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This article is number 1 in a planned series of 3 articles covering the (in
my opinion) most important mathematical aspects of poker:
I have a feeling that many poker players, both experienced and beginners,
could do with a brush-up on how to calculate poker pot odds. In this article I
will try to explain the concepts so they make sense. Hope I succeed:-)
Firstly when it comes to odds calculations there are basically 3 different
systems:
- The Fractional Odds System favoured among bookmakers in the
UK. In the fractional odds system you will see odds displayed as fractions such
as 6/1 or more commonly 6:1
- The European Decimal System used mostly by bookmakers in
Europe (no surprises here). The European decimal system displays odds like
decimal numbers such as 1,3, 2,7, 6 etc.
- The American Moneyline System favoured by bookmakers in the
US, hence the name of the system. In the American Moneyline System you will find
odds like +500, -123, +345 etc.
I favour the European Decimal System (I’m European what can I say?) but
a quick glance at the available poker literature out there will quickly
convince you that the fractional odds system is favoured among most poker
writers (including my guru Dan Harrington). Luckily this article will give you
an idea of how poker pot odds are calculated in all three systems.
Moving on the actual math: let’s say you are playing an online tournament and
the pot after the flop is 2500. Your only remaining opponent bets 500, what are
then your pot odds for calling? With your opponent’s bet of 500 the pot is now
3000 and you have to call 500 to stay in the pot. Here’s how you would calculate
the pot odds for calling in each of the odds systems described about:
- In the Fractional Odds System the fraction quotes how much
profit the bettor will make relative to his stake. A fractional odds of 3:1
therefore means that the bettor will make a 300$ profit for every 100$ staked. A
fractional odds of 1:3 on the other hand means that the bettor will make a 33$
(100$*1/3) profit for every 100$ staked. In both cases the bettor will receive
his original stake back. This means that in the 3:1 example the bettor will
receive 400$ (300$+100$) in return and in the 1:3 example the bettor will
receive 133$ (100$+33$) in return. Returning to the poker example from above, by
calling your opponent’s bet of 500 you could potentially win a pot of 3000. A
bet of 500 with a profit of 3000 gives a fractional pot odds of 6:1 (3000/500).
As written earlier your initial stake is returned to you along with your profit
which means that you in total will receive 3500.
- The European decimal system differs from the other two
systems in as much as the bettor in effect hands over his stake to
the bookmaker. The decimal odds then reflects the total amount that will be
returned to the bettor; that is both his stake and his profit. Let’s see how
this works in the 3:1 and 1:3 examples from above. When staking 100$ to win 300$
the bettor parts with his stake and is paid back his stake plus his profit which
equals 400$ (100$+400$). In this case his decimal odds are quoted as 4
(400$/100$). In the 1:3 example, the decimal odds are 1,33 (133$/100$).
Revisiting the poker pot odds example, the decimal poker pot odds are 7
(3500/500).
- In the American Moneyline system the odds are either
positive or negative. The fractional odds of 3:1 from the example above would be
written as +300 indicating the amount of money to be won on a 100$ wager. The
1:3 fractional odds would be written as -300 indicating that you would have to
wager 300$ to win 100$. Going back to the poker pot odds example the 6:1 pot
odds therefore corresponds to +600 in the American moneyline system. As a
concluding remark I do not think the American moneyline system is well suited
for calculating poker pot odds, so if I were you I would focus on getting
familiar with either the fractional or the decimal odds system.
Given the explanations above, converting poker pot odds between the three
systems is pretty straightforward. I have listed some examples below. Fill in
the blanks yourself to practice converting odds.
- Fractional odds to decimal odds: write the fraction as its
corresponding decimal number and then add one. Thus 8:1 corresponds to 9, 1:4
corresponds to 1,25, 1:8 corresponds to 1,125 and so on.
- Fractional odds to moneyline odds: if the odds is more than
even (i.e the decimal odds is larger than 2), convert the fraction to its
decimal number and multiply by 100. If the odds is less than even invert the
fraction, convert to its decimal number and multiply by -100. For example 7:1
becomes +700, 2:1 becomes +200, 1/4 becomes -400, 1/9 becomes -900 and so on.
- Decimal odds to fractional odds:
- Decimal odds to moneyline odds:
- Moneyline odds to decimal odds:
- Moneyline odds to fractional odds:
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