test]
fn binomial_coeffs() {
    assert_eq!(binomial_coefficient(1, 0), 1);
    assert_eq!(binomial_coefficient(2, 1), 2);
    assert_eq!(binomial_coefficient(3, 1), 3);
    assert_eq!(binomial_coefficient(4, 1), 4);
    assert_eq!(binomial_coefficient(4, 2), 6);
    assert_eq!(binomial_coefficient(5, 0), 1);
    assert_eq!(binomial_coefficient(5, 1), 5);
    assert_eq!(binomial_coefficient(5, 2), 10);
    assert_eq!(binomial_coefficient(5, 3), 10);
}

mtg-land-count-analysis.md

40-card Decks

	P(S = 0)	P(S = 1)	P(S = 2)	P(S = 3)	P(S = 4)	P(S = 5)	P(S = 6)	max. range
10 lands	10.920%	31.849%	34.397%	17.639%	4.573%	0.588%	0.034%	1-2: 66.2%
11 lands	8.372%	28.027%	35.034%	21.020%	6.468%	1.006%	0.072%	1-2: 63.1%
12 lands	6.351%	24.249%	34.792%	24.161%	8.698%	1.606%	0.139%	1-2: 59.0%
13 lands	4.763%	20.641%	33.775%	26.922%	11.218%	2.423%	0.249%	2-3: 60.7%
14 lands	3.528%	17.289%	32.107%	29.189%	13.960%	3.490%	0.419%	2-3: 61.3%
15 lands	2.578%	14.249%	29.923%	30.873%	16.840%	4.832%	0.671%	2-3: 60.8%
16 lands	1.856%	11.551%	27.358%	31.918%	19.758%	6.466%	1.031%	2-3: 59.3%
17 lands	1.315%	9.205%	24.546%	32.297%	22.608%	8.397%	1.527%	2-3: 56.8%
18 lands	0.915%	7.204%	21.611%	32.017%	25.276%	10.616%	2.191%	3-4: 57.3%
19 lands	0.624%	5.530%	18.664%	31.107%	27.651%	13.098%	3.056%	3-4: 58.8%
20 lands	0.416%	4.158%	15.800%	29.626%	29.626%	15.800%	4.158%	3-4: 59.3%

	P(S = 1)	P(2 lands on T2)	P(3 lands on T3)	P(4 lands on T4)	P(5 lands on T5)
10 lands	31.85%	27.27% / 47.73%	6.82% / 17.38%	1.54% / 5.23%	0.31% / 1.33%
11 lands	28.03%	30.30% / 52.08%	8.52% / 21.17%	2.20% / 7.26%	0.51% / 2.14%
12 lands	24.25%	33.33% / 56.25%	10.42% / 25.20%	3.02% / 9.68%	0.81% / 3.25%
13 lands	20.64%	36.36% / 60.23%	12.50% / 29.44%	4.03% / 12.50%	1.21% / 4.71%
14 lands	17.29%	39.39% / 64.02%	14.77% / 33.83%	5.24% / 15.73%	1.75% / 6.57%
15 lands	14.25%	42.42% / 67.61%	17.23% / 38.36%	6.67% / 19.35%	2.45% / 8.86%
16 lands	11.55%	45.45% / 71.02%	19.89% / 42.98%	8.34% / 23.35%	3.34% / 11.62%
17 lands	9.20%	48.48% / 74.24%	22.73% / 47.65%	10.26% / 27.71%	4.45% / 14.88%
18 lands	7.20%	51.52% / 77.27%	25.76% / 52.35%	12.46% / 32.40%	5.82% / 18.65%
19 lands	5.53%	54.55% / 80.11%	28.98% / 57.02%	14.96% / 37.39%	7.48% / 22.95%
20 lands	4.16%	57.58% / 82.77%	32.39% / 61.64%	17.76% / 42.62%	9.47% / 27.76%

	P(S = 2)	P(3 lands on T3)	P(4 lands on T4)	P(5 lands on T5)	P(6 lands on T6)
10 lands	34.40%	43.18% / 57.84%	13.86% / 24.12%	3.59% / 7.84%	0.76% / 2.02%
11 lands	35.03%	47.73% / 62.90%	17.38% / 29.52%	5.23% / 11.10%	1.33% / 3.42%
12 lands	34.79%	52.08% / 67.54%	21.17% / 35.08%	7.26% / 14.93%	2.14% / 5.34%
13 lands	33.78%	56.25% / 71.77%	25.20% / 40.73%	9.68% / 19.31%	3.25% / 7.84%
14 lands	32.11%	60.23% / 75.62%	29.44% / 46.37%	12.50% / 24.18%	4.71% / 10.97%
15 lands	29.92%	64.02% / 79.11%	33.83% / 51.94%	15.73% / 29.46%	6.57% / 14.74%
16 lands	27.36%	67.61% / 82.24%	38.36% / 57.38%	19.35% / 35.08%	8.86% / 19.16%
17 lands	24.55%	71.02% / 85.04%	42.98% / 62.61%	23.35% / 40.95%	11.62% / 24.19%
18 lands	21.61%	74.24% / 87.54%	47.65% / 67.60%	27.71% / 46.97%	14.88% / 29.78%
19 lands	18.66%	77.27% / 89.74%	52.35% / 72.29%	32.40% / 53.03%	18.65% / 35.84%
20 lands	15.80%	80.11% / 91.66%	57.02% / 76.65%	37.39% / 59.05%	22.95% / 42.29%

	P(S = 3)	P(4 lands on T4)	P(5 lands on T5)	P(6 lands on T6)	P(7 lands on T7)
10 lands	17.64%	52.35% / 63.47%	18.99% / 28.19%	5.19% / 9.29%	1.08% / 2.29%
11 lands	21.02%	57.84% / 69.09%	24.12% / 34.97%	7.84% / 13.65%	2.02% / 4.18%
12 lands	24.16%	62.90% / 74.03%	29.52% / 41.80%	11.10% / 18.77%	3.42% / 6.83%
13 lands	26.92%	67.54% / 78.36%	35.08% / 48.51%	14.93% / 24.53%	5.34% / 10.31%
14 lands	29.19%	71.77% / 82.12%	40.73% / 55.00%	19.31% / 30.78%	7.84% / 14.64%
15 lands	30.87%	75.62% / 85.37%	46.37% / 61.17%	24.18% / 37.39%	10.97% / 19.78%
16 lands	31.92%	79.11% / 88.16%	51.94% / 66.93%	29.46% / 44.18%	14.74% / 25.65%
17 lands	32.30%	82.24% / 90.53%	57.38% / 72.24%	35.08% / 51.01%	19.16% / 32.13%
18 lands	32.02%	85.04% / 92.52%	62.61% / 77.05%	40.95% / 57.71%	24.19% / 39.09%
19 lands	31.11%	87.54% / 94.18%	67.60% / 81.35%	46.97% / 64.16%	29.78% / 46.33%
20 lands	29.63%	89.74% / 95.55%	72.29% / 85.12%	53.03% / 70.22%	35.84% / 53.67%

