Friday, November 8, 2013

Probability you have best preflop hand

The game of hold em is complicated. Some hands are stronger in multiway pots where flushes and straights are more likely to be needed to win, other hands are stronger in heads up situations where ace high and any high pair has a very good chance of being best. Even so, some are better off choosing hands which won't run into kicker troubles and strong drawing hands, while others are more skilled with high cards. With that being said there are still ways to determine the best hand range and construct a rough estimate. What we are looking to do when playing a hand is determine what the probability of the hand being the best preflop rank. Nevermind that it might have another hand favored against it, poker is a dynamic game where against some ranges suited connectors play best, and against others, suited aces and kings play best.

But what we are after is
1)a hand range that either can come from behind, play in lots of pots looking to hit some sort of draw and find creative ways to pull equity out and bluff and use implied odds, but still has a 40% chance or better of being the best starting hand at the table.
2)A hand range that statistically has a 50% chance of being best or better. This is good for game theorists who balance their ranges and look to be very calculated.
3)A hand range that statistically has a 60% chance of being best. This is great for those who prefer to proceed aggressively. Since you are representing a tighter range of hands, opponents will have to give you respect and fold, or if they don't they will often run into a lot of situations where they pay you off. You can be very aggressive but still calculated with this approach
4)A hand range that statistically is best preflop 75% of the time in a given spot. With a powerhouse hand range like this, you don't have to really use much discretion at all and can play very aggressively.

The following data gives you the % chance of being best, then the number of players other than yourself left.
For those curious on the math, it is (1-% hand range you play)^number of players= probability hand is best. For example top 5% hand range and 4 players left to act is
1-5% or 1-.05=.95 .95^4 players left =~.8145 or 81.45% chance of being best preflop.

You can use this information when it folds to you, although keep in mind, it pays to be a bit tighter as the information that people have fold should actually change the odds of hand being good as the information of a fold provides enough information to adjust your assumptions slightly.


40% chance of best hand
8 77+, AJ+, KQ, A8s+, KTs+, QTs+,JTs (10.82%)
7 12.27% 77+,AJ+,KQ,A8s+,K9s+,QTs+,JTs,T8s+,98s,87s,76s,
6 14.16% 77+,AJ+,KQ,A2s+,K9s+,Q9s+,JTs,T8s+,98s,87s,76s
5 16.75% 77+.AJ+.kQ,Qj,JT,A2s+,K9s+,Q9s+,J9s+,T8s+,98s,87s,76s,
4 20.47% 77+,At+,KT+,QT+,JT+,A2s+,K9s+,Q9s+,J9s+,T8s+,98s,87s,76s,
3 26.32% 22+,A9+,KT+,QT+,JT+,A2s+,K6s+,Q8s+,J8s+,T7s+,97s,87s,76s,65s,54s
2 36.75% 22+,A9+,KT+,Q9+,J9+,T8+,98,87,76,A2s+,K2s+,Q7s+,J7s+,T6s+,96s,86s,75s+,64s+,53s+,43s
1 60% LOL Everything except like Q2-Q4,J or lower with 6 high or lower kicker, and a few really bad suited cards.

50% chance of having best hand
8 8.3 88+, AJ+,ATs+,KTs+,QJs
7 9.43 88+, AJ+, KQ, ATs+,KTs+,QJs,JTs
6 10.91 66+, AJ+, KQ, ATs+,KTs+,QTs+,JTs,T9s
5 12.95 66+, AJ+, KQ, ATs+,KTs+,QTs+,J9s+,T8s+,98s,87s,76s,65s,54s
4 15.91 66+, AJ+, KQ,QJ,JT, A8s+,KTs+,QTs+,J9s+,T8s+,97s+,87s,76s,65s,54s
3 20.63 55+, AT+,KT+,QT+,JT,A7s+,KTs+,Q9s+,J9s+,T8s+,97s+,87s,76s,65s,54s
2 29.29 22+, A9+,KT+,QT+,JT,T9,98,87,76,65,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,87s,76s,65s,54s
1 50 Just a bunch of hands. Any king any ace, gap connectors, suited 2 and 3 gappers, etc

60% chance of having best hand
8 6.19 99+,AQ+,AJs+,KQs,QJs,JTs,
7 7.04 88+,AQ+,AJs+,KQs,QJs,JTs, T9s,98s
6 8.16 88+,AJ+,AJs+,KQs,QJs,JTs,T9s,
5 9.71 88+,AJ+,KQ,A9s+,KJs+,QJs,JTs,T9s
4 11.99 88+,AJ+,KQ,A2s+,KJs+,QJs,JTs,T9s,98s
3 15.66 77+,AJ+,KQ,QJ,JT,T9,A2s+,KTs+,QTs,JTs,T9s,98s
2 22.54 22+,AT+,KJ+,QJ,JT,T9,A2s+,K2s+,QTs,JTs,T9s,98s
1 40 22+, A2+, K9+,Q9+,J9+,T9,98,87,K2s+,Q8s+,J8s+,T8s+,97s+,86s+,75s,64s,54s,43s

75% chance of having best hand
8 3.53 JJ+,AK,AJs+
7 4.03 JJ+,AQ+,AJs+
6 4.68 JJ+,AQ+,AJs+
5 5.59 TT+,AQ+,AJs+,KQs
4 6.94 99+,AJ+, ATs+,KQs
3 9.14 77+,AT+,A9s+,KQs,
2 13.40 66+,At+,KQ,A2s,KQs,QJs,JTs,T9s
1 25 22+,A8+,KT+,QT+,JT+,A2s+,K7s+,Q9s+,J9s+,T8s+,98s,87s,76s

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