# Poker equity question

• Basic
Joined: 28.01.2016
Hi all

In Bill Chen's book 'The Mathematics of Poker', it states that "the equity of our random hand against a distribution of AA-JJ and AK is about 24.95%". This refers to a game of no-limit holdem, 2 players left, where the pot is \$45 (big blind, small blind and one \$30 bet), and the player is risking \$190 to jam the pot.

It starts by saying we have an equity of about 45%, which I'm fairly certain comes from equity = cost of call/new pot size (in this 190/415).

Despite my best efforts, I haven't been able to figure out where 24.95% comes from though.

Any ideas would be greatly appreciated. Thanks
• 4 replies
• Coach
Coach
Joined: 09.07.2010

It is the average preflop equity versus a range of AA, KK, QQ, JJ and AK.

When you have a random hand (any 2 cards) and opponent has randomly one of those above hands, you will win the preflop allin 24,95% of times on average.
• Basic
Joined: 28.01.2016

Do you happen to know how it is calculated?

And what do you you mean by "win the pre flop all in"?

Thank you!
• Coach
Coach
Joined: 09.07.2010
Preflop allin means that you both put all of your chips to the pot preflop, so there flop, turn and river is dealt without any actions and the one with the better hand after river wins the pot. Your equity (24,95%) means that it is your chance to win the pot, thus your equity shares. Of course you can't win 24,95% of the pot, you either win it or lose it (or in rare occasions you have a tie). But if the same situation happens countless of times, that would be your average chance to win.

Think about flipping a coin, you have 50% chance to win it. If we flip it, it can't be a tie. Either one of us win it, but on average you will win 50% of flips.
• Moderator
Moderator
Joined: 12.11.2008
Don’t forget that you can check your equity in spots yourself with our free tool PokerStrategy equilab for hold’em players and/or PokerStrategy equilab omaha for our Omaha and Omaha high/low players.

Cheers,
SDK1987