Simulation #3
- Independent Chip Modeling Part 1: Derivation and Sample Analysis
- Simulation #1
- Simulation #2
- Simulation #3
- Simulation #4
- Independent Chip Modeling Part 2: Positive Chip EV Doesn’t Mean Positive Monetary EV
- Independent Chip Modeling Part 3: Pushing Decisions from the Small Blind on the STT Bubble As A Function Of Stack Size
- Independent Chip Modeling Part 4: Beyond ICM
- ICM Calculator
Simulation #3
| Total Big Blinds In Tournament | Big Blinds in P1’s Stack | Big Blinds in P2’s Stack | Simulated P(P1 Wins) | Expected P(Player 1 Wins) | Difference Between Theory and Simulation | ||
| 4 | 2 | 1 | 0.49991 | ± | 0.00016 | 0.50000 | 0.00009 |
| 6 | 2 | 2 | 0.33350 | ± | 0.00015 | 0.33333 | -0.00017 |
| 6 | 3 | 2 | 0.49992 | ± | 0.00016 | 0.50000 | 0.00008 |
| 6 | 4 | 1 | 0.66656 | ± | 0.00015 | 0.66667 | 0.00011 |
| 10 | 4 | 3 | 0.39994 | ± | 0.00015 | 0.40000 | 0.00006 |
| 10 | 4 | 4 | 0.40007 | ± | 0.00015 | 0.40000 | -0.00007 |
| 10 | 5 | 3 | 0.50003 | ± | 0.00016 | 0.50000 | -0.00003 |
| 10 | 5 | 4 | 0.49995 | ± | 0.00016 | 0.50000 | 0.00005 |
| 10 | 6 | 2 | 0.60010 | ± | 0.00015 | 0.60000 | -0.00010 |
| 10 | 6 | 3 | 0.59998 | ± | 0.00015 | 0.60000 | 0.00002 |
| 10 | 7 | 2 | 0.70002 | ± | 0.00014 | 0.70000 | -0.00002 |
| 10 | 8 | 1 | 0.79978 | ± | 0.00013 | 0.80000 | 0.00022 |
| 14 | 5 | 5 | 0.35719 | ± | 0.00015 | 0.35714 | -0.00005 |
| 14 | 6 | 4 | 0.42863 | ± | 0.00016 | 0.42857 | -0.00006 |
| 14 | 6 | 5 | 0.42847 | ± | 0.00016 | 0.42857 | 0.00010 |
| 14 | 6 | 6 | 0.42881 | ± | 0.00016 | 0.42857 | -0.00024 |
| 14 | 7 | 4 | 0.49995 | ± | 0.00016 | 0.50000 | 0.00005 |
| 14 | 7 | 5 | 0.49999 | ± | 0.00016 | 0.50000 | 0.00001 |
| 14 | 7 | 6 | 0.49977 | ± | 0.00016 | 0.50000 | 0.00023 |
| 14 | 8 | 3 | 0.57132 | ± | 0.00016 | 0.57143 | 0.00011 |
| 14 | 8 | 4 | 0.57153 | ± | 0.00016 | 0.57143 | -0.00010 |
| 14 | 8 | 5 | 0.57164 | ± | 0.00016 | 0.57143 | -0.00021 |
| 14 | 9 | 3 | 0.64276 | ± | 0.00015 | 0.64286 | 0.00010 |
| 14 | 9 | 4 | 0.64322 | ± | 0.00015 | 0.64286 | -0.00036 |
| 14 | 10 | 2 | 0.71415 | ± | 0.00014 | 0.71429 | 0.00014 |
