Poker mathematics tutorial 1.2: a very tight strategy and rake.

The rake you will pay while playing very tight

In this artikel we will discuss a very tight strategy and how much money you will pay to the pokersite. The rake you pay will make a large difference in the outcome. In general you pay 5%  of the pot at showdown in rake to the house. We will show how much  rake that is by taking a tight strategy and making an excel calculation.

A very tight preflop all in strategy

The idea is to play so tight that you can basically move all in preflop and be profitable from that strategy because of those drunken chinese players calling all ins with J5s just because they like to play suited hands. This is the all-in handselection i am talking about:

AA,KK,QQ,JJ,TT,

AKs, AQs

AKo

Which is the top 3,77% of hands.

Lets analyse the hands from a basic 1vs1  all-in point of view.

AA wins 85% of the time vs all hands

KK wins on average 82% vs all hands except AA. KK vs AA wins only 19% of the time, however the chances of facing an opponent with AA are quite low. The amount of starting hands are: (52*51)/2=1326. There are only 6 ways to deal AA ((4*3)/2), this gives a chance of 6/1326= 0,45% or 1 out of 221.

Other general examples:

KKvs TT = 81%

TTvs AKo=56%

AKo vs AQo=74%

Ako vs AJs= 70%

TT vs 98s= 81%

TT vs KQs= 54%

AQs vs QJs= 70%

AKo vs QJs= 61%

As you can see no matter what your opponent is having, you dominate him with a higher kicker (AK vs KQ, or AQ vs QJ ) or a pocket pair which usually wins against drawing hands as well as lower pairs.

Risk of facing a higher hand

The only case you are losing is if your opponent has a higher pair. But as we allready calculated, the chance of having a certain pair is only 1 out of 221. If you play TT the chances of another playing having a higher pocket pair(AA,KK,QQ,JJ) is approximately: 4/221.  So lets say there are 9 other players on the table, in that case the chance is only 1-(1-4/221)^9 = 15,15% that somebody else is having a higher pair then you.

The majority of the time they will call you with hands they consider to be good. For instance AK, AQ, AJ, ATs, KQ, KJs QJs, 88, 99 (top8% of hands). These hands are being dealth in 106 ways, while AA,KK,QQ and JJ can only be dealth in 24 ways. As you can see the loose players will give you positive “expectancy” +-76% of the time.  I used equilab to calculate that the top 3,77% will have a winrate of 60,22% against the top 8% call.

Running calculations in excel

So now we figured this out we can run a very opportunistic monte- carlo analysis in excel. Lets say you start with 10 buy ins (1buy in to get seated on one table with 100bb) and you get into all- in situations 10 000 times. What will happen to your account?

super tight strategy zonder onkosten

You went from 10 buy ins to 2187 buy ins. Wow i am going to pre-order a ferrari!!

Please don’t fall into this trap

You have to play 265200 hands on 1cent/2cent tables to win 2187*100*2ct=4374 dollar, because higher blinds wil not give you this winrate… Besides that the costs of playing poker where not taken into account.

There are some mistakes in this calculation. One of them is the fact that you will lose blinds (approximately -1,5 BB per 10 hands). You will only get AA-TT Ak, AQs 3,77% of the time, so for 100 all-ins you will need to play 2652 hands. You will lose (2652/10)*1,5=397 bigblinds, which will be trown away waiting for those good hands, this is approximately 4 buy ins each 100 all ins.

And another problem is rake during these games. Rake is the profit of the house, after you win a pot you only get 95% of the pot or something like that, depending on the site you play on.  So instead of winning 1 buy in from your opponent, the 2 buy ins in the pot will be reduced to: 2*0,95= 1,9 buy ins, which means you win only 0,9 times your buy in, while you lose 1 buy in if you lose the hand.

Another problem is that your all-in wil not be called a lot of times, resulting in gaining only the blinds.

Let’s say your opponents call your all-in with approximately the top 8% of hands:

88+, ATs+, KJs+, QJs+ AQo+,KQo.

Yes, i know that is quite loose, but on low levels it happens quite often that players call with even far worse hands then these.

In this case at a table of 10 players your all-in will be called  1-(1-0,08)^9=0,5278, or +- 53% of the time. The other 47% of the time you will gain 1,5 bigblind (which is an assumption).

Running the calculations inclusive the rake paid

So lets rerun our monte carlo analysis. This case we will first determine if your all in is called, or folded, inwhich case you only can win the blinds (1,5bb). In case you win your all-in you will gain 0,9 buy ins, because 5% of the pot of 2 buy ins wil go to the house in earnings. Besides all of this we asume a stable loss of 1,5bb per 10 hands. In this case for 100 all- ins we expect +-397 big blinds being thrown away, or aproximately -0,04 buy in for each all-in.

super tight strategy met rake bb loss en kans om niet gecalled te worden

 

As you can see the very tight strategy is actually paying off, however the basic costs of playing the game reduced the profit by 2187 – 478= 1709 buy ins per 10 000 all ins, or 3418 dollar in rake. If you would have played these 265200 hands you would have gained 468*2=936 dollar given the fact that this system only works at the worst tables.

If you can find these conditions at the worst of tables you will be having a winrate of 18bb/ 100 hands though, which is insane if you take into account that 5bb/100 hands is considered to be the highest amount for professionals. However 18bb/ 100 is considered to be mediocre at 1cent/2cent tables. A true professional wil make 40bb/100 hands on those bad tables by playing more hands : 20-28% depending on which table size (i remember a pro showing his statistics on this).

Why the simple tight all in strategy won’t work

I want to end this blogpost by showing what will happen with your account if you play against players that aren’t drunk and using a tight handselection to call your all in with (5%, instead of the 8% of the drunken bastards, you will have 55,5% winrate instead of the former 60,22%, however that might be not enough because of all the costs).

poker hands 3,77% vs 5%

This shows that a winrate of a strategy can change so rapidly that you should always keep in mind that a simple strategy will lose very hard against normal players.

The next tutorial will show a very easy way to estimate your preflop chances, regardless of which hands you are holding.  Use the following link:

poker tutorial 1.3 Preflop chances

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