Backdoor draws and splits in equity calculation
Two things I don’t understand when trying to do equity approximations.
When we count combos, how do we deal with backdoor draws? I heard backdoor draws have around 4% of hitting by the river. But how much of that do we add to our equity on the flop when facing a bet?
Also, say we have a river decision, how do we value combos for which we split the pot? Ignoring them seems wrong since, if there is significant money in the pot, they still give us +EV compared to folding.
Thanks!
6 Replies
Two things I don’t understand when trying to do equity approximations.
When we count combos, how do we deal with backdoor draws? I heard backdoor draws have around 4% of hitting by the river. But how much of that do we add to our equity on the flop when facing a bet?
Example: you have AK on Qxx combo and are facing AQ. Your equity and hope to spike a K only:
Board:
[Qh 2d 2c]
Equity Win Tie
MP2 14.29% 14.04% 0.25% AcKd
MP3 85.71% 85.45% 0.25% AsQs
Now the same with AKs that has BDFD.
Board:
[Qh 2d 2c]
Equity Win Tie
MP2 17.83% 17.58% 0.25% AcKc
MP3 82.17% 81.92% 0.25% AsQs
Result: +3.54% equity, which is almost one out, when counted from flop to river.
Also, say we have a river decision, how do we value combos for which we split the pot? Ignoring them seems wrong since, if there is significant money in the pot, they still give us +EV compared to folding.
Thanks!
I just ignore them. You have 50% against them, so no matter how much money you put against them, you will be 0EV - at least in theory, cause in reality you are just pumping more rake.
Well, we don't assume folding, these are two different scenarios.
#1 - You are IP and can decide to bet or check back
Besides rake, the decision is 0EV against THAT HAND that you split with, due to reasons stated above. But against the whole range, where he has weaker holdings, checking has EV > 0.
#2 - You are OOP and might face a bet
If he will fold you out of a split, then you resign from a part of a pot that simply "belongs" to you. If you only look at the EV at the very end of the decision tree (so on the river), then yes, folding has 0EV and calling a split will win you 50% of the pot.
Example: you have AK on Qxx combo and are facing AQ. Your equity and hope to spike a K only: Board: [Qh 2d 2c] Equity Win Tie MP2 14.29% 14.04% 0.25% AcKd MP3 85.71% 85.45% 0.25% AsQs Now the same with AKs that has BDFD. Board: [Qh 2d 2c] Equity Win Tie MP2 17.83% 17.58% 0.25% AcKc MP3 82.17% 81.92% 0.25% AsQs Result: +3.54% equity, which is almost one out,
I’m not sure ignoring chops is valid. Consider a spot, for instance where the board is 6666K and you have some hand without an ace. Suppose the pot is $100 and villain bets $100. If you fold your EV is zero. If opponent has an ace with probability p, your EV is 50(1-p) - 100p (you win 50 when you chop and lose 100 when he has the ace). This equals 50-150p which is zero if and only if p=1/3. In this spot villain should be bluffing 2/3 of the time. If he is overbluffing, it’s a +EV call. Conversely, if he underbluffs it’s a -EV call.
I’m not sure ignoring chops is valid. Consider a spot, for instance where the board is 6666K and you have some hand without an ace. Suppose the pot is $100 and villain bets $100. If you fold your EV is zero. If opponent has an ace with probability p, your EV is 50(1-p) - 100p (you win 50 when you chop and lose 100 when he has the ace). This equals 50-150p which is zero if and o
This is a very, very specific spot, where you hope to split, but can lose 😀 Mostly we are talking about a whole range, like board is A2247 and you have AQ, but your opponent may have AK-AJ. You can basically ignore AQ combos and just focus whether there are more AK or AJ - this is more typical scenario 😀
This is a very, very specific spot, where you hope to split, but can lose 😀 Mostly we are talking about a whole range, like board is A2247 and you have AQ, but your opponent may have AK-AJ. You can basically ignore AQ combos and just focus whether there are more AK or AJ - this is more typical scenario 😀
Ok, suppose in your spot villain has a range of AJ+. He has 8 combos of AK, 6 combos of AQ, and 8 combos of AJ. That’s 22 total combos in his range, so we chop 6/22 =27.3%. Again assume a $100 pot and a $100 villain bet. A fold is zero EV. A call has EV of (200*8/22 - 100*8/22) + 50*6/22. The value in parentheses is the EV of the call if you ignore the AQ combos. Obviously ignoring the AQ combos yields a different EV, $36.36 for ignoring AQ combos vs $50 when considering them.
This is a very, very specific spot, where you hope to split, but can lose 😀 Mostly we are talking about a whole range, like board is A2247 and you have AQ, but your opponent may have AK-AJ. You can basically ignore AQ combos and just focus whether there are more AK or AJ - this is more typical scenario 😀
I think I see what you were saying and it works, but not in general. It only worked for the specific example you gave because our winning and losing probabilities were the same. The formula you were using was win%/(win%+lose%), where win% + lose% does not necessarily equal 100 since ties are possible. In the specific spot you posted, win% = lose% = 8/22 or 36.4%. Your formula gives a correct equity of 50%. The correct foemula though is win% + 0.5*tie%. In this specific spot, it also gives 50% (easier to see in fractions - tie percentage is 6/22, so 8/22 + 3/22 is 11/22 or 50%).
These formulas no longer agree if we win more than we lose (or lose more than we win). For example, consider a spot with 80% wins, 10% losses and 10% ties. Ignoring ties we get an equity of 80/90 or 88.9%. The correct value is 80% wins + 1/2 of 10% ties or 85%. Your idea is close but not the same
If we are talking about equity, then obviously they are taken into account. I was trying to just simply calculate the combos you beat vs the ones that have you beaten.
Can you give an example where the amount of combos that we beat is smaller than the ones that have us beaten, but for some reason, due to ties - we have over 50% equity, which would justify a value bet?