| 14 | 10 | 3 | 0.71436 | ± | 0.00014 | 0.71429 | -0.00007 |
| 14 | 11 | 2 | 0.78566 | ± | 0.00013 | 0.78571 | 0.00005 |
| 14 | 12 | 1 | 0.85701 | ± | 0.00011 | 0.85714 | 0.00013 |
| 20 | 7 | 7 | 0.35020 | ± | 0.00015 | 0.35000 | -0.00020 |
| 20 | 8 | 6 | 0.40011 | ± | 0.00015 | 0.40000 | -0.00011 |
| 20 | 8 | 7 | 0.39986 | ± | 0.00015 | 0.40000 | 0.00014 |
| 20 | 8 | 8 | 0.39992 | ± | 0.00015 | 0.40000 | 0.00008 |
| 20 | 9 | 6 | 0.45005 | ± | 0.00016 | 0.45000 | -0.00005 |
| 20 | 9 | 7 | 0.45011 | ± | 0.00016 | 0.45000 | -0.00011 |
| 20 | 9 | 8 | 0.44982 | ± | 0.00016 | 0.45000 | 0.00018 |
| 20 | 9 | 9 | 0.44991 | ± | 0.00016 | 0.45000 | 0.00009 |
| 20 | 10 | 5 | 0.50012 | ± | 0.00016 | 0.50000 | -0.00012 |
| 20 | 10 | 6 | 0.49983 | ± | 0.00016 | 0.50000 | 0.00017 |
| 20 | 10 | 7 | 0.49990 | ± | 0.00016 | 0.50000 | 0.00010 |
| 20 | 10 | 8 | 0.49987 | ± | 0.00016 | 0.50000 | 0.00013 |
| 20 | 10 | 9 | 0.50019 | ± | 0.00016 | 0.50000 | -0.00019 |
| 20 | 11 | 5 | 0.54999 | ± | 0.00016 | 0.55000 | 0.00001 |
| 20 | 11 | 6 | 0.55003 | ± | 0.00016 | 0.55000 | -0.00003 |
| 20 | 11 | 7 | 0.55006 | ± | 0.00016 | 0.55000 | -0.00006 |
| 20 | 11 | 8 | 0.55019 | ± | 0.00016 | 0.55000 | -0.00019 |
| 20 | 12 | 4 | 0.60004 | ± | 0.00015 | 0.60000 | -0.00004 |
| 20 | 12 | 5 | 0.59995 | ± | 0.00015 | 0.60000 | 0.00005 |
| 20 | 12 | 6 | 0.60006 | ± | 0.00015 | 0.60000 | -0.00006 |
| 20 | 12 | 7 | 0.59974 | ± | 0.00015 | 0.60000 | 0.00026 |
| 20 | 13 | 4 | 0.65003 | ± | 0.00015 | 0.65000 | -0.00003 |
| 20 | 13 | 5 | 0.64987 | ± | 0.00015 | 0.65000 | 0.00013 |
| 20 | 13 | 6 | 0.65005 | ± | 0.00015 | 0.65000 | -0.00005 |
| 20 | 14 | 3 | 0.70008 | ± | 0.00014 | 0.70000 | -0.00008 |
| 20 | 14 | 4 | 0.70011 | ± | 0.00014 | 0.70000 | -0.00011 |
| 20 | 14 | 5 | 0.69971 | ± | 0.00014 | 0.70000 | 0.00029 |
| 20 | 15 | 3 | 0.75035 | ± | 0.00014 | 0.75000 | -0.00035 |
| 20 | 15 | 4 | 0.74989 | ± | 0.00014 | 0.75000 | 0.00011 |
| 20 | 16 | 2 | 0.80003 | ± | 0.00013 | 0.80000 | -0.00003 |
| 20 | 16 | 3 | 0.79983 | ± | 0.00013 | 0.80000 | 0.00017 |
| 20 | 17 | 2 | 0.85017 | ± | 0.00011 | 0.85000 | -0.00017 |
| 20 | 18 | 1 | 0.90008 | ± | 0.00009 | 0.90000 | -0.00008 |
