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# basic math question

• Basic
Joined: 23.04.2014
Dear all,

I am reading your strategy articles on SnG and others. Everything is perfect and clear except one aspect. Can you explain me how you obtain the percentage of ''probability of winning'' or ''probability of loosing''? Is it just approximate assumption that comes with practice or are there real calculation or tool to obtain those probabilities?

Kind Regards,

jaquare
• 3 replies
• Basic
Joined: 23.04.2014
Also i forgot one more thing, for instance in the article : chip value(1): The principal of diminishing chip value. You give an example with AA on a double or nth SnG with five players all in before you. And you give 40% as your equity to win. How did you obtain this number? Sorry it might be a dumb question.

Regards,

Jaquare
• Bronze
Joined: 05.07.2011
equilab, under the poker tools section.
• Super Moderator
Super Moderator
Joined: 02.09.2010
Originally posted by Jaquare
Also i forgot one more thing, for instance in the article : chip value(1): The principal of diminishing chip value. You give an example with AA on a double or nth SnG with five players all in before you. And you give 40% as your equity to win. How did you obtain this number? Sorry it might be a dumb question.

Regards,

Jaquare
Hi Jaquare,
As martinemem, we use a tool called Equilab which is free to all PokerStrategy.com members.

Equilab uses one of two methods to determine a hand's equity (equity="theoretical share of the pot")
In one method, it compares all hands in each of two (or more) ranges to each other, and gives the probability of each range winning, losing and trying.

Comparing AA vs 5 random hands would take far longer than is practical to find a solution.
So for such situations, it does a "Monte Carlo" simulation -- it just starts simulating games and printing the results. When I use this method, I just run it until the numbers stop changing.

Here is Equilab's output after 600,000,000 hand:

Equity     Win     Tie
MP2    49.23%  49.01%   0.23% { AA }
MP3    10.15%   9.52%   0.63% { random }
CO     10.16%   9.53%   0.62% { random }
BU     10.15%   9.53%   0.62% { random }
SB     10.16%   9.53%   0.62% { random }
BB     10.16%   9.53%   0.62% { random }

If 5 players are all all-in ahead of you, they're not just playing random junk.
So here is the same thing if 5 people ahead of you all had a top 10% hand:

I tried to enumerate all, but it has been almost 5 minutes and it still says "0% complete".
When I use the Monte Carlo method it looks like this after 600,000,000 games, which took less than 5 minutes to complete.

Equity     Win     Tie
MP2    47.59%  46.59%   0.99% { AA }
MP3    10.52%  10.00%   0.52% { 77+, A9s+, KTs+, QTs+, AJo+, KQo }
CO     10.48%   9.96%   0.52% { 77+, A9s+, KTs+, QTs+, AJo+, KQo }
BU     10.46%   9.94%   0.51% { 77+, A9s+, KTs+, QTs+, AJo+, KQo }
SB     10.50%   9.98%   0.52% { 77+, A9s+, KTs+, QTs+, AJo+, KQo }
BB     10.46%   9.94%   0.52% { 77+, A9s+, KTs+, QTs+, AJo+, KQo }

Note that even though AA has the best chance of all the hands, it is less than 50% to actually win. In a double-or-nothing you are more likely to get in the money by folding your AA in this spot, since with 5 all-ins ahead of you there are bound to be some eliminations.

The relative equity of hands has been long established in the poker world. I suspect that they were determined using computer simulations, since the number of possibilities is extremely high.

Best of luck,
--VS