
import math
from math import comb as MC
import matplotlib as mpl
import matplotlib.pyplot as plt
from matplotlib.ticker import StrMethodFormatter as SMF
import pandas as pd
import seaborn as sns


suits = []
nothings = []
pairs = []
twopairs = []
threekinds = []
straights = []
flushes = []
fullhouses = []
fourkinds = []
straightflushes = []
royalflushes = []
fivekinds = []


for i in range(3, 31) :
    suits.append(i)
    
    d = MC(13*i, 5)
    
    pair = 13 * MC(i, 2) * MC(12, 3) * i ** 3 / d
    pairs.append(pair)
    
    twopair = MC(13, 2) * MC(i, 2) * MC(i, 2) * 11 * i / d
    twopairs.append(twopair)
    
    threekind = 13 * MC(i, 3) * MC(12, 2) * i ** 2 / d
    threekinds.append(threekind)
    
    straight = (10 * i**5 - 10*i) / d
    straights.append(straight)
    
    flush = (i * MC(13, 5) - 10*i) / d
    flushes.append(flush)
    
    fullhouse = 13 * MC(i, 3) * 12 * MC(i, 2) / d
    fullhouses.append(fullhouse)
    
    fourkind = 13 * MC(i, 4) * 12 * i / d
    fourkinds.append(fourkind)
    
    straightflush = 9*i / d
    straightflushes.append(straightflush)
    
    royalflush = i / d
    royalflushes.append(royalflush)

    if i < 5 :
        fivekind = 0
    else :
        fivekind = 13 * MC(i, 5) / d
    fivekinds.append(fivekind)
    
    nothing = 1 - (pair + twopair + threekind + straight + flush + fullhouse + fourkind + straightflush + royalflush + fivekind)
    nothings.append(nothing)

    print(i, straight, fullhouse)

3 0.0041684252210568 0.000812842918106076
4 0.003924646781789639 0.0014405762304921968
5 0.0037772909269471935 0.0018886454634735967
6 0.00368052999631947 0.00221684432210748
7 0.0036125568864817216 0.002465570075023775
8 0.003562320823744282 0.002659866215062397
9 0.0035237298766689173 0.002815546116089603
10 0.0034931763896239266 0.0029429460852277186
11 0.0034683960063883875 0.003049061243320939
12 0.003447898684091633 0.0031387767331041076
13 0.0034306649990944052 0.0032155997815041175
14 0.0034159744838844035 0.0032821099000489335
15 0.0034033037818858316 0.0033402447792900487
16 0.0033922636852760707 0.0033914872458882758
17 0.0033825588115379618 0.003436990792413285
18 0.003373960976704669 0.00347766588251496
19 0.00336629113689718 0.00351424056227849
20 0.0033594068494756215 0.003547303848181597
21 0.0033531933832349477 0.0035773373259645564
22 0.003347557297278997 0.0036047385257656044
23 0.003342421724858308 0.003629838460915699
24 0.0033377228568075104 0.0036529149590981995
25 0.003333407283323185 0.0036742029161229996
26 0.003329429959362441 0.0036939022690448222
27 0.0033257526294943576 0.003712184258410654
28 0.0033223425956096938 0.003729196392580513
29 0.003319171743509136 0.0037450664171061986
30 0.0033162157670933792 0.003759905514027895


data = list(zip(suits,
                nothings,
                pairs,
                twopairs,
                threekinds,
                straights,
                flushes,
                fullhouses,
                fourkinds,
                straightflushes,
                royalflushes,
                fivekinds))

names = ["Suits",
         "High Card",
         "Pair",
         "Two Pair",
         "Three-of-a-Kind",
         "Straight",
         "Flush",
         "Full House",
         "Four-of-a-Kind",
         "Straight Flush",
         "Royal Flush",
         "Five-of-a-Kind"]

df = pd.DataFrame(data = data,
                  columns = names)

df


df.reset_index()
df = pd.DataFrame.melt(df,
                       id_vars = 'Suits',
                       var_name = "Hand",
                       value_name = "Probability")
df


df.Hand.unique().tolist()

['High Card',
 'Pair',
 'Two Pair',
 'Three-of-a-Kind',
 'Straight',
 'Flush',
 'Full House',
 'Four-of-a-Kind',
 'Straight Flush',
 'Royal Flush',
 'Five-of-a-Kind']


plot1 = sns.lmplot(x ='Suits',
                   y = 'Probability',
                   data = df,
                   hue = 'Hand',
                   fit_reg = False,
                   palette = 'viridis',
                   height = 6,
                   aspect = 2,
                   scatter_kws = {"s": 75} )
#Title setup.
plt.title('Probabilities of Hands with N Suits', fontsize = 24)

#X-axis setup.
plt.xlabel('Suits', fontsize = 22)

#Y-axis setup.
plt.ylabel('Probability', fontsize = 22)

plt.tick_params(axis = 'both', which = 'major', labelsize = 18)
plt.show()
plot1.savefig("2023.03.17 Classic1.png")


plot2 = sns.lmplot(x ='Suits',
                   y = 'Probability',
                   data = df.loc[df.Hand.isin(['Straight', 'Full House'])],
                   hue = 'Hand',
                   fit_reg=False,
                   palette = 'viridis',
                   height = 6,
                   aspect = 2,
                   scatter_kws = {"s": 75} )
#Title setup.
plt.title('Probabilities of Hands with N Suits', fontsize = 24)