| 30 | 10 | 10 | 0.33305 | ± | 0.00015 | 0.33333 | 0.00028 |
| 30 | 11 | 10 | 0.36661 | ± | 0.00015 | 0.36667 | 0.00006 |
| 30 | 11 | 11 | 0.36645 | ± | 0.00015 | 0.36667 | 0.00022 |
| 30 | 12 | 9 | 0.39994 | ± | 0.00015 | 0.40000 | 0.00006 |
| 30 | 12 | 10 | 0.40013 | ± | 0.00015 | 0.40000 | -0.00013 |
| 30 | 12 | 11 | 0.40001 | ± | 0.00015 | 0.40000 | -0.00001 |
| 30 | 12 | 12 | 0.39997 | ± | 0.00015 | 0.40000 | 0.00003 |
| 30 | 13 | 9 | 0.43322 | ± | 0.00016 | 0.43333 | 0.00011 |
| 30 | 13 | 10 | 0.43340 | ± | 0.00016 | 0.43333 | -0.00007 |
| 30 | 13 | 11 | 0.43321 | ± | 0.00016 | 0.43333 | 0.00012 |
| 30 | 13 | 12 | 0.43325 | ± | 0.00016 | 0.43333 | 0.00008 |
| 30 | 13 | 13 | 0.43311 | ± | 0.00016 | 0.43333 | 0.00022 |
| 30 | 14 | 8 | 0.46664 | ± | 0.00016 | 0.46667 | 0.00003 |
| 30 | 14 | 9 | 0.46659 | ± | 0.00016 | 0.46667 | 0.00008 |
| 30 | 14 | 10 | 0.46654 | ± | 0.00016 | 0.46667 | 0.00013 |
| 30 | 14 | 11 | 0.46673 | ± | 0.00016 | 0.46667 | -0.00006 |
| 30 | 14 | 12 | 0.46660 | ± | 0.00016 | 0.46667 | 0.00007 |
| 30 | 14 | 13 | 0.46655 | ± | 0.00016 | 0.46667 | 0.00012 |
| 30 | 14 | 14 | 0.46655 | ± | 0.00016 | 0.46667 | 0.00012 |
| 30 | 15 | 8 | 0.50012 | ± | 0.00016 | 0.50000 | -0.00012 |
| 30 | 15 | 9 | 0.49995 | ± | 0.00016 | 0.50000 | 0.00005 |
| 30 | 15 | 10 | 0.50010 | ± | 0.00016 | 0.50000 | -0.00010 |
| 30 | 15 | 11 | 0.49993 | ± | 0.00016 | 0.50000 | 0.00007 |
| 30 | 15 | 12 | 0.50038 | ± | 0.00016 | 0.50000 | -0.00038 |
| 30 | 15 | 13 | 0.49980 | ± | 0.00016 | 0.50000 | 0.00020 |
| 30 | 15 | 14 | 0.50030 | ± | 0.00016 | 0.50000 | -0.00030 |
| 30 | 16 | 7 | 0.53323 | ± | 0.00016 | 0.53333 | 0.00010 |
| 30 | 16 | 8 | 0.53343 | ± | 0.00016 | 0.53333 | -0.00010 |
| 30 | 16 | 9 | 0.53340 | ± | 0.00016 | 0.53333 | -0.00007 |
| 30 | 16 | 10 | 0.53305 | ± | 0.00016 | 0.53333 | 0.00028 |
| 30 | 16 | 11 | 0.53323 | ± | 0.00016 | 0.53333 | 0.00010 |
| 30 | 16 | 12 | 0.53353 | ± | 0.00016 | 0.53333 | -0.00020 |
| 30 | 16 | 13 | 0.53350 | ± | 0.00016 | 0.53333 | -0.00017 |
| 30 | 17 | 7 | 0.56668 | ± | 0.00016 | 0.56667 | -0.00001 |
