Page 86-87 -I donÂ’t understand how heÂ’s getting his preflop equity vs opponents range . I understand how to get pot odds but not how heÂ’s getting heroes equity against villains possible range of hands preflop . I understand it clearly with a flop shown bc you can count the outs and combinations on the board . But without a board I donÂ’t understand how heÂ’s getting an equity value from just the villains whole cards and hero whole cards. See scenario below:
Pot odds 1.4:1
Hero: AKs
Tight small blindÂ’s range: JJ+ and AK.
AA: 3 combos - 12%
KK: 3 combos - 34%
QQ: 6 combos -46%
JJ: 6 combos -46%
AK: 9 combos -51%

Earlier in the chapter he discusses how to figure your equity but all examples use a flop. So IÂ’m just confused and would like someone to spell this out to me as simple as possible. Thanks

First, it's important to note that the equity is a showdown equity, i.e. it is based on the assumption that the hand is checked down. Therefore, folding and it's resultant realized equity is not considered,

Given that, an equity calculator can be used to determine this equity. These calculators use enumeration and simulation to essentially deal out all possible showdowns for each hand in villain's range and count how many times each player wins.

I have to assume this is what he used. A free and popular one is Equilab.

Are you asking how he gets the equity vs each individual hand, such as AK vs AA (12%) or how he gets the overall equity vs villain’s entire assumed% range? For the former, it’s basically the “all in preflop” probability of AK beating the given hand of five random cards from the remaining deck are dealt. Equity calculators exist for this problem, but the basic idea is to consider each possible board (there are 48C5 such boards, or 1,712,304 of them) and count how many make AK better (All boards with 2 kings and no ace, all with a Q,J and T, etc.).

To get the equity vs the range, you simply do the first calculation for each hand in the range, then do a weighted average of these values, weighted by the number of possible combos for each hand in the range.

For the given example this would be 3x12% + 3x34% + 6x46% + 6x46% + 9x51% =1149 divided by the total combos (27) which gives 42.6% equity vs the range.