	P(S = 4)	P(5 lands on T5)	P(6 lands on T6)	P(7 lands on T7)	P(8 lands on T8)
10 lands	4.57%	57.11% / 65.98%	21.62% / 29.54%	5.77% / 9.29%	1.08% / 2.02%
11 lands	6.47%	63.47% / 72.28%	28.19% / 37.64%	9.29% / 14.54%	2.29% / 4.18%
12 lands	8.70%	69.09% / 77.61%	34.97% / 45.63%	13.65% / 20.76%	4.18% / 7.37%
13 lands	11.22%	74.03% / 82.09%	41.80% / 53.31%	18.77% / 27.73%	6.83% / 11.65%
14 lands	13.96%	78.36% / 85.82%	48.51% / 60.50%	24.53% / 35.19%	10.31% / 17.01%
15 lands	16.84%	82.12% / 88.90%	55.00% / 67.11%	30.78% / 42.89%	14.64% / 23.33%
16 lands	19.76%	85.37% / 91.43%	61.17% / 73.05%	37.39% / 50.60%	19.78% / 30.45%
17 lands	22.61%	88.16% / 93.47%	66.93% / 78.30%	44.18% / 58.08%	25.65% / 38.12%
18 lands	25.28%	90.53% / 95.10%	72.24% / 82.85%	51.01% / 65.16%	32.13% / 46.11%
19 lands	27.65%	92.52% / 96.39%	77.05% / 86.72%	57.71% / 71.68%	39.09% / 54.13%
20 lands	29.63%	94.18% / 97.39%	81.35% / 89.94%	64.16% / 77.53%	46.33% / 61.93%

60-card Decks

	P(S = 0)	P(S = 1)	P(S = 2)	P(S = 3)	P(S = 4)	P(S = 5)	P(S = 6)	max. range
15 lands	11.750%	31.635%	33.217%	17.553%	5.015%	0.770%	0.058%	1-2: 64.9%
16 lands	9.922%	29.245%	33.744%	19.684%	6.241%	1.070%	0.091%	1-2: 63.0%
17 lands	8.344%	26.835%	33.897%	21.729%	7.605%	1.447%	0.138%	1-2: 60.7%
18 lands	6.985%	24.449%	33.700%	23.649%	9.096%	1.910%	0.202%	1-2: 58.1%
19 lands	5.821%	22.121%	33.181%	25.409%	10.698%	2.469%	0.288%	2-3: 58.6%
20 lands	4.827%	19.877%	32.372%	26.976%	12.395%	3.131%	0.401%	2-3: 59.3%
21 lands	3.983%	17.741%	31.307%	28.325%	14.163%	3.904%	0.548%	2-3: 59.6%
22 lands	3.268%	15.726%	30.022%	29.434%	15.978%	4.793%	0.734%	2-3: 59.5%
23 lands	2.666%	13.845%	28.555%	30.286%	17.815%	5.803%	0.967%	2-3: 58.8%
24 lands	2.161%	12.104%	26.941%	30.870%	19.645%	6.933%	1.255%	2-3: 57.8%
25 lands	1.741%	10.507%	25.217%	31.182%	21.438%	8.185%	1.605%	2-3: 56.4%
26 lands	1.393%	9.054%	23.416%	31.221%	23.164%	9.555%	2.027%	2-3: 54.6%
27 lands	1.106%	7.743%	21.570%	30.991%	24.793%	11.037%	2.529%	3-4: 55.8%
28 lands	0.872%	6.570%	19.710%	30.503%	26.296%	12.622%	3.122%	3-4: 56.8%
29 lands	0.681%	5.529%	17.862%	29.770%	27.643%	14.298%	3.813%	3-4: 57.4%
30 lands	0.527%	4.612%	16.051%	28.810%	28.810%	16.051%	4.612%	3-4: 57.6%

	P(S = 1)	P(2 lands on T2)	P(3 lands on T3)	P(4 lands on T4)	P(5 lands on T5)
15 lands	31.63%	26.42% / 46.23%	6.60% / 16.70%	1.55% / 5.19%	0.34% / 1.43%
16 lands	29.24%	28.30% / 48.98%	7.62% / 18.97%	1.94% / 6.37%	0.47% / 1.91%
17 lands	26.84%	30.19% / 51.67%	8.71% / 21.34%	2.39% / 7.70%	0.62% / 2.50%
18 lands	24.45%	32.08% / 54.28%	9.87% / 23.80%	2.90% / 9.17%	0.81% / 3.20%
19 lands	22.12%	33.96% / 56.82%	11.10% / 26.34%	3.48% / 10.80%	1.04% / 4.03%
20 lands	19.88%	35.85% / 59.29%	12.41% / 28.96%	4.14% / 12.57%	1.32% / 5.00%
21 lands	17.74%	37.74% / 61.68%	13.79% / 31.63%	4.87% / 14.50%	1.65% / 6.11%
22 lands	15.73%	39.62% / 64.01%	15.24% / 34.36%	5.68% / 16.58%	2.04% / 7.38%
23 lands	13.84%	41.51% / 66.26%	16.76% / 37.14%	6.57% / 18.80%	2.50% / 8.82%
24 lands	12.10%	43.40% / 68.43%	18.36% / 39.96%	7.56% / 21.17%	3.02% / 10.43%
25 lands	10.51%	45.28% / 70.54%	20.03% / 42.81%	8.64% / 23.67%	3.63% / 12.22%
26 lands	9.05%	47.17% / 72.57%	21.77% / 45.68%	9.82% / 26.31%	4.32% / 14.19%
27 lands	7.74%	49.06% / 74.53%	23.58% / 48.56%	11.10% / 29.08%	5.11% / 16.36%
28 lands	6.57%	50.94% / 76.42%	25.47% / 51.44%	12.49% / 31.96%	5.99% / 18.71%
29 lands	5.53%	52.83% / 78.23%	27.43% / 54.32%	13.98% / 34.96%	6.99% / 21.26%
30 lands	4.61%	54.72% / 79.97%	29.46% / 57.19%	15.60% / 38.06%	8.11% / 24.00%