| 30 | 17 | 8 | 0.56676 | ± | 0.00016 | 0.56667 | -0.00009 |
| 30 | 17 | 9 | 0.56644 | ± | 0.00016 | 0.56667 | 0.00023 |
| 30 | 17 | 10 | 0.56707 | ± | 0.00016 | 0.56667 | -0.00040 |
| 30 | 17 | 11 | 0.56671 | ± | 0.00016 | 0.56667 | -0.00004 |
| 30 | 17 | 12 | 0.56647 | ± | 0.00016 | 0.56667 | 0.00020 |
| 30 | 18 | 6 | 0.59968 | ± | 0.00015 | 0.60000 | 0.00032 |
| 30 | 18 | 7 | 0.59963 | ± | 0.00015 | 0.60000 | 0.00037 |
| 30 | 18 | 8 | 0.59998 | ± | 0.00015 | 0.60000 | 0.00002 |
| 30 | 18 | 9 | 0.60029 | ± | 0.00015 | 0.60000 | -0.00029 |
| 30 | 18 | 10 | 0.59979 | ± | 0.00015 | 0.60000 | 0.00021 |
| 30 | 18 | 11 | 0.60018 | ± | 0.00015 | 0.60000 | -0.00018 |
| 30 | 19 | 6 | 0.63331 | ± | 0.00015 | 0.63333 | 0.00002 |
| 30 | 19 | 7 | 0.63345 | ± | 0.00015 | 0.63333 | -0.00012 |
| 30 | 19 | 8 | 0.63362 | ± | 0.00015 | 0.63333 | -0.00029 |
| 30 | 19 | 9 | 0.63363 | ± | 0.00015 | 0.63333 | -0.00030 |
| 30 | 19 | 10 | 0.63343 | ± | 0.00015 | 0.63333 | -0.00010 |
| 30 | 20 | 5 | 0.66650 | ± | 0.00015 | 0.66667 | 0.00017 |
| 30 | 20 | 6 | 0.66683 | ± | 0.00015 | 0.66667 | -0.00016 |
| 30 | 20 | 7 | 0.66684 | ± | 0.00015 | 0.66667 | -0.00017 |
| 30 | 20 | 8 | 0.66651 | ± | 0.00015 | 0.66667 | 0.00016 |
| 30 | 20 | 9 | 0.66686 | ± | 0.00015 | 0.66667 | -0.00019 |
| 30 | 21 | 5 | 0.70003 | ± | 0.00014 | 0.70000 | -0.00003 |
| 30 | 21 | 6 | 0.69993 | ± | 0.00014 | 0.70000 | 0.00007 |
| 30 | 21 | 7 | 0.69986 | ± | 0.00014 | 0.70000 | 0.00014 |
| 30 | 21 | 8 | 0.70012 | ± | 0.00014 | 0.70000 | -0.00012 |
| 30 | 22 | 4 | 0.73356 | ± | 0.00014 | 0.73333 | -0.00023 |
| 30 | 22 | 5 | 0.73333 | ± | 0.00014 | 0.73333 | 0.00000 |
| 30 | 22 | 6 | 0.73338 | ± | 0.00014 | 0.73333 | -0.00005 |
| 30 | 22 | 7 | 0.73362 | ± | 0.00014 | 0.73333 | -0.00029 |
| 30 | 23 | 4 | 0.76649 | ± | 0.00013 | 0.76667 | 0.00018 |
| 30 | 23 | 5 | 0.76660 | ± | 0.00013 | 0.76667 | 0.00007 |
| 30 | 23 | 6 | 0.76638 | ± | 0.00013 | 0.76667 | 0.00029 |
| 30 | 24 | 3 | 0.79994 | ± | 0.00013 | 0.80000 | 0.00006 |
| 30 | 24 | 4 | 0.79996 | ± | 0.00013 | 0.80000 | 0.00004 |
| 30 | 24 | 5 | 0.79997 | ± | 0.00013 | 0.80000 | 0.00003 |