#X-axis setup.
plt.xlabel('Suits', fontsize = 22)

#Y-axis setup.
plt.ylabel('Probability', fontsize = 22)

plt.tick_params(axis = 'both', which = 'major', labelsize = 18)
plt.show()
plot2.savefig("2023.03.17 Classic2.png")

	Suits	High Card	Pair	Two Pair	Three-of-a-Kind	Straight	Flush	Full House	Four-of-a-Kind	Straight Flush	Royal Flush	Five-of-a-Kind
0	3	0.532308	0.402357	0.040236	0.013412	0.004168	6.653849e-03	0.000813	0.000000	4.689478e-05	5.210532e-06	0.000000
1	4	0.501177	0.422569	0.047539	0.021128	0.003925	1.965402e-03	0.001441	0.000240	1.385169e-05	1.539077e-06	0.000000
2	5	0.482360	0.432815	0.051938	0.025969	0.003777	7.730129e-04	0.001889	0.000472	5.448016e-06	6.053351e-07	0.000002
3	6	0.470004	0.438935	0.054867	0.029262	0.003681	3.629372e-04	0.002217	0.000665	2.557897e-06	2.842108e-07	0.000004
4	7	0.461324	0.442981	0.056955	0.031641	0.003613	1.922181e-04	0.002466	0.000822	1.354709e-06	1.505232e-07	0.000006
5	8	0.454908	0.445844	0.058517	0.033438	0.003562	1.110887e-04	0.002660	0.000950	7.829277e-07	8.699196e-08	0.000008
6	9	0.449980	0.447973	0.059730	0.034842	0.003524	6.859456e-05	0.002816	0.001056	4.834386e-07	5.371539e-08	0.000010
7	10	0.446079	0.449617	0.060698	0.035969	0.003493	4.461232e-05	0.002943	0.001144	3.144173e-07	3.493526e-08	0.000011
8	11	0.442914	0.450922	0.061489	0.036894	0.003468	3.025370e-05	0.003049	0.001220	2.132211e-07	2.369123e-08	0.000013
9	12	0.440297	0.451984	0.062148	0.037665	0.003448	2.123447e-05	0.003139	0.001284	1.496556e-07	1.662840e-08	0.000014
10	13	0.438096	0.452864	0.062704	0.038319	0.003431	1.533949e-05	0.003216	0.001340	1.081092e-07	1.201213e-08	0.000015
11	14	0.436220	0.453604	0.063181	0.038880	0.003416	1.135546e-05	0.003282	0.001389	8.003064e-08	8.892293e-09	0.000017
12	15	0.434602	0.454237	0.063593	0.039367	0.003403	8.584898e-06	0.003340	0.001432	6.050437e-08	6.722708e-09	0.000017
13	16	0.433192	0.454782	0.063954	0.039793	0.003392	6.610087e-06	0.003391	0.001470	4.658636e-08	5.176263e-09	0.000018
14	17	0.431953	0.455258	0.064272	0.040170	0.003383	5.171848e-06	0.003437	0.001504	3.644999e-08	4.049999e-09	0.000019
15	18	0.430855	0.455677	0.064554	0.040505	0.003374	4.104356e-06	0.003478	0.001534	2.892655e-08	3.214061e-09	0.000020
16	19	0.429875	0.456047	0.064807	0.040804	0.003366	3.298614e-06	0.003514	0.001562	2.324787e-08	2.583096e-09	0.000021
17	20	0.428996	0.456378	0.065034	0.041074	0.003359	2.681243e-06	0.003547	0.001587	1.889678e-08	2.099642e-09	0.000021
18	21	0.428203	0.456675	0.065239	0.041318	0.003353	2.201783e-06	0.003577	0.001610	1.551766e-08	1.724184e-09	0.000022
19	22	0.427483	0.456944	0.065426	0.041540	0.003348	1.824862e-06	0.003605	0.001631	1.286120e-08	1.429023e-09	0.000022
20	23	0.426827	0.457187	0.065596	0.041743	0.003342	1.525255e-06	0.003630	0.001650	1.074964e-08	1.194405e-09	0.000023
21	24	0.426227	0.457408	0.065752	0.041929	0.003338	1.284688e-06	0.003653	0.001668	9.054180e-09	1.006020e-09	0.000023
22	25	0.425676	0.457611	0.065896	0.042100	0.003333	1.089734e-06	0.003674	0.001684	7.680190e-09	8.533544e-10	0.000024
23	26	0.425168	0.457798	0.066029	0.042258	0.003329	9.303971e-07	0.003694	0.001699	6.557223e-09	7.285803e-10	0.000024
24	27	0.424699	0.457969	0.066151	0.042405	0.003326	7.991469e-07	0.003712	0.001713	5.632202e-09	6.258002e-10	0.000024
25	28	0.424263	0.458128	0.066265	0.042540	0.003322	6.902460e-07	0.003729	0.001726	4.864694e-09	5.405215e-10	0.000025
26	29	0.423858	0.458275	0.066371	0.042667	0.003319	5.992793e-07	0.003745	0.001739	4.223581e-09	4.692868e-10	0.000025
27	30	0.423481	0.458412	0.066470	0.042785	0.003316	5.228164e-07	0.003760	0.001750	3.684689e-09	4.094099e-10	0.000025

Rohan Lewis¶

2023.03.20¶