	P(S = 2)	P(3 lands on T3)	P(4 lands on T4)	P(5 lands on T5)	P(6 lands on T6)
15 lands	33.22%	43.40% / 57.82%	14.54% / 24.93%	4.15% / 8.82%	1.04% / 2.66%
16 lands	33.74%	46.23% / 60.99%	16.70% / 28.22%	5.19% / 10.83%	1.43% / 3.58%
17 lands	33.90%	48.98% / 63.99%	18.97% / 31.58%	6.37% / 13.06%	1.91% / 4.70%
18 lands	33.70%	51.67% / 66.83%	21.34% / 34.99%	7.70% / 15.50%	2.50% / 6.02%
19 lands	33.18%	54.28% / 69.52%	23.80% / 38.43%	9.17% / 18.13%	3.20% / 7.56%
20 lands	32.37%	56.82% / 72.06%	26.34% / 41.89%	10.80% / 20.95%	4.03% / 9.32%
21 lands	31.31%	59.29% / 74.46%	28.96% / 45.34%	12.57% / 23.94%	5.00% / 11.31%
22 lands	30.02%	61.68% / 76.71%	31.63% / 48.76%	14.50% / 27.09%	6.11% / 13.54%
23 lands	28.56%	64.01% / 78.83%	34.36% / 52.15%	16.58% / 30.37%	7.38% / 16.00%
24 lands	26.94%	66.26% / 80.81%	37.14% / 55.48%	18.80% / 33.77%	8.82% / 18.70%
25 lands	25.22%	68.43% / 82.67%	39.96% / 58.75%	21.17% / 37.28%	10.43% / 21.62%
26 lands	23.42%	70.54% / 84.40%	42.81% / 61.94%	23.67% / 40.85%	12.22% / 24.75%
27 lands	21.57%	72.57% / 86.02%	45.68% / 65.04%	26.31% / 44.49%	14.19% / 28.08%
28 lands	19.71%	74.53% / 87.51%	48.56% / 68.04%	29.08% / 48.16%	16.36% / 31.60%
29 lands	17.86%	76.42% / 88.90%	51.44% / 70.92%	31.96% / 51.84%	18.71% / 35.28%
30 lands	16.05%	78.23% / 90.18%	54.32% / 73.69%	34.96% / 55.51%	21.26% / 39.10%

	P(S = 3)	P(4 lands on T4)	P(5 lands on T5)	P(6 lands on T6)	P(7 lands on T7)
15 lands	17.55%	54.50% / 65.42%	21.73% / 31.54%	7.02% / 12.13%	1.91% / 3.87%
16 lands	19.68%	57.82% / 68.79%	24.93% / 35.67%	8.82% / 14.97%	2.66% / 5.28%
17 lands	21.73%	60.99% / 71.91%	28.22% / 39.81%	10.83% / 18.07%	3.58% / 6.98%
18 lands	23.65%	63.99% / 74.79%	31.58% / 43.93%	13.06% / 21.42%	4.70% / 8.97%
19 lands	25.41%	66.83% / 77.45%	34.99% / 47.99%	15.50% / 24.97%	6.02% / 11.26%
20 lands	26.98%	69.52% / 79.88%	38.43% / 51.97%	18.13% / 28.70%	7.56% / 13.86%
21 lands	28.33%	72.06% / 82.12%	41.89% / 55.84%	20.95% / 32.58%	9.32% / 16.74%
22 lands	29.43%	74.46% / 84.16%	45.34% / 59.60%	23.94% / 36.57%	11.31% / 19.91%
23 lands	30.29%	76.71% / 86.03%	48.76% / 63.21%	27.09% / 40.63%	13.54% / 23.34%
24 lands	30.87%	78.83% / 87.72%	52.15% / 66.67%	30.37% / 44.74%	16.00% / 27.01%
25 lands	31.18%	80.81% / 89.25%	55.48% / 69.96%	33.77% / 48.85%	18.70% / 30.89%
26 lands	31.22%	82.67% / 90.64%	58.75% / 73.07%	37.28% / 52.94%	21.62% / 34.94%
27 lands	30.99%	84.40% / 91.89%	61.94% / 76.00%	40.85% / 56.96%	24.75% / 39.14%
28 lands	30.50%	86.02% / 93.01%	65.04% / 78.74%	44.49% / 60.90%	28.08% / 43.44%
29 lands	29.77%	87.51% / 94.01%	68.04% / 81.29%	48.16% / 64.72%	31.60% / 47.81%
30 lands	28.81%	88.90% / 94.89%	70.92% / 83.64%	51.84% / 68.40%	35.28% / 52.19%

	P(S = 4)	P(5 lands on T5)	P(6 lands on T6)	P(7 lands on T7)	P(8 lands on T8)
15 lands	5.02%	61.78% / 70.36%	27.45% / 36.39%	9.58% / 14.71%	2.73% / 4.81%
16 lands	6.24%	65.42% / 73.89%	31.54% / 41.24%	12.13% / 18.32%	3.87% / 6.70%
17 lands	7.61%	68.79% / 77.07%	35.67% / 46.02%	14.97% / 22.24%	5.28% / 8.97%
18 lands	9.10%	71.91% / 79.94%	39.81% / 50.68%	18.07% / 26.40%	6.98% / 11.62%
19 lands	10.70%	74.79% / 82.51%	43.93% / 55.18%	21.42% / 30.76%	8.97% / 14.65%
20 lands	12.39%	77.45% / 84.81%	47.99% / 59.49%	24.97% / 35.26%	11.26% / 18.04%
21 lands	14.16%	79.88% / 86.86%	51.97% / 63.60%	28.70% / 39.84%	13.86% / 21.76%
22 lands	15.98%	82.12% / 88.69%	55.84% / 67.48%	32.58% / 44.46%	16.74% / 25.78%
23 lands	17.82%	84.16% / 90.30%	59.60% / 71.11%	36.57% / 49.06%	19.91% / 30.05%
24 lands	19.64%	86.03% / 91.73%	63.21% / 74.50%	40.63% / 53.60%	23.34% / 34.52%
25 lands	21.44%	87.72% / 92.98%	66.67% / 77.63%	44.74% / 58.04%	27.01% / 39.15%
26 lands	23.16%	89.25% / 94.08%	69.96% / 80.51%	48.85% / 62.32%	30.89% / 43.87%
27 lands	24.79%	90.64% / 95.03%	73.07% / 83.14%	52.94% / 66.43%	34.94% / 48.63%
28 lands	26.30%	91.89% / 95.86%	76.00% / 85.52%	56.96% / 70.33%	39.14% / 53.38%
29 lands	27.64%	93.01% / 96.58%	78.74% / 87.66%	60.90% / 73.99%	43.44% / 58.05%
30 lands	28.81%	94.01% / 97.19%	81.29% / 89.57%	64.72% / 77.41%	47.81% / 62.61%

