Analysis of a situation of call or raise on the flop
In my last article, I started the analysis of a specific hand in no-limit Hold'em ' em that I hope will have raised interesting questions to your learning - the question was what to do when one was faced with a bet with a medium strength hand. In my example, our hero was faced with a bet of $ 70 in a pot of $ 85 on a given board Q-9-4 Rainbow, a player who had opened with a raise in middle position. Our hero had two and ten blacks.
Suppose that our hero decides raiser. He has $ 500 in front of him, which is enough for raiser to say $ 220. What good with raise, is that in most cases, our opponent would fold. Suppose nevertheless that it call (or, sometimes, reraise) with K - Q or better (something like A - Q, an overpair or a set) and half the time with J - J. Based on his range of hands that I record in my last article, our opponent fold 58% of the time and plays the other 42% of the time. When our opponent plays, if it reraise, we lie, is it call, we cease to invest money in that pot less than a ten out on the board. I do that gives us very little equity if our raise is calle. I believe 4% the number of times where we will win this pot in this case - even though when we win, we are doubling.
With this information, we can calculate the EV of a raise:
EV (Raise) =.58 x ($155) +.42 x [(.04 x $585) - $220] = $89.90 - $82.57 = $7.33
My instinct tells me that raiser here is more profitable to folder and I note that this analysis supports my instinct. What is interesting, is that in my last column, I made an initial estimate of the EV for a call of $ 49.50. This analysis took a few more paragraphs and it did not account for the action on the River (for example, I gave an estimate of our equity assuming that action ended on the turn). At the bottom, to serve our analysis of the EV of a call, let's say our heroes call the flop and call also turn if a map safe falls (it may also be that the action of the turn is check-check, but we'll get to in a few minutes).
Have to play an extra round (River) definitely diminishes our equity because we will always be in a difficult situation if our update opponent. I had assumed during my last column that a bet on the River would not diminish our equity. Let's see if this analysis still holds the road.
First, suppose that our opponent bets the turn, we callions and it puts us all in on the river. What is this third update will be a bluff or just a way to add value to the pot? Give credit to our opponent and assume that he put that optimally, i.e. that it not bluffera that so rarely, that it would not be the penalty of the caller. To the River, there would be $ 525 in the pot and our hero would have $ 280 in front of him. This means that if our opponents play optimally, it bluffera 280 ÷ (525 + 280 + 280) = 26% of the time. Using the range of hands that I gave in my last column, we can therefore anticipate the action of the river.
If our opponent value-bet K - Q or better on the River, it will build safely 41% of the time after that he has bet the turn. It will build as any as or King 17% of the time on the river. Therefore, it will build again the 3e round (River) 17% + [(1-17%) x 41%] = 51% of the time. When our opponent will build the River, we obviously bed.
According to my last column, the action at the turn was check-check 35% of the time. Suppose that our opponent bets $ 150 on the River with the strongest hand after checke (top set, middle set, A - Q, K - K, and also a few bluffs). Say what it bluff with A - K.
With these estimates, we can begin to put everything in place. After our opponent has bet $ 70 on the flop and we have calle:
17% of the time, the turn will be an ACE or a King, our adversary will build and we folderons. EV =-$70
54% of the time, there will be a turning point safe, our adversary will build and we callerons. After that, our adversary will build 51% of the time the River (and 100% of the time when there will be an ACE or a King) and we have more equity in the pot - which means that we will lose an average of $ 220. About 6% of the time, the action of the River will be check-check and we will lose again, costing US $ 220; 43% of the time, the action will be check-check and we will win $ 305 NET.
29% of the time, the action at the turn will be check-check. Still, we callerons the river if no as or no King falls. If our opponent check the turning point, it is bad news for us because in this case, according to my previous analysis, I think 16% the number of chances that we have the best hand. Finally, we prefer that our opponent bets the turn, giving us more clues on his hand. After a check-check on the turn, 17% of the time, our adversary will build the river and we shall sleep losing $ 70. Our EV for the remaining 83% time is $-120.
Finally, overall we have:
EV (Call) = [.17 x (-$70)] +.54 x [(.57 x-$220) +(.43 x $305)] +.29 x [(.17 x-$70) + (.83 x-$120)] =-$11.90 + $3.11 - $32.34 =-$41.13
Wow, this is a bad result. It remains for me plenty of room, but quickly go slightly changing the policy.
If, after a check-check on the turn, we lie on a bet on the River:
EV (Call) =-$28.21
These adjustments, suppose we callions an update on the turn if a King falls, but not on the river.
This helps us no more.
So after all this analysis, the EV of a call (with the best strategy at the turn and river) =-28,21$ EV (Fold) = $0, and EV (Raise) = + $7.33. We have demonstrated that raise it was the best game not true? Not so fast. Remember that each game depends on the opponent.
Poles work in general when we are faced with a difficult and intelligent opponent who does not continue to bet the turn and the River with nothing most of the time and has a range of reasonable hands for raiser to the preflop. But even math are not perfect. I have not evaluated fairness if a ten fell in my analysis on the EV (call). I do not figured it because in general, it will not change much to the final result. In addition, this opponent will always build when an ACE or a King will fall. Is there no check ever, this will add to our EV. Finally, our opponent in this example, no bluff - never raisera on the flop. Against an opponent who could do, should recalculate everything.
And to return to the last sentence, these last two Chronicles prove nothing. They are based on estimates, assumptions, estimates and the vulgar model of how a (solid-aggressive) decent online player would play this hand. Any of my assumptions could be next to the track and I was perhaps wrong calculation any (believe it or not, but I does not engage a team of mathematicians to do my calculations). Therefore, it is important when we do an analysis like this, think of what we have learned. I think that this particular analysis showed to me, it is that even when you do not want better value or bluffing and even when your hand has not improved, it is sometimes a good game raiser - especially if your opponent is a strong, without being a maniac player.
A medium strength hand - part 1Next >