Pad0n0k: переводы

→Frequency of Favorable Flops

→1)The frequency of favorable flops
2) How much one should expect to win on average on a favorable flop.

→I define the implied value of a hand to be the average value of a hand when it hits a favorable flop. The term encapsulates the germ of truth behind the implied odds fallacy and better reflects how we should really think about preflop decisions. Determining the implied value of a hand comes down to estimating:

→What makes AKo a strong hand, but a better 22 not so strong? The answer is that AKo will flop a very favorable hand about 1/3 of the time, but 22 will only flop a favorable hand about 1/9 of the time.

→Before I define implied value, I want to dissect some preflop decisions a little more closely. Suppose you have AKo and there are three limpers in front of you. What is your action? Of course you raise, but why? I suspect the answers will generally sound like “you have a strong hand.” But why is it such a strong hand? Well, it is often the best hand preflop. But if you follow that logic, you should also raise 22 in this situation because 22 has an even better chance of being the best hand. Yet we don't raise 22 preflop because it isn't a “strong hand.” Some players will then commit the PokerStove fallacy and show you what great equity you have as a reason for raising (AKo has 32% equity against 4 random hands, but 22 only has about 18% equity).

→Implied Value

→For example, suppose that have you have 22 preflop on the button and you expect the pot to be 7-handed postflop. Suppose further that you expect to win 7 BB on average when you flop a set. You implied odds for limping are 14:1. Since you are 8:1 to flop a set, you can play because you have good implied odds. What happens if you raise? If your implied odds are to increase, you might conclude that you will need to win at least 14 BB when you flop a set. This is already a somewhat difficult (not impossible) task, but this number does not correctly factor in the increased losses when you do not flop a set. You do not flop a set about 88% of the time, which means that you must make up for the extra .5 BB loss a vast majority of the time. In essence, your preflop raise is roughly equivalent to facing a preflop raise. It is still a profitable situation and it might even be more profitable because of the extra money in the pot, but your implied odds are cut down because of the larger initial investment and the infrequency with which you actually flop a set.

→Some players try to use implied odds to justify making raises. “By making the pot bigger,” they say, “we're increasing our implied odds.” In no-limit, this might be a valid statement as a bigger preflop pot may entice a player to become pot-committed, whereas in a smaller pot he still has the option to fold. But in limit hold ‘em, this statement is nonsense. Because implied odds are a ratio of investment to future pot size, a preflop raise will only increase your implied odds if you expect to win at least twice as much as a result of the raise.

→By definition, implied odds are the ratio of the total expected win to the size of the investment. This concept is often used in postflop play when determining whether to call. When the pot odds are not sufficient to make a call you can sometimes justify calling because of the added bets you will win if you make your hand. This implies that the pot is actually bigger than what it seems.

→The Implied Odds Fallacy

→All the hands in between AA/KK and the junk are very volatile. For example, AKo has about 32% equity preflop, but it jumps up to 62% when it pairs up, and drops down to around 17% when it doesn't. Q9s is even more volatile. It starts at about 26% equity, which drops down to around 15% when it flops nothing. It goes up to 35-45% equity for flush draws (depending on the texture) and similarly for straight draws. If it pairs up the equity is in the 40-50% range. All of this variation comes as a result of the flop textures, and since PokerStove deals out the flop, turn, and river all together, it fails to see these effects.

→I don’t believe that PokerStove is an effective tool for making multiway preflop decisions. For our purposes, multiway pots have at least three limpers in front of you, and the two blinds left to act behind, so that we expect at least 5 players to see the flop regardless of whether we call or raise. One of the major flaws of PokerStove is that it does not estimate the value of volatile hands very well.

→In fact, those two hands are the only ones where you can have a highly predictable postflop equity. The offsuit junk hands have medium volatility. They tend to have 10-15% equity preflop. This goes down to 5-10% postflop if they don't pair up and anywhere between 15% and 25% equity postflop for one pair, depending on the size of the paired card. Suited junk has a sharp spike in equity when it flops a flush draw.

→What are volatile hands? Volatile hands are those hands whose preflop and postflop equity values are often very different against the same range of hands. What hands does this include? Perhaps it would be easier to talk about the hands that it excludes, as this list is short. AA-KK are hands that are strong preflop and usually remain strong postflop. For example, AA against 4 random hands has approximately 56% equity. If you pick a random flop and repeat the equity simulation, you'll find that the postflop equity (against the same range) remains close to 56%. Similarly, KK has approximately 50% equity preflop against 4 random hands, and its postflop equity remains near 50% except when there is an ace on the flop (this happens about 17% of the time and the equity falls to 35-40%, depending on the precise flop texture).