80-card Decks

	P(S = 0)	P(S = 1)	P(S = 2)	P(S = 3)	P(S = 4)	P(S = 5)	P(S = 6)	max. range
20 lands	12.157%	31.519%	32.665%	17.499%	5.219%	0.864%	0.073%	1-2: 64.2%
21 lands	10.739%	29.786%	33.095%	19.055%	6.125%	1.096%	0.101%	1-2: 62.9%
22 lands	9.465%	28.031%	33.320%	20.568%	7.105%	1.370%	0.136%	1-2: 61.4%
23 lands	8.323%	26.273%	33.347%	22.022%	8.156%	1.691%	0.181%	1-2: 59.6%
24 lands	7.301%	24.530%	33.187%	23.401%	9.272%	2.060%	0.237%	1-2: 57.7%
25 lands	6.388%	22.814%	32.852%	24.693%	10.447%	2.484%	0.307%	2-3: 57.5%
26 lands	5.575%	21.138%	32.355%	25.884%	11.673%	2.963%	0.391%	2-3: 58.2%
27 lands	4.852%	19.512%	31.708%	26.962%	12.942%	3.502%	0.494%	2-3: 58.7%
28 lands	4.211%	17.944%	30.925%	27.919%	14.244%	4.102%	0.617%	2-3: 58.8%
29 lands	3.644%	16.441%	30.022%	28.745%	15.570%	4.766%	0.763%	2-3: 58.8%
30 lands	3.144%	15.007%	29.013%	29.433%	16.909%	5.495%	0.935%	2-3: 58.4%
31 lands	2.704%	13.646%	27.913%	29.980%	18.249%	6.290%	1.136%	2-3: 57.9%
32 lands	2.318%	12.361%	26.735%	30.381%	19.579%	7.151%	1.369%	2-3: 57.1%
33 lands	1.980%	11.154%	25.496%	30.634%	20.887%	8.076%	1.639%	2-3: 56.1%
34 lands	1.685%	10.025%	24.207%	30.739%	22.161%	9.066%	1.947%	2-3: 54.9%
35 lands	1.429%	8.974%	22.884%	30.697%	23.389%	10.117%	2.299%	3-4: 54.1%
36 lands	1.206%	8.000%	21.537%	30.511%	24.558%	11.227%	2.698%	3-4: 55.1%
37 lands	1.014%	7.101%	20.181%	30.185%	25.657%	12.391%	3.147%	3-4: 55.8%
38 lands	0.849%	6.275%	18.825%	29.724%	26.675%	13.604%	3.650%	3-4: 56.4%
39 lands	0.708%	5.520%	17.480%	29.134%	27.601%	14.862%	4.211%	3-4: 56.7%
40 lands	0.587%	4.833%	16.157%	28.423%	28.423%	16.157%	4.833%	3-4: 56.8%

	P(S = 1)	P(2 lands on T2)	P(3 lands on T3)	P(4 lands on T4)	P(5 lands on T5)
20 lands	31.52%	26.03% / 45.55%	6.51% / 16.40%	1.56% / 5.16%	0.36% / 1.47%
21 lands	29.79%	27.40% / 47.56%	7.23% / 18.02%	1.83% / 6.00%	0.45% / 1.81%
22 lands	28.03%	28.77% / 49.54%	7.99% / 19.70%	2.14% / 6.90%	0.55% / 2.21%
23 lands	26.27%	30.14% / 51.48%	8.79% / 21.42%	2.48% / 7.89%	0.67% / 2.66%
24 lands	24.53%	31.51% / 53.39%	9.63% / 23.19%	2.85% / 8.95%	0.81% / 3.17%
25 lands	22.81%	32.88% / 55.25%	10.50% / 25.00%	3.25% / 10.09%	0.98% / 3.75%
26 lands	21.14%	34.25% / 57.08%	11.42% / 26.85%	3.70% / 11.31%	1.16% / 4.40%
27 lands	19.51%	35.62% / 58.87%	12.37% / 28.74%	4.18% / 12.60%	1.37% / 5.12%
28 lands	17.94%	36.99% / 60.62%	13.36% / 30.66%	4.70% / 13.97%	1.61% / 5.91%
29 lands	16.44%	38.36% / 62.33%	14.38% / 32.62%	5.27% / 15.43%	1.88% / 6.79%
30 lands	15.01%	39.73% / 64.00%	15.45% / 34.60%	5.87% / 16.95%	2.18% / 7.75%
31 lands	13.65%	41.10% / 65.64%	16.55% / 36.60%	6.53% / 18.56%	2.52% / 8.79%
32 lands	12.36%	42.47% / 67.24%	17.69% / 38.63%	7.23% / 20.24%	2.89% / 9.93%
33 lands	11.15%	43.84% / 68.80%	18.87% / 40.67%	7.97% / 21.99%	3.30% / 11.16%
34 lands	10.03%	45.21% / 70.32%	20.09% / 42.73%	8.77% / 23.81%	3.76% / 12.48%
35 lands	8.97%	46.58% / 71.80%	21.35% / 44.80%	9.62% / 25.70%	4.26% / 13.89%
36 lands	8.00%	47.95% / 73.25%	22.64% / 46.88%	10.52% / 27.66%	4.81% / 15.41%
37 lands	7.10%	49.32% / 74.66%	23.97% / 48.96%	11.48% / 29.68%	5.41% / 17.02%
38 lands	6.28%	50.68% / 76.03%	25.34% / 51.04%	12.49% / 31.77%	6.07% / 18.73%
39 lands	5.52%	52.05% / 77.36%	26.75% / 53.12%	13.56% / 33.91%	6.78% / 20.54%
40 lands	4.83%	53.42% / 78.65%	28.20% / 55.20%	14.69% / 36.10%	7.56% / 22.45%

