A Mistake or Not?

I have Ace-Queen. I raise 6 times the blind, a standard raise at $100 NL. I get 3 callers, 2 of them before me, 1 after me. The flop is 5-10-2, with 2 hearts. I don't have much of a hand and only 2 backdoor draws. The first two players check, and I bet $15 hoping to take down the pot. The player to my right raises me to $45. The other two players fold.

I'm fairly confident that at that moment, my Ace high was good, and he was just trying to make a move on the pot. Either that, or he had top pair or something, in which case I might be able to push him off of the hand. He had shown a proficiency for bluffing, and I put him on a semi-bluff.

I asked him how many more chips he had. He had $61 after the $45 raise. In my opinion, my only move was to raise him or to fold. A call gives him an opportunity to catch or bluff again on the turn.

The only raise that was feasible was an all-in raise. I knew he would call an all-in and if I simply minimum re-raised him to $75 total, he was going to go all-in anyway.

All I had was Ace high, and 2 backdoor draws. However, I was pretty sure I had the best hand. However, I was also pretty sure I was up against a monster draw. Since I was unpaired, he not only had flush draw outs, he had outs to hit a pair. I figured it was about 50/50 and decided to fold and wait for a better spot. He showed King-7 of hearts so he had the monster draw, but I had the best hand.

The odds on the flop were 53.13% in my favor. I should have put him all-in.

Even though it was close to 50/50 that I lose an additional $106 on the hand, the pot odds were in my favor. Assuming he calls the all-in, which he would have, the pot would be $260. I'd be risking $106 to win $154. Those are odds of 1.45 to 1. I was a 1.13 to 1 favorite to win the hand.

In 1,000 instances of this hand after the flop, if I put him all-in, I lose 469 times, and win 531 times. In the times I lose, I lose $49,714. In the times I win, I make $81,774. That's $32,060 profit over 1,000 hands, or $32 a hand. Risking $106 to win, on average, $32 of profit isn't that much, but over the long run it adds up. I should have put him all-in.

I should have realized the benefits of my hand. Yes, the King-7 had a great deal of outs, but even if they hit, I would still have outs. If he hits the flush, I'm still 16% to win the hand. If he hits a pair of 7s, I'm still 11.4% to win the hand. If he hits a pair of Kings, I'm still 13.6% to win with an overcard and a gutshot straight draw.

Also, I have many cards in the deck that improve my hand. An Ace on the turn makes me 81.8% to win the hand. A Queen makes me 75.0% to win.

Even though 47.87% of the time I'd lose an extra $106 on the hand, the fold I made loses $27 100% of the time. Over 1,000 occurrences, that is losing $27,000. Granted, over the same number of instances, I'm only winning $32,000, but that is a $59,000 swing compared to folding. In other words, by folding, I saw an average down swing of $59 on my bankroll.

Mathematically, going all-in was the right decision to make. It also would have been beneficial in terms of gameplay. Here is why:

1. It shows an overly aggressive player with position on me that he won't be able to push me around. Even if I lose, he'll think twice before trying to force me out of hands when he only has a draw. He might only call the next time he has a drawing hand.

2. It shows the entire table that they will have difficulty pushing me around. Because I'm so tight, aggressive players sometimes can push me off of winning hands. This costs me money in the long run.

3. It shows the table that I will bet with hands that aren't the nuts. This will give me action in the long run. I often don't get action from good players even when they have great hands because of my tight reputation.

4. If I lose, I reload and my stack goes back to $100, only about $30 below what it was before the hand. If I win, my stack is at $260, which means I'd be $130 more powerful at the table. I could be more aggressive, chase more cards, and win bigger pots against the other big stacks at the table.