| 30 | 25 | 3 | 0.83336 | ± | 0.00012 | 0.83333 | -0.00003 |
| 30 | 25 | 4 | 0.83312 | ± | 0.00012 | 0.83333 | 0.00021 |
| 30 | 26 | 2 | 0.86662 | ± | 0.00011 | 0.86667 | 0.00005 |
| 30 | 26 | 3 | 0.86664 | ± | 0.00011 | 0.86667 | 0.00003 |
| 30 | 27 | 2 | 0.90003 | ± | 0.00009 | 0.90000 | -0.00003 |
| 30 | 28 | 1 | 0.93343 | ± | 0.00008 | 0.93333 | -0.00010 |
| 50 | 17 | 17 | 0.33993 | ± | 0.00015 | 0.34000 | 0.00007 |
| 50 | 18 | 16 | 0.36012 | ± | 0.00015 | 0.36000 | -0.00012 |
| 50 | 18 | 17 | 0.35994 | ± | 0.00015 | 0.36000 | 0.00006 |
| 50 | 18 | 18 | 0.35991 | ± | 0.00015 | 0.36000 | 0.00009 |
| 50 | 19 | 16 | 0.38003 | ± | 0.00015 | 0.38000 | -0.00003 |
| 50 | 19 | 17 | 0.37990 | ± | 0.00015 | 0.38000 | 0.00010 |
| 50 | 19 | 18 | 0.37990 | ± | 0.00015 | 0.38000 | 0.00010 |
| 50 | 19 | 19 | 0.37988 | ± | 0.00015 | 0.38000 | 0.00012 |
| 50 | 20 | 15 | 0.40018 | ± | 0.00015 | 0.40000 | -0.00018 |
| 50 | 20 | 16 | 0.40012 | ± | 0.00015 | 0.40000 | -0.00012 |
| 50 | 20 | 17 | 0.40012 | ± | 0.00015 | 0.40000 | -0.00012 |
| 50 | 20 | 18 | 0.40008 | ± | 0.00015 | 0.40000 | -0.00008 |
| 50 | 20 | 19 | 0.39984 | ± | 0.00015 | 0.40000 | 0.00016 |
| 50 | 20 | 20 | 0.40023 | ± | 0.00015 | 0.40000 | -0.00023 |
| 50 | 21 | 15 | 0.41997 | ± | 0.00016 | 0.42000 | 0.00003 |
| 50 | 21 | 16 | 0.42004 | ± | 0.00016 | 0.42000 | -0.00004 |
| 50 | 21 | 17 | 0.41986 | ± | 0.00016 | 0.42000 | 0.00014 |
| 50 | 21 | 18 | 0.41982 | ± | 0.00016 | 0.42000 | 0.00018 |
| 50 | 21 | 19 | 0.41993 | ± | 0.00016 | 0.42000 | 0.00007 |
| 50 | 21 | 20 | 0.41996 | ± | 0.00016 | 0.42000 | 0.00004 |
| 50 | 21 | 21 | 0.41999 | ± | 0.00016 | 0.42000 | 0.00001 |
| 50 | 22 | 14 | 0.44008 | ± | 0.00016 | 0.44000 | -0.00008 |
| 50 | 22 | 15 | 0.43990 | ± | 0.00016 | 0.44000 | 0.00010 |
| 50 | 22 | 16 | 0.43991 | ± | 0.00016 | 0.44000 | 0.00009 |
| 50 | 22 | 17 | 0.44032 | ± | 0.00016 | 0.44000 | -0.00032 |
| 50 | 22 | 18 | 0.44011 | ± | 0.00016 | 0.44000 | -0.00011 |
| 50 | 22 | 19 | 0.44001 | ± | 0.00016 | 0.44000 | -0.00001 |
| 50 | 22 | 20 | 0.44007 | ± | 0.00016 | 0.44000 | -0.00007 |
| 50 | 22 | 21 | 0.43981 | ± | 0.00016 | 0.44000 | 0.00019 |
