Real players winning hands compared to odds calculators
A number of on line odds calculators, as well as the starting hand exercise holsted here predict winning odds based strictly on mathematical ranking of card combinations. Curious to see how well real world hand choices coincide to the odd calculator recommendations, I generated a winning hand stats chart based on real game history data.
Utilizing game history data from about 1/4 million IRC “no robot holdem” hands played by a couple thousand players from 1988 to 2000, to create a chart comparably to statistically generated tables. Some issues:
- Winning and tied hands are combined here (it’s more work to separate ties)
- Some data skewing may result from the exclusion of foldout wins in which the hole cards aren’t revealed.
- The size of the sampled tables varied, probably more weak winners sneaked in from small tables.
Perhaps the most interest, but not surprising difference between the theoretical and real world hand choices, is the lower success of junk hands (those ranked below 36 of 169) of real world players (in Red). This no doubt is due to lousy hands being folded well before the river, while the calculated odds (in Blue) assume all hands are played to the end.
The complete comparison table is shown belowThe Calculated odds values combine winning and tie hands, as does the IRC History data.
| # | Hand | Calculated_Odds | Hand | IRC_History |
| 1 | AA | 31.50% | AA | 35.91% |
| 2 | KK | 26.60% | KK | 32.60% |
| 3 | 22.80% | 29.78% | ||
| 4 | AKs | 22.10% | JJ | 27.37% |
| 5 | AQs | 20.90% | AKs | 24.60% |
| 6 | KQs | 20.20% | TT | 23.64% |
| 7 | JJ | 20.00% | AQs | 22.66% |
| 8 | AJs | 20.00% | AKo | 22.40% |
| 9 | KJs | 19.50% | 99 | 21.22% |
| 10 | ATs | 19.30% | AJs | 20.90% |
| 11 | QJs | 19.00% | AQo | 20.30% |
| 12 | AKo | 18.70% | ATs | 20.27% |
| 13 | KTs | 18.70% | 88 | 20.03% |
| 14 | JTs | 18.60% | QJs | 19.87% |
| 15 | QTs | 18.40% | KJs | 19.72% |
| 16 | TT | 17.90% | KQs | 19.55% |
| 17 | A9s | 17.30% | AJo | 19.30% |
| 18 | AQo | 17.20% | A9s | 18.28% |
| 19 | A8s | 16.80% | KQo | 18.00% |
| 20 | T9s | 16.80% | KTs | 17.79% |
| 21 | A5s | 16.70% | 77 | 17.60% |
| 22 | K9s | 16.70% | ATo | 17.59% |
| 23 | KQo | 16.60% | QTs | 17.47% |
| 24 | A7s | 16.40% | JTs | 17.31% |
| 25 | J9s | 16.30% | A7s | 16.91% |
| 26 | A4s | 16.30% | 66 | 16.81% |
| 27 | 99 | 16.20% | A5s | 16.56% |
| 28 | Q9s | 16.20% | KJo | 16.55% |
| 29 | AJo | 16.10% | A6s | 16.28% |
| 30 | A6s | 16.10% | A8s | 16.24% |
| 31 | A3s | 16.00% | T9s | 15.87% |
| 32 | KJo | 15.70% | QJo | 15.81% |
| 33 | QJo | 15.40% | A4s | 15.81% |
| 34 | K8s | 15.40% | A2s | 15.55% |
| 35 | T8s | 15.40% | K9s | 15.44% |
| 36 | A2s | 15.30% | J9s | 15.41% |
| 37 | ATo | 15.20% | Q9s | 15.32% |