	P(S = 2)	P(3 lands on T3)	P(4 lands on T4)	P(5 lands on T5)	P(6 lands on T6)
20 lands	32.67%	43.49% / 57.82%	14.84% / 25.28%	4.40% / 9.24%	1.18% / 2.96%
21 lands	33.10%	45.55% / 60.12%	16.40% / 27.65%	5.16% / 10.70%	1.47% / 3.64%
22 lands	33.32%	47.56% / 62.34%	18.02% / 30.05%	6.00% / 12.27%	1.81% / 4.43%
23 lands	33.35%	49.54% / 64.47%	19.70% / 32.49%	6.90% / 13.95%	2.21% / 5.32%
24 lands	33.19%	51.48% / 66.52%	21.42% / 34.95%	7.89% / 15.73%	2.66% / 6.31%
25 lands	32.85%	53.39% / 68.49%	23.19% / 37.42%	8.95% / 17.62%	3.17% / 7.42%
26 lands	32.35%	55.25% / 70.38%	25.00% / 39.91%	10.09% / 19.60%	3.75% / 8.64%
27 lands	31.71%	57.08% / 72.19%	26.85% / 42.40%	11.31% / 21.67%	4.40% / 9.98%
28 lands	30.93%	58.87% / 73.93%	28.74% / 44.88%	12.60% / 23.83%	5.12% / 11.44%
29 lands	30.02%	60.62% / 75.59%	30.66% / 47.35%	13.97% / 26.07%	5.91% / 13.03%
30 lands	29.01%	62.33% / 77.19%	32.62% / 49.81%	15.43% / 28.38%	6.79% / 14.73%
31 lands	27.91%	64.00% / 78.71%	34.60% / 52.24%	16.95% / 30.76%	7.75% / 16.55%
32 lands	26.74%	65.64% / 80.16%	36.60% / 54.65%	18.56% / 33.20%	8.79% / 18.49%
33 lands	25.50%	67.24% / 81.54%	38.63% / 57.02%	20.24% / 35.70%	9.93% / 20.54%
34 lands	24.21%	68.80% / 82.86%	40.67% / 59.36%	21.99% / 38.23%	11.16% / 22.70%
35 lands	22.88%	70.32% / 84.11%	42.73% / 61.65%	23.81% / 40.81%	12.48% / 24.98%
36 lands	21.54%	71.80% / 85.31%	44.80% / 63.90%	25.70% / 43.41%	13.89% / 27.35%
37 lands	20.18%	73.25% / 86.44%	46.88% / 66.09%	27.66% / 46.04%	15.41% / 29.82%
38 lands	18.83%	74.66% / 87.51%	48.96% / 68.23%	29.68% / 48.68%	17.02% / 32.38%
39 lands	17.48%	76.03% / 88.52%	51.04% / 70.32%	31.77% / 51.32%	18.73% / 35.03%
40 lands	16.16%	77.36% / 89.48%	53.12% / 72.34%	33.91% / 53.96%	20.54% / 37.74%

	P(S = 3)	P(4 lands on T4)	P(5 lands on T5)	P(6 lands on T6)	P(7 lands on T7)
20 lands	17.50%	55.43% / 66.26%	22.96% / 33.00%	7.90% / 13.44%	2.36% / 4.68%
21 lands	19.05%	57.82% / 68.67%	25.28% / 35.97%	9.24% / 15.53%	2.96% / 5.77%
22 lands	20.57%	60.12% / 70.94%	27.65% / 38.94%	10.70% / 17.76%	3.64% / 7.01%
23 lands	22.02%	62.34% / 73.10%	30.05% / 41.90%	12.27% / 20.12%	4.43% / 8.41%
24 lands	23.40%	64.47% / 75.13%	32.49% / 44.85%	13.95% / 22.58%	5.32% / 9.95%
25 lands	24.69%	66.52% / 77.04%	34.95% / 47.76%	15.73% / 25.15%	6.31% / 11.65%
26 lands	25.88%	68.49% / 78.84%	37.42% / 50.63%	17.62% / 27.81%	7.42% / 13.51%
27 lands	26.96%	70.38% / 80.53%	39.91% / 53.45%	19.60% / 30.55%	8.64% / 15.51%
28 lands	27.92%	72.19% / 82.12%	42.40% / 56.21%	21.67% / 33.35%	9.98% / 17.66%
29 lands	28.74%	73.93% / 83.61%	44.88% / 58.91%	23.83% / 36.21%	11.44% / 19.95%
30 lands	29.43%	75.59% / 85.01%	47.35% / 61.54%	26.07% / 39.11%	13.03% / 22.37%
31 lands	29.98%	77.19% / 86.31%	49.81% / 64.09%	28.38% / 42.03%	14.73% / 24.92%
32 lands	30.38%	78.71% / 87.53%	52.24% / 66.56%	30.76% / 44.98%	16.55% / 27.58%
33 lands	30.63%	80.16% / 88.66%	54.65% / 68.94%	33.20% / 47.92%	18.49% / 30.35%
34 lands	30.74%	81.54% / 89.72%	57.02% / 71.24%	35.70% / 50.85%	20.54% / 33.21%
35 lands	30.70%	82.86% / 90.70%	59.36% / 73.44%	38.23% / 53.76%	22.70% / 36.15%
36 lands	30.51%	84.11% / 91.60%	61.65% / 75.54%	40.81% / 56.64%	24.98% / 39.16%
37 lands	30.19%	85.31% / 92.44%	63.90% / 77.55%	43.41% / 59.48%	27.35% / 42.22%
38 lands	29.72%	86.44% / 93.22%	66.09% / 79.46%	46.04% / 62.26%	29.82% / 45.31%
39 lands	29.13%	87.51% / 93.93%	68.23% / 81.27%	48.68% / 64.97%	32.38% / 48.44%
40 lands	28.42%	88.52% / 94.59%	70.32% / 82.98%	51.32% / 67.62%	35.03% / 51.56%

