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Statistics: VPIP and PFR

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Many poker players nowadays make use of so-called poker-software like Poker Tracker, Hold'em Manager and Poker Office. These nifty little programs are very handy because you can project your opponents statistics via a HUD on the poker table.
The most important statistics are: VPIP (Voluntary Put in Pot), which shows you how many hands someone has played, and PFR (Pre-flop raise), which shows you how many hands players raise pre-flop.

Both statistics are shown as a percentage of the total possible hands. If a player for instance shows VPIP/PFR 20/10, then he plays 20% of all hands and raises 10% of those.

Now, it's fine to know these percentages, but what you want is to calculate your opponents handrange on the basis of his pre-flop actions.
For instance, if you are the big blind and the player on the button (who has VPIP/PFR 20/10) raises. This player raises 10% of his hands pre-flop, which is an average for all positions, you can assume that this player will raise a bit more on the button let's say 12.5%.

But what exactly does this 12.5% mean? The hand range below corresponds with a PFR of 12.5%:

(77+,A9s+,KTs+,QTs+,JTs,ATo+,KJo+)

It is of course not etched in stone that your opponent will have this range, maybe he will not raise
KJo, but will raise 66, but it will give you a fair indication of his hand range.
Listed below is an overview of the different percentages with the matching hand ranges.

1% KK+
2.5% QQ+,AK
5% 99+, AQ+
7.5% 88+, ATs+, AQ+, KTs+, QJs
10% 88+,A9s+,KTs+,QTs+,AJo+,KQo
12.5% 77+,A9s+,KTs+,QTs+,JTs,ATo+,KJo+
15% 77+,A7s+,K9s+,QTs+,JTs,ATo+,KTo+,Qjo
20% 66+,A4s+,K8s+,Q9s+,J9s+,T9s,A9o+,KTo+,QTo+,JTo
25% 66+,A2s+,K6s+,Q8s+,J8s+,T8s+,A7o+,K9o+,QTo+,JTo
30% 55+,A2s+,K5s+,Q7s+,J8s+,T8s+,98s,A7o+,A5o,K9o+,Q9o+,J9o+,T9o

You can also take a hand range and then calculate the percentage. Take for instance the
following hand range:

(22+, AJ+,KQs)

Let's say that a player raises these hands pre-flop, what would be his PFR percentage?

In total there are (52*51)/2=1326 unique starting hands. Of each pocket pair there are 6 different combinations, of a non-paired off suit hand 16 and of a non-paired suited hand 4.

In the above shown hand range, there are 13 pocket pairs, 3 non-paired off suit hands and 1 non-pair suited hand. This makes 13*6 + 3*16 + 4 = 130 in total or 130/1324=9.8% of the total.
The PFR% of this player would be 9.8%.

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