What Do You Want to Know?

We have to decide what statistical information we're going to extract. There are many pieces of information one can get out a set of actual poker hands. In the last article I wrote, Getting Off to a Good Start, I said that in my simulation I gave 6 points for each win, and 1 point for each loss. I also said that this ratio is much higher than one sees in actual games, and guessed that a value of 3 was probably closer to reality. In other words, for every $1 you bet in a hand you end up winning, I was predicting that you would get back on average about $3.

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In reality, the amount you win will depend on when your fellow players fold or run out of money. If there are 4 players at the end of the hand, the pot will have at least 4 times the amount any player bet (not counting the rake that gets taken out of the pot, so may actually be somewhat smaller). If you bet and no one calls, that's money you put in and they didn't, so the ratio of your winnings to the amount you bet (which I'll call your win ratio) will be lower. If another player goes all in, and you win the hand, that also lowers your win ratio—because it's money the player would normally have bet to stay in the hand, but didn't (because they ran out).

The win ratio is also affected by split pots, when multiple players split the pot because they have the same winning hand. Fortunately, this doesn't happen very often—but when it does, it cuts your win ratio dramatically. You can even end up putting more in the pot than you take out (giving a win ratio of less than 1), because the rake takes part of your bet out of the pot.

It would be nice to know what the win ratio is, on average, for a table you're playing at. If the ratio is low (like 1.5), you need to play tight. You don't get paid well enough for taking chances. On the other hand, if the ratio were high (like 4), you can play many draw hands (like flush draws), because you make enough money when you win to compensate for the times you don't.

Extracting Information

In fact, it turns out you can calculate a win ratio for a specific hand: take the total amount the winner collects (subtracting any rake the house takes), add up all the bets the winner made in the hand, and divide the winnings by the bets to get the win ratio.

For example, let's look again at the sample hand we saw in Part I:

***** Hand History for Game 1252041001 *****
$0.5/$1 Hold'em - Thursday, December 02, 22:49:52 EDT 2004
Table Rags To Riches (Real Money)
Seat 3 is the button
Total number of players : 3 
Seat 3: Player1 ( $36.87 )
Seat 7: Player2 ( $52.75 )
Seat 8: Player3 ( $61.5 )
Player2 posts small blind [$0.25].
Player3 posts big blind [$0.5].
** Dealing down cards **
PLAYERX has joined the table.
Player1 calls [$0.5].
Player2 calls [$0.25].
Player3 checks.
** Dealing Flop ** [ 6d, Jc, 3h ]
Player2 bets [$0.5].
Player3 folds.
Player1 calls [$0.5].
** Dealing Turn ** [ 4c ]
Player2 bets [$1].
Player1 calls [$1].
** Dealing River ** [ 2d ]
Player2 checks.
Player1 checks.
Player2 shows [ 3d, 3s ] three of a kind, threes.
Player1 shows [ Ac, 6s ] a pair of sixes.
Player2 wins $4.5 from  the main pot with
   three of a kind, threes.
PLAYERY has joined the table.
    

We see that Player 2 won $4.50 (there was no rake taken). Looking at the hand, Player 2 posted the small blind for 25¢, called for another 25¢, then bet 50¢ after the flop and $1 after the turn card—for a total of $2. So the win ratio for this hand is $4.50/$2, or 2.25.

One Hand is not Enough

Looking at one hand, we calculated a win ratio of 2.25. Is this average? Better than average? To find out, we need to look at lots of hands and average the results out. The more hands you look at, the closer your results will be to the actual average—but it takes time to gather the hands and do the analysis. I decided a good amount would be 100 hands.

And I wanted to use hands from multiple tables, at different days and times, because one table can have particularly loose or tight (or poor!) players. So I took 5 hands each from 20 different tables I collected on different days. All were 50¢/$1 Limit Hold'Em tables, so the results are comparable. Of course, you want to record hands from tables that play the specific game(s) and bet amount(s) you play.

The Results

So what were the results? In 100 hands, the winners won $723.13 and bet $289.25, for an average win ratio of just over 2.5 (so I was right about it being closer to 3 than 6). Different tables had different win ratios: the low was about 2 and the high about 3.4, so there was a wide range. Looking at specific hands, the lowest win ratio was just less than 1 (a split pot), the high was over 4.2 ($14.75 won, $3.50 bet). So your win ratio can (and will) vary significantly from table to table, and from hand to hand. But with an average value of 2.5, you can play quality drawing hands (like open-ended straight draws) as well as "made hands" like high two pair or three-of-a-kind.

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In the weeks and months to come, I plan to write more articles containing statistical information from actual hand histories. If you have any questions or comments about getting statistics using actual table data, please feel free to write me (Todd Gross) at Internet-Poker.com, and I'll try to answer your questions. In closing, I leave you with a couple of questions to think about: Do you think your win ratio will, on average, be different depending on how many players are at the table? If yes, how will it differ? And can you verify it by analyzing hands like we did here?