| 38 | 88 | 15.10% | A3s | 15.29% |
| 39 | 98s | 15.00% | 55 | 15.15% |
| 40 | J8s | 15.00% | KTo | 15.06% |
| 41 | KTo | 15.00% | 98s | 14.40% |
| 42 | Q8s | 14.90% | K8s | 14.31% |
| 43 | K7s | 14.90% | QTo | 14.22% |
| 44 | JTo | 14.90% | JTo | 14.21% |
| 45 | QTo | 14.80% | 44 | 13.80% |
| 46 | K6s | 14.60% | T8s | 13.69% |
| 47 | K5s | 14.50% | K7s | 13.66% |
| 48 | 77 | 14.30% | A9o | 13.46% |
| 49 | 87s | 14.30% | Q8s | 13.04% |
| 50 | T7s | 14.20% | J8s | 12.91% |
| 51 | 97s | 14.10% | K6s | 12.63% |
| 52 | K4s | 14.10% | 87s | 12.45% |
| 53 | 76s | 13.80% | 33 | 12.21% |
| 54 | K3s | 13.80% | A8o | 11.94% |
| 55 | Q7s | 13.80% | K5s | 11.82% |
| 56 | 66 | 13.70% | K3s | 11.77% |
| 57 | J7s | 13.70% | 76s | 11.77% |
| 58 | K2s | 13.60% | 65s | 11.76% |
| 59 | Q6s | 13.60% | 97s | 11.66% |
| 60 | 86s | 13.50% | K4s | 11.65% |
| 61 | Q5s | 13.40% | Q7s | 11.43% |
| 62 | 65s | 13.30% | K2s | 11.28% |
| 63 | T9o | 13.20% | J7s | 11.18% |
| 64 | 55 | 13.10% | A7o | 11.01% |
| 65 | 54s | 13.10% | T9o | 10.93% |
| 66 | 96s | 13.10% | T7s | 10.87% |
| 67 | 75s | 13.00% | 22 | 10.85% |
| 68 | T6s | 13.00% | A5o | 10.48% |
| 69 | A9o | 13.00% | K9o | 10.46% |
| 70 | Q4s | 12.90% | J9o | 10.37% |
| 71 | Q3s | 12.80% | A3o | 10.03% |
| 72 | J6s | 12.80% | 86s | 10.02% |
| 73 | J5s | 12.70% | A6o | 9.99% |
| 74 | 44 | 12.60% | A4o | 9.95% |
| 75 | J9o | 12.60% | 54s | 9.84% |
| 76 | K9o | 12.50% | Q5s | 9.82% |
| 77 | 33 | 12.40% | Q4s | 9.58% |
| 78 | 64s | 12.40% | A2o | 9.46% |
| 79 | Q2s | 12.40% | Q6s | 9.40% |
| 80 | 85s | 12.40% | 75s | 9.19% |
| 81 | Q9o | 12.40% | Q9o | 9.18% |
| 82 | A8o | 12.40% | Q2s | 9.06% |
| 83 | J4s | 12.30% | 96s | 9.05% |
| 84 | A5o | 12.30% | T6s | 9.03% |
| 85 | 22 | 12.20% | J6s | 8.95% |
| 86 | 53s | 12.20% | 98o | 8.72% |
| 87 | T5s | 12.10% | Q3s | 8.62% |
| 88 | J3s | 12.00% | 85s | 8.43% |
| 89 | 95s | 12.00% | 64s | 8.38% |
| 90 | A7o | 12.00% | 43s | 8.37% |
| 91 | A4o | 11.90% | J5s | 8.20% |
| 92 | 74s | 11.80% | J4s | 8.01% |
| 93 | T4s | 11.80% | 53s | 7.85% |
| 94 | J2s | 11.70% | 95s | 7.78% |
| 95 | T8o | 11.70% | 87o | 7.76% |
| 96 | 43s | 11.60% | T5s | 7.76% |
| 97 | A6o | 11.60% | K8o | 7.71% |
| 98 | A3o | 11.50% | J3s | 7.49% |
| 99 | T3s | 11.50% | J2s | 7.33% |
| 100 | 98o | 11.40% | T8o | 7.16% |
| 101 | 63s | 11.30% | T3s | 7.05% |
| 102 | K8o | 11.30% | J8o | 7.02% |
| 103 | 84s | 11.20% | T4s | 7.00% |
| 104 | J8o | 11.20% | 74s | 7.00% |
| 105 | T2s | 11.20% | K7o | 6.95% |
| 106 | 52s | 11.10% | 63s | 6.94% |
| 107 | Q8o | 11.00% | 84s | 6.73% |
| 108 | 94s | 11.00% | Q8o | 6.72% |
| 109 | A2o | 10.90% | 32s | 6.61% |
| 110 | 87o | 10.80% | 76o | 6.46% |
| 111 | K7o | 10.80% | T2s | 6.24% |
| 112 | 73s | 10.70% | 52s | 6.14% |