| 50 | 22 | 22 | 0.44013 | ± | 0.00016 | 0.44000 | -0.00013 |
| 50 | 23 | 14 | 0.46008 | ± | 0.00016 | 0.46000 | -0.00008 |
| 50 | 23 | 15 | 0.46011 | ± | 0.00016 | 0.46000 | -0.00011 |
| 50 | 23 | 16 | 0.45983 | ± | 0.00016 | 0.46000 | 0.00017 |
| 50 | 23 | 17 | 0.46016 | ± | 0.00016 | 0.46000 | -0.00016 |
| 50 | 23 | 18 | 0.45995 | ± | 0.00016 | 0.46000 | 0.00005 |
| 50 | 23 | 19 | 0.46007 | ± | 0.00016 | 0.46000 | -0.00007 |
| 50 | 23 | 20 | 0.46012 | ± | 0.00016 | 0.46000 | -0.00012 |
| 50 | 23 | 21 | 0.46002 | ± | 0.00016 | 0.46000 | -0.00002 |
| 50 | 23 | 22 | 0.45992 | ± | 0.00016 | 0.46000 | 0.00008 |
| 50 | 23 | 23 | 0.46022 | ± | 0.00016 | 0.46000 | -0.00022 |
| 50 | 24 | 13 | 0.48006 | ± | 0.00016 | 0.48000 | -0.00006 |
| 50 | 24 | 14 | 0.47997 | ± | 0.00016 | 0.48000 | 0.00003 |
| 50 | 24 | 15 | 0.47980 | ± | 0.00016 | 0.48000 | 0.00020 |
| 50 | 24 | 16 | 0.47975 | ± | 0.00016 | 0.48000 | 0.00025 |
| 50 | 24 | 17 | 0.48019 | ± | 0.00016 | 0.48000 | -0.00019 |
| 50 | 24 | 18 | 0.47997 | ± | 0.00016 | 0.48000 | 0.00003 |
| 50 | 24 | 19 | 0.48009 | ± | 0.00016 | 0.48000 | -0.00009 |
| 50 | 24 | 20 | 0.48003 | ± | 0.00016 | 0.48000 | -0.00003 |
| 50 | 24 | 21 | 0.47968 | ± | 0.00016 | 0.48000 | 0.00032 |
| 50 | 24 | 22 | 0.48003 | ± | 0.00016 | 0.48000 | -0.00003 |
| 50 | 24 | 23 | 0.47992 | ± | 0.00016 | 0.48000 | 0.00008 |
| 50 | 24 | 24 | 0.48003 | ± | 0.00016 | 0.48000 | -0.00003 |
| 50 | 25 | 13 | 0.50006 | ± | 0.00016 | 0.50000 | -0.00006 |
| 50 | 25 | 14 | 0.50019 | ± | 0.00016 | 0.50000 | -0.00019 |
| 50 | 25 | 15 | 0.49994 | ± | 0.00016 | 0.50000 | 0.00006 |
| 50 | 25 | 16 | 0.49986 | ± | 0.00016 | 0.50000 | 0.00014 |
| 50 | 25 | 17 | 0.50021 | ± | 0.00016 | 0.50000 | -0.00021 |
| 50 | 25 | 18 | 0.50009 | ± | 0.00016 | 0.50000 | -0.00009 |
| 50 | 25 | 19 | 0.49990 | ± | 0.00016 | 0.50000 | 0.00010 |
| 50 | 25 | 20 | 0.50011 | ± | 0.00016 | 0.50000 | -0.00011 |
| 50 | 25 | 21 | 0.49999 | ± | 0.00016 | 0.50000 | 0.00001 |
| 50 | 25 | 22 | 0.50020 | ± | 0.00016 | 0.50000 | -0.00020 |
| 50 | 25 | 23 | 0.49970 | ± | 0.00016 | 0.50000 | 0.00030 |
| 50 | 25 | 24 | |||||