	P(S = 4)	P(5 lands on T5)	P(6 lands on T6)	P(7 lands on T7)	P(8 lands on T8)
20 lands	5.22%	63.71% / 72.12%	30.05% / 39.33%	11.48% / 17.30%	3.72% / 6.40%
21 lands	6.12%	66.26% / 74.57%	33.00% / 42.78%	13.44% / 20.01%	4.68% / 7.93%
22 lands	7.11%	68.67% / 76.84%	35.97% / 46.19%	15.53% / 22.85%	5.77% / 9.65%
23 lands	8.16%	70.94% / 78.95%	38.94% / 49.53%	17.76% / 25.82%	7.01% / 11.57%
24 lands	9.27%	73.10% / 80.89%	41.90% / 52.80%	20.12% / 28.90%	8.41% / 13.69%
25 lands	10.45%	75.13% / 82.70%	44.85% / 55.98%	22.58% / 32.05%	9.95% / 15.98%
26 lands	11.67%	77.04% / 84.36%	47.76% / 59.06%	25.15% / 35.27%	11.65% / 18.45%
27 lands	12.94%	78.84% / 85.89%	50.63% / 62.04%	27.81% / 38.54%	13.51% / 21.09%
28 lands	14.24%	80.53% / 87.30%	53.45% / 64.90%	30.55% / 41.83%	15.51% / 23.88%
29 lands	15.57%	82.12% / 88.60%	56.21% / 67.64%	33.35% / 45.12%	17.66% / 26.81%
30 lands	16.91%	83.61% / 89.79%	58.91% / 70.26%	36.21% / 48.41%	19.95% / 29.87%
31 lands	18.25%	85.01% / 90.87%	61.54% / 72.76%	39.11% / 51.66%	22.37% / 33.02%
32 lands	19.58%	86.31% / 91.87%	64.09% / 75.12%	42.03% / 54.87%	24.92% / 36.26%
33 lands	20.89%	87.53% / 92.77%	66.56% / 77.35%	44.98% / 58.02%	27.58% / 39.57%
34 lands	22.16%	88.66% / 93.59%	68.94% / 79.45%	47.92% / 61.10%	30.35% / 42.93%
35 lands	23.39%	89.72% / 94.34%	71.24% / 81.43%	50.85% / 64.09%	33.21% / 46.31%
36 lands	24.56%	90.70% / 95.01%	73.44% / 83.27%	53.76% / 66.98%	36.15% / 49.69%
37 lands	25.66%	91.60% / 95.62%	75.54% / 84.99%	56.64% / 69.76%	39.16% / 53.07%
38 lands	26.68%	92.44% / 96.17%	77.55% / 86.58%	59.48% / 72.42%	42.22% / 56.40%
39 lands	27.60%	93.22% / 96.66%	79.46% / 88.06%	62.26% / 74.97%	45.31% / 59.69%
40 lands	28.42%	93.93% / 97.10%	81.27% / 89.42%	64.97% / 77.38%	48.44% / 62.91%

99-card Decks

	P(S = 0)	P(S = 1)	P(S = 2)	P(S = 3)	P(S = 4)	P(S = 5)	P(S = 6)	max. range
24 lands	13.333%	32.462%	31.998%	16.525%	4.820%	0.792%	0.068%	1-2: 64.5%
25 lands	12.088%	31.109%	32.462%	17.777%	5.508%	0.964%	0.088%	1-2: 63.6%
26 lands	10.945%	29.731%	32.791%	19.009%	6.246%	1.161%	0.113%	1-2: 62.5%
27 lands	9.895%	28.336%	32.989%	20.214%	7.031%	1.386%	0.143%	1-2: 61.3%
28 lands	8.933%	26.937%	33.059%	21.382%	7.861%	1.641%	0.180%	1-2: 60.0%
29 lands	8.052%	25.541%	33.007%	22.505%	8.733%	1.926%	0.223%	1-2: 58.5%
30 lands	7.247%	24.157%	32.839%	23.577%	9.645%	2.246%	0.275%	1-2: 57.0%
31 lands	6.512%	22.792%	32.560%	24.590%	10.592%	2.600%	0.336%	2-3: 57.1%
32 lands	5.842%	21.451%	32.177%	25.537%	11.572%	2.991%	0.408%	2-3: 57.7%
33 lands	5.231%	20.141%	31.697%	26.414%	12.578%	3.420%	0.491%	2-3: 58.1%
34 lands	4.676%	18.864%	31.126%	27.214%	13.607%	3.888%	0.587%	2-3: 58.3%
35 lands	4.173%	17.627%	30.473%	27.934%	14.654%	4.396%	0.698%	2-3: 58.4%
36 lands	3.716%	16.431%	29.745%	28.569%	15.713%	4.946%	0.824%	2-3: 58.3%
37 lands	3.304%	15.279%	28.949%	29.116%	16.779%	5.537%	0.968%	2-3: 58.1%
38 lands	2.931%	14.173%	28.093%	29.572%	17.845%	6.170%	1.131%	2-3: 57.7%
39 lands	2.594%	13.115%	27.185%	29.935%	18.907%	6.845%	1.315%	2-3: 57.1%
40 lands	2.292%	12.107%	26.231%	30.205%	19.957%	7.563%	1.521%	2-3: 56.4%
41 lands	2.020%	11.147%	25.239%	30.380%	20.990%	8.321%	1.752%	2-3: 55.6%
42 lands	1.776%	10.238%	24.216%	30.461%	21.999%	9.120%	2.009%	2-3: 54.7%
43 lands	1.558%	9.378%	23.170%	30.447%	22.979%	9.958%	2.293%	2-3: 53.6%
44 lands	1.363%	8.568%	22.106%	30.341%	23.923%	10.833%	2.608%	3-4: 54.3%
45 lands	1.190%	7.807%	21.031%	30.144%	24.825%	11.744%	2.954%	3-4: 55.0%
46 lands	1.035%	7.094%	19.951%	29.859%	25.679%	12.688%	3.335%	3-4: 55.5%
47 lands	0.899%	6.427%	18.872%	29.487%	26.479%	13.663%	3.751%	3-4: 56.0%
48 lands	0.778%	5.807%	17.799%	29.034%	27.219%	14.665%	4.204%	3-4: 56.3%
49 lands	0.671%	5.230%	16.737%	28.502%	27.895%	15.691%	4.697%	3-4: 56.4%

