Recently I started noticing I was entirely incorrect about how to approach the problem of what hands to raise with at "equilibrium" and many assumptions that I made have been wrong. Even so I am not convinced it's the best way to go about things since I do not know how to estimate the value of position and whether playing MORE hands or less is better entirely.
Yet, I have realized that the approach was wrong about determining which hand is "best" preflop. Previously if there was me and one other opponent I would estimate that you just take one divided by the number of players remaining to determine their average hand and anything above that range was best. Now I realize that is wrong. The chance that a top X% of hand is best is equal to (1-X)^# of other players in the pot. So top 5% hand is best 95% of the time vs a random hand. Vs 2 other opponents it is best (.95)^2 or .95*.95 or 90.25% of the time.
Now using this, we can begin to construct a chart that determines what hand range one should play with X opponents to give themselves a 50% chance of having the best hand.
| SB/BB | 50.00% |
| button | 29.28% |
| cutoff | 20.65% |
| hijack | 15.90% |
| lojack | 12.95% |
| UTG+2 | 10.90% |
| UTG+1 | 9.44% |
| UTG | 8.30% |
So compare that to the previous strategy and you will see that unfortunately that is MUCH tighter preflop.
So lets scrap the last strategy and construct a NEW fundamental strategy that gives us a 50% chance of the best hand.
Depending on if you end hands on flop, river, or preflop and how you adapt to other opponent's playing range, and number of players in the flop and how much implied odds, you could use the generic raising range of something that might look like this:
The SB: 22+, A7+, K7+, Q8+, J8+, T6+, 97+, 85+, 75+, A2s+, K2s+, Q3s+, J4s+, T6s+, 96s+, 86s+, 74s+, 63s+, 53s+
Button: 33+, A8+, K9+, QT+, JT, T9, A2s+, K4s+, Q7s+, J7s+, T7s+, 97s+, 86s+, 76s, 65s
Cutoff: 55+, AT+, KT+, QT+, A2s+, K7s+, Q9s+J9s+, T8s+, 98s
Hijack: 66+, AT+, KJ+, QJ, A4s+, K9s+Q9s+, J9s+, T9s
Lojack: 77+, AT+, KJ+, A8s+, K9s+, QTs+, JTs
UTG+ 2: 77+, AJ+, KQ, A8s+, KTs+, QTs+, JTs
UTG+ 1: 77+, AJ+, A9s+, KTs+, QTs+
1stAct: 88+, AJ+, ATs+, KTs+, QJs
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Now that is not entirely correct either. Afterall, we have basically come up with something not looking at equity vs given number of opponents. What we should do is determine that the hand has 50% equity vs X% of opponents or better, that is probably the next stage. However for now, we will continue constructing a strategy based upon this opening hand range.
If that is the range, we can assume opponent raising from a given position has that hand range. To have a hand with a 50% chance of being better than the range, we need one that is in the upper HALF of that range. So 3bet (reraise) with this range.
| SB/BB | 0.25 |
| button | 0.146415 |
| cutoff | 0.10325 |
| hijack | 0.0795 |
| lojack | 0.06475 |
| UTG+2 | 0.0545 |
| UTG+1 | 0.0472 |
| UTG | 0.0415 |
4 bet to keep up with blinds and prevent opponent from being able to 3bet us with 1/3 of this range.
| SB/BB | 0.1666667 |
| button | 0.09761 |
| cutoff | 0.0688333 |
| hijack | 0.053 |
| lojack | 0.0431667 |
| UTG+2 | 0.0363333 |
| UTG+1 | 0.0314667 |
| UTG | 0.0276667 |
This strategy will be standard 3x big blind and we will add one that gives us a 60% chance of being best for tight aggressive style with 4x bet, and 40% chance of being best for more of a loose aggressive exploitative style 2xBB bet.
Hand ranges to come, and the spreadsheet will be updated. I will let you know.
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