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/Apr/2013

Pricing Opps Out Post-flop

By: JWK24 @ 14:37 (EDT) / 908 / Comment ( 12 )

Here is how pricing out the opponents works.  When I have the best hand (and will do the same with my bluffs and semi-bluffs), I want to size my bets so that the opps are making a –EV play to call, a play where they expect to lose chips on average. 

The most likely draws that they can have are a flush draw (9 outs) or OESD (8 outs).  Each out that the opp has is worth 2% of equity per street, so due to this, a flush draw is worth 18% and OESD is 16%.  If the opp has a combination draw, then they will have 15 outs (OESD/flush), so they will then have 30% equity.  Since these equity numbers are per street, I will need to make the same bets on both the flop and the turn, so that the opps will make a negative play on both streets. 

 
If the opp calls a bet that has more than this % of pot equity, then they will expect to lose the difference on average, each and every time.  The expected value of a call is the hand equity – the pot equity.  From this, I need to bet both the flop and the turn, as if I check one of them, they will expect to gain chips, as their hand equity will be higher than their pot equity, which will be zero.  For example, if I check and they have a flush draw, then they would then expect to gain 18%.  I want to do whatever I can in order to have the opp expect to lose chips to me each and every street that I’m involved in a pot.
 

The way to calculate the pot equity is to take the amount of chips that you need to put into the pot and divide it by the amount that the pot will be. 
 

For being in a heads-up pot, the typical bet that I’ll make is a 1/2 pot bet.  If the opp calls the bet, the pot will be double what it started at, so their pot equity will be 1/2 divided by 2 or 25%.  This means that if the opp has a draw, they will expect to lose 7% of the chips they put into the pot if they have a flush draw, 9% if they have an open-ended straight draw, or even more if they have a draw to something with less outs. 
 

If I’m in a pot with 2 opps, then I will bet 2/3 pot.  The first opp that calls will then be putting 2/3 into a pot that will be 7/3 what it originally was, or 28.6%.  The second opp will be putting 2/3 into a pot that will be 9/3 or 22%.  Since both opps will have to put into the pot more than what their hand is worth, they expect to lose chips to me every time that they call with one of these draws (or any draw with fewer outs).
 

If there are 3 opps, then I will bet 3/4 pot.  The first opp that calls will be putting 3/4 into a pot that will be 10/4 (30%).  The second opp that calls puts 3/4 into a pot that will be 13/4 (23%) and if the third opp calls, they’re putting 3/4 into a pot that will be 16/4 (18.8%).  Once again, all of these are higher than what their hand is worth if they have a flush or straight draw, so I expect to gain chips from each one that calls.
 

If there are 4 opps, I will make a pot-sized bet.  The first opp calls 1 into 3 (33%), the second opp calls 1 into 4 (25%), the third opp calls 1 into 5 (20%) and the last opp calls 1 into 6 (16.7%).  Here is where the breakpoint is… I can’t price the last opp out if they have a flush draw, as due to having too many opps in the pot, they will always be getting the correct odds to play if everyone stays.  The same will hold for more than 4 opps in the pot, as each opp down the line will have less and less invested into the pot.  The best I can do is to make a pot-sized bet, which is the smallest bet that I can make that will price out the maximum number of opponents.
 

If I think that the opp could have a combination draw, then I need to bet more and will be able to price out less and less opps due to this.  If I’m heads-up, then I will need to bet 3/4 pot, as from above, this gives the opp a 30% pot equity.  In multi-way pots, if the last opp has a combo draw, then I’m not able to price them out, so I’ll make a pot-size bet and price out as many opps and draws as possible.


By keeping all of my post-flop bets standard, based on the pot-size, number of opps and board texture, the opps won’t know whether I’m value betting them with the nuts, have total air or anything in-between. 
 

The more -EV plays that the opps make, the more chips that I expect to gain from them over time.  Yes, the opps will get lucky and hit their draws a given % of the time, so in the short term I can lose chips…BUT, I will be gaining chips from them over the long term each and every time that I can get them to make a  -EV call.
 

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