	P(S = 1)	P(2 lands on T2)	P(3 lands on T3)	P(4 lands on T4)	P(5 lands on T5)
24 lands	32.46%	25.00% / 43.96%	6.04% / 15.31%	1.41% / 4.69%	0.32% / 1.31%
25 lands	31.11%	26.09% / 45.58%	6.59% / 16.56%	1.61% / 5.31%	0.38% / 1.56%
26 lands	29.73%	27.17% / 47.18%	7.17% / 17.84%	1.83% / 5.97%	0.45% / 1.83%
27 lands	28.34%	28.26% / 48.76%	7.76% / 19.15%	2.07% / 6.68%	0.54% / 2.14%
28 lands	26.94%	29.35% / 50.31%	8.39% / 20.50%	2.33% / 7.43%	0.63% / 2.48%
29 lands	25.54%	30.43% / 51.84%	9.03% / 21.87%	2.61% / 8.24%	0.73% / 2.86%
30 lands	24.16%	31.52% / 53.34%	9.70% / 23.28%	2.91% / 9.09%	0.85% / 3.28%
31 lands	22.79%	32.61% / 54.83%	10.39% / 24.71%	3.23% / 9.99%	0.98% / 3.74%
32 lands	21.45%	33.70% / 56.28%	11.11% / 26.17%	3.58% / 10.94%	1.13% / 4.25%
33 lands	20.14%	34.78% / 57.72%	11.85% / 27.65%	3.95% / 11.94%	1.29% / 4.80%
34 lands	18.86%	35.87% / 59.13%	12.61% / 29.15%	4.34% / 12.99%	1.46% / 5.39%
35 lands	17.63%	36.96% / 60.51%	13.40% / 30.68%	4.77% / 14.08%	1.66% / 6.04%
36 lands	16.43%	38.04% / 61.87%	14.21% / 32.22%	5.21% / 15.23%	1.87% / 6.73%
37 lands	15.28%	39.13% / 63.21%	15.05% / 33.78%	5.69% / 16.42%	2.11% / 7.47%
38 lands	14.17%	40.22% / 64.52%	15.91% / 35.36%	6.19% / 17.66%	2.36% / 8.27%
39 lands	13.12%	41.30% / 65.81%	16.79% / 36.95%	6.72% / 18.95%	2.64% / 9.13%
40 lands	12.11%	42.39% / 67.08%	17.70% / 38.55%	7.28% / 20.28%	2.94% / 10.04%
41 lands	11.15%	43.48% / 68.32%	18.63% / 40.17%	7.87% / 21.66%	3.27% / 11.00%
42 lands	10.24%	44.57% / 69.54%	19.59% / 41.79%	8.49% / 23.08%	3.62% / 12.03%
43 lands	9.38%	45.65% / 70.74%	20.57% / 43.42%	9.14% / 24.55%	4.01% / 13.11%
44 lands	8.57%	46.74% / 71.91%	21.57% / 45.06%	9.83% / 26.06%	4.42% / 14.25%
45 lands	7.81%	47.83% / 73.05%	22.60% / 46.70%	10.55% / 27.61%	4.86% / 15.46%
46 lands	7.09%	48.91% / 74.18%	23.65% / 48.35%	11.30% / 29.20%	5.33% / 16.72%
47 lands	6.43%	50.00% / 75.27%	24.73% / 50.00%	12.09% / 30.83%	5.84% / 18.05%
48 lands	5.81%	51.09% / 76.35%	25.82% / 51.65%	12.91% / 32.50%	6.38% / 19.44%
49 lands	5.23%	52.17% / 77.40%	26.95% / 53.30%	13.77% / 34.20%	6.96% / 20.89%

	P(S = 2)	P(3 lands on T3)	P(4 lands on T4)	P(5 lands on T5)	P(6 lands on T6)
24 lands	32.00%	42.31% / 56.41%	14.10% / 24.09%	4.12% / 8.66%	1.09% / 2.75%
25 lands	32.46%	43.96% / 58.28%	15.31% / 25.93%	4.69% / 9.76%	1.31% / 3.25%
26 lands	32.79%	45.58% / 60.09%	16.56% / 27.81%	5.31% / 10.93%	1.56% / 3.82%
27 lands	32.99%	47.18% / 61.85%	17.84% / 29.71%	5.97% / 12.17%	1.83% / 4.45%
28 lands	33.06%	48.76% / 63.56%	19.15% / 31.63%	6.68% / 13.48%	2.14% / 5.14%
29 lands	33.01%	50.31% / 65.22%	20.50% / 33.56%	7.43% / 14.86%	2.48% / 5.90%
30 lands	32.84%	51.84% / 66.82%	21.87% / 35.51%	8.24% / 16.29%	2.86% / 6.72%
31 lands	32.56%	53.34% / 68.38%	23.28% / 37.47%	9.09% / 17.80%	3.28% / 7.62%
32 lands	32.18%	54.83% / 69.88%	24.71% / 39.43%	9.99% / 19.36%	3.74% / 8.59%
33 lands	31.70%	56.28% / 71.34%	26.17% / 41.39%	10.94% / 20.98%	4.25% / 9.63%
34 lands	31.13%	57.72% / 72.75%	27.65% / 43.36%	11.94% / 22.65%	4.80% / 10.75%
35 lands	30.47%	59.13% / 74.11%	29.15% / 45.32%	12.99% / 24.37%	5.39% / 11.94%
36 lands	29.75%	60.51% / 75.43%	30.68% / 47.27%	14.08% / 26.15%	6.04% / 13.20%
37 lands	28.95%	61.87% / 76.70%	32.22% / 49.21%	15.23% / 27.97%	6.73% / 14.54%
38 lands	28.09%	63.21% / 77.93%	33.78% / 51.14%	16.42% / 29.83%	7.47% / 15.96%
39 lands	27.18%	64.52% / 79.11%	35.36% / 53.05%	17.66% / 31.74%	8.27% / 17.44%
40 lands	26.23%	65.81% / 80.25%	36.95% / 54.95%	18.95% / 33.67%	9.13% / 19.00%
41 lands	25.24%	67.08% / 81.35%	38.55% / 56.82%	20.28% / 35.64%	10.04% / 20.63%
42 lands	24.22%	68.32% / 82.40%	40.17% / 58.67%	21.66% / 37.64%	11.00% / 22.33%
43 lands	23.17%	69.54% / 83.42%	41.79% / 60.50%	23.08% / 39.66%	12.03% / 24.10%
44 lands	22.11%	70.74% / 84.39%	43.42% / 62.30%	24.55% / 41.71%	13.11% / 25.93%
45 lands	21.03%	71.91% / 85.33%	45.06% / 64.06%	26.06% / 43.77%	14.25% / 27.82%
46 lands	19.95%	73.05% / 86.23%	46.70% / 65.80%	27.61% / 45.84%	15.46% / 29.77%
47 lands	18.87%	74.18% / 87.09%	48.35% / 67.50%	29.20% / 47.92%	16.72% / 31.78%
48 lands	17.80%	75.27% / 87.91%	50.00% / 69.17%	30.83% / 50.00%	18.05% / 33.84%
49 lands	16.74%	76.35% / 88.70%	51.65% / 70.80%	32.50% / 52.08%	19.44% / 35.95%

