So in the post titled "How Patient Can You Be?" We listed a table that listed the hand range in which you had around a 50% chance or better of seeing a hand in that particular range given X # of hands.
The problem with that list is it is a "one size fits all" list. In other words, AK is MUCH MUCH stronger when dealt to the small blind and it folds around then when you are first to act because the probability of it being the best hand with only one player left is so much greater. As a result, our strategy of patience should reflect this and we should adapt by position and players left.
Now what I have done is I looked at hand ranges if everyone folds and there are X players left and determined the odds that the particular range is best for each of 8 positions. I added 1 of them twice because you will be dealt a hand in the big blind as well. Both small blind and big blind have 1 opponent. I then averaged them. As a result I have the makings of a number that will lead to a strategy that can adjust by position. The number tells you the best average expected probability that your hand is best given such a hand range that you expect to see 50% of the time or more with X hands left.
Please note: The following range does NOT have anything to do with your actual chance of WINNING the hand, but is instead based upon the odds of a particular hand ranking being better than opponents, by percentile ranking. i.e. something in the "top 5% of hands" while not easily definable is better than something "outside of it" whatever that ranking actual is depends upon number of opponents, calling ranges of opponents and other variables. While A8s might be good against opponents who call with suited connectors and king high cards, it's not as good for those who really value 88+, and A9o+. The opponent actually will change WHAT hand should go in the rankings AND the odds of that hand winning IF called as well as the odds that it gets called.
The strategy is only meant as a means for constructing a robust, profitable strategy.
Hands left | Probability hand range you wait for IS CURRENTLY the best hand.
1 N/A
2 0.173177083
3 0.341631187
4 0.4598062
5 0.544378725
6 0.606950086
7 0.654804828
8 0.692465699
9 0.722821208
10 0.747782507
11 0.768655592
12 0.786361415
13 0.801564513
14 0.81475818
15 0.826313524
16 0.836517568
17 0.845592395
18 0.853715929
19 0.861029433
20 0.867648205
25 0.893115257
30 0.910371515
35 0.922834139
40 0.93225555
50 0.945553277
60 0.954488125
65 0.95793944
70 0.960904321
140 0.980323983
Note: The hands between 20 and 25 and 30 and 35 and many others were not included as the actual hands you play are effectively the same, and it seemed redundent. There may turn out to be minor differences if I really break them all down but it is close enough to ignore in my opinion.
-
Now, the next step will be reverse engineering this. Basically, if we know we can wait for situations that arise where we have a 85% chance of having the best preflop hand on average we want to FIND what hand range given X players left satisfy that...
This way, we can adjust for the known information and the changing variables that may allow us to play 99 on the button, as it will be more favorable than TT under the gun. By finding the hand strength equivilent (ranked by probability hand is strongest hand dealt given position and information) of the hand range we can wait for by position, we correctly adapt and will find more accurate decision making.
Once this is done, this is not even close to being the "end result". We still have to convert a baseline strategy FROM this information based upon what our "push range" all in equivilent is and thus our 4bet, 3bet (as a percentage of opponent's raising range), and raising range that allows for a balanced 4bet range (1/3rd of raising range to 4bet often enough to not be exploitable).
Based upon that, we still may want to initially open up with a wider or tighter range depending upon likelihood to be called and/or raised.
Ultimately, I still feel POSTFLOP is the best opportunity to get your money in good, but even that will depend on the amount of flops you get to see as a result of raising strategy. So this work is still needed even to determine that, and the probability of getting all in action after the flop is probably not nearly as good.
Either way, there is a stage late in a tournament where one should merely be trying to prolong survival rather than aggressively accumulate chips at risk of elimination, as ironically that will likely give you the best chance of winning through gradual accumulation and minimal risk of going broke, as there is a LIMIT to how many chips you can win over how much time you can win them. Having a faster win rate per rotation will only finish the tournament more quickly, not result in more chips or a better chance of winning. At any rate, survival also will drastically increase the payout as you move up the money, and get you in good position to pick up the aggression midway through the final table when your image is rock tight and the blinds are close to as high as they ever will be. The opportunity cost of missing such steals is not worth the bennefit of a more reckless strategy that eliminates you more than 50% of the time.
No comments:
Post a Comment