| 113 | 93s | 10.60% | 94s | 5.95% |
| 114 | 42s | 10.60% | K6o | 5.91% |
| 115 | 97o | 10.50% | 42s | 5.83% |
| 116 | K6o | 10.50% | 73s | 5.76% |
| 117 | 92s | 10.40% | 65o | 5.57% |
| 118 | 76o | 10.30% | 93s | 5.50% |
| 119 | T7o | 10.30% | 92s | 5.45% |
| 120 | 83s | 10.20% | 97o | 5.35% |
| 121 | 62s | 10.10% | K5o | 5.27% |
| 122 | K5o | 10.10% | 83s | 5.26% |
| 123 | 65o | 10.00% | Q7o | 5.24% |
| 124 | 32s | 10.00% | 62s | 5.23% |
| 125 | 82s | 9.90% | 82s | 5.12% |
| 126 | J7o | 9.90% | K4o | 5.05% |
| 127 | 86o | 9.80% | K3o | 4.77% |
| 128 | Q7o | 9.80% | T7o | 4.66% |
| 129 | K4o | 9.80% | 72s | 4.64% |
| 130 | 72s | 9.70% | 54o | 4.58% |
| 131 | 54o | 9.70% | J7o | 4.57% |
| 132 | K3o | 9.50% | 86o | 4.46% |
| 133 | Q6o | 9.50% | K2o | 4.40% |
| 134 | 75o | 9.40% | Q6o | 4.20% |
| 135 | 96o | 9.30% | Q5o | 3.95% |
| 136 | K2o | 9.20% | Q4o | 3.79% |
| 137 | T6o | 9.20% | 75o | 3.54% |
| 138 | Q5o | 9.20% | 96o | 3.47% |
| 139 | 64o | 8.90% | J6o | 3.47% |
| 140 | 85o | 8.80% | Q3o | 3.38% |
| 141 | Q4o | 8.80% | T6o | 3.24% |
| 142 | J6o | 8.80% | Q2o | 3.22% |
| 143 | 53o | 8.70% | J5o | 3.22% |
| 144 | Q3o | 8.60% | 43o | 3.21% |
| 145 | J5o | 8.50% | 64o | 3.03% |
| 146 | Q2o | 8.30% | 85o | 2.99% |
| 147 | 95o | 8.20% | J4o | 2.99% |
| 148 | J4o | 8.20% | J3o | 2.64% |
| 149 | 74o | 8.20% | 53o | 2.63% |
| 150 | T5o | 8.20% | T5o | 2.63% |
| 151 | 43o | 8.00% | 95o | 2.51% |
| 152 | J3o | 7.90% | J2o | 2.50% |
| 153 | T4o | 7.80% | 63o | 2.46% |
| 154 | 63o | 7.60% | T4o | 2.39% |
| 155 | J2o | 7.60% | 74o | 2.26% |
| 156 | 84o | 7.60% | 84o | 2.25% |
| 157 | T3o | 7.60% | T3o | 2.19% |
| 158 | 52o | 7.50% | 32o | 2.16% |
| 159 | T2o | 7.20% | T2o | 2.10% |
| 160 | 94o | 7.10% | 94o | 2.00% |
| 161 | 42o | 7.00% | 42o | 1.89% |
| 162 | 73o | 6.90% | 52o | 1.87% |
| 163 | 93o | 6.70% | 93o | 1.83% |
| 164 | 92o | 6.50% | 92o | 1.75% |
| 165 | 32o | 6.40% | 73o | 1.74% |
| 166 | 62o | 6.40% | 62o | 1.73% |
| 167 | 83o | 6.40% | 83o | 1.66% |
| 168 | 82o | 6.10% | 72o | 1.59% |
| 169 | 72o | 5.90% | 82o | 1.48% |
The data used here was derived from a free and handy source of online game history data, the game histories of the Internet Relay Chat (IRC) poker server. predating the the commercial poker web sites, the IRC free games included some serious players including Chris Ferguson (who happens to hold an advanced computer science degree)
Another real world starting hand Expected Value table can be found at Holdem Tight. Hi s “worst played” hand is 32s, noteably A2s does nearly as bad, ranked at 162. There’s a coincidental match of the point on his table, rank 43, where all hands below have loosing EVs and the point on my comparison graph where real world wins drop below the presdicted percentages.