	P(S = 3)	P(4 lands on T4)	P(5 lands on T5)	P(6 lands on T6)	P(7 lands on T7)
24 lands	16.52%	54.49% / 65.23%	22.27% / 32.03%	7.63% / 12.96%	2.30% / 4.53%
25 lands	17.78%	56.41% / 67.19%	24.09% / 34.37%	8.66% / 14.57%	2.75% / 5.36%
26 lands	19.01%	58.28% / 69.06%	25.93% / 36.71%	9.76% / 16.27%	3.25% / 6.28%
27 lands	20.21%	60.09% / 70.85%	27.81% / 39.06%	10.93% / 18.04%	3.82% / 7.29%
28 lands	21.38%	61.85% / 72.57%	29.71% / 41.40%	12.17% / 19.90%	4.45% / 8.40%
29 lands	22.51%	63.56% / 74.21%	31.63% / 43.72%	13.48% / 21.82%	5.14% / 9.60%
30 lands	23.58%	65.22% / 75.77%	33.56% / 46.03%	14.86% / 23.81%	5.90% / 10.90%
31 lands	24.59%	66.82% / 77.26%	35.51% / 48.32%	16.29% / 25.87%	6.72% / 12.29%
32 lands	25.54%	68.38% / 78.68%	37.47% / 50.58%	17.80% / 27.97%	7.62% / 13.77%
33 lands	26.41%	69.88% / 80.04%	39.43% / 52.81%	19.36% / 30.12%	8.59% / 15.35%
34 lands	27.21%	71.34% / 81.32%	41.39% / 55.01%	20.98% / 32.32%	9.63% / 17.02%
35 lands	27.93%	72.75% / 82.55%	43.36% / 57.16%	22.65% / 34.55%	10.75% / 18.77%
36 lands	28.57%	74.11% / 83.71%	45.32% / 59.28%	24.37% / 36.81%	11.94% / 20.61%
37 lands	29.12%	75.43% / 84.82%	47.27% / 61.35%	26.15% / 39.10%	13.20% / 22.54%
38 lands	29.57%	76.70% / 85.86%	49.21% / 63.37%	27.97% / 41.40%	14.54% / 24.54%
39 lands	29.94%	77.93% / 86.86%	51.14% / 65.35%	29.83% / 43.71%	15.96% / 26.61%
40 lands	30.21%	79.11% / 87.79%	53.05% / 67.27%	31.74% / 46.03%	17.44% / 28.74%
41 lands	30.38%	80.25% / 88.68%	54.95% / 69.13%	33.67% / 48.35%	19.00% / 30.94%
42 lands	30.46%	81.35% / 89.52%	56.82% / 70.94%	35.64% / 50.66%	20.63% / 33.20%
43 lands	30.45%	82.40% / 90.31%	58.67% / 72.69%	37.64% / 52.95%	22.33% / 35.51%
44 lands	30.34%	83.42% / 91.06%	60.50% / 74.39%	39.66% / 55.23%	24.10% / 37.85%
45 lands	30.14%	84.39% / 91.76%	62.30% / 76.02%	41.71% / 57.48%	25.93% / 40.24%
46 lands	29.86%	85.33% / 92.42%	64.06% / 77.60%	43.77% / 59.71%	27.82% / 42.65%
47 lands	29.49%	86.23% / 93.04%	65.80% / 79.11%	45.84% / 61.90%	29.77% / 45.09%
48 lands	29.03%	87.09% / 93.62%	67.50% / 80.56%	47.92% / 64.05%	31.78% / 47.54%
49 lands	28.50%	87.91% / 94.16%	69.17% / 81.95%	50.00% / 66.16%	33.84% / 50.00%

	P(S = 4)	P(5 lands on T5)	P(6 lands on T6)	P(7 lands on T7)	P(8 lands on T8)
24 lands	4.82%	63.18% / 71.55%	29.71% / 38.85%	11.43% / 17.17%	3.78% / 6.46%
25 lands	5.51%	65.23% / 73.52%	32.03% / 41.57%	12.96% / 19.28%	4.53% / 7.65%
26 lands	6.25%	67.19% / 75.39%	34.37% / 44.27%	14.57% / 21.48%	5.36% / 8.96%
27 lands	7.03%	69.06% / 77.15%	36.71% / 46.94%	16.27% / 23.76%	6.28% / 10.39%
28 lands	7.86%	70.85% / 78.80%	39.06% / 49.57%	18.04% / 26.11%	7.29% / 11.94%
29 lands	8.73%	72.57% / 80.36%	41.40% / 52.15%	19.90% / 28.52%	8.40% / 13.61%
30 lands	9.65%	74.21% / 81.83%	43.72% / 54.67%	21.82% / 30.99%	9.60% / 15.39%
31 lands	10.59%	75.77% / 83.20%	46.03% / 57.14%	23.81% / 33.50%	10.90% / 17.28%
32 lands	11.57%	77.26% / 84.50%	48.32% / 59.55%	25.87% / 36.05%	12.29% / 19.28%
33 lands	12.58%	78.68% / 85.71%	50.58% / 61.89%	27.97% / 38.62%	13.77% / 21.37%
34 lands	13.61%	80.04% / 86.84%	52.81% / 64.15%	30.12% / 41.20%	15.35% / 23.56%
35 lands	14.65%	81.32% / 87.90%	55.01% / 66.35%	32.32% / 43.79%	17.02% / 25.84%
36 lands	15.71%	82.55% / 88.89%	57.16% / 68.47%	34.55% / 46.38%	18.77% / 28.19%
37 lands	16.78%	83.71% / 89.82%	59.28% / 70.51%	36.81% / 48.96%	20.61% / 30.62%
38 lands	17.85%	84.82% / 90.68%	61.35% / 72.48%	39.10% / 51.52%	22.54% / 33.11%
39 lands	18.91%	85.86% / 91.49%	63.37% / 74.36%	41.40% / 54.05%	24.54% / 35.65%
40 lands	19.96%	86.86% / 92.23%	65.35% / 76.16%	43.71% / 56.54%	26.61% / 38.23%
41 lands	20.99%	87.79% / 92.93%	67.27% / 77.88%	46.03% / 58.99%	28.74% / 40.84%
42 lands	22.00%	88.68% / 93.57%	69.13% / 79.52%	48.35% / 61.40%	30.94% / 43.48%
43 lands	22.98%	89.52% / 94.16%	70.94% / 81.09%	50.66% / 63.75%	33.20% / 46.14%
44 lands	23.92%	90.31% / 94.72%	72.69% / 82.57%	52.95% / 66.04%	35.51% / 48.80%
45 lands	24.82%	91.06% / 95.22%	74.39% / 83.97%	55.23% / 68.26%	37.85% / 51.45%
46 lands	25.68%	91.76% / 95.69%	76.02% / 85.29%	57.48% / 70.42%	40.24% / 54.09%
47 lands	26.48%	92.42% / 96.12%	77.60% / 86.54%	59.71% / 72.50%	42.65% / 56.70%
48 lands	27.22%	93.04% / 96.52%	79.11% / 87.71%	61.90% / 74.51%	45.09% / 59.28%
49 lands	27.90%	93.62% / 96.88%	80.56% / 88.81%	64.05% / 76.43%	47.54% / 61.82%