I had been reminiscing about the hands of poker that I have played since I started this blog. I searched through my posts thinking that I had written about the first time that I made a Royal Flush, only to learn that the only thing that existed was a tweet. It’s been so long that my only question is, what can I analyze about it? I can’t review my play because there wasn’t much to review. To be honest it wasn’t even all that interesting. I could probably tell you about the entire hand in a few sentences, but instead I am going to compare my hand to what a solver would do and share what I might do with the knowledge that I have now.

This hand took place at Caesars Palace on a Monday night. The world was still bouncing back from the events that had taken place in 2020 and poker felt like it was booming. I remember that this happened before I started to form my strong opinions about playing blind vs blind and that the kid who decided to complete the small blind seemed to be new at playing poker. After calling my raise of $10; I flopped the nuts, a diamond royal flush. After checking the flop, I made a $10 bet on the turn that was called and then followed that by a $15 bet on the river that was also called. There was a little bit of cheering amongst the players at the table, but it was generally an uneventful hand. The only thing to question was if I managed to get the maximum value out of my opponent.

I have no idea what my opponent had called me down with. My guess is that they probably had a flush or a straight, at worse two pair. I have noticed that a lot of players who are playing at a casino for the first time or new to playing poker will not bet their hands very aggressively. It is like they don’t want to scare away the card shark and think they need to trap us. Funny thing is that even if they did bet, some players would probably trap themselves in a hand. The dilemma I had was that I wasn’t sure how to bet it. How does one extract value when you know that your opponent can’t improve much? Well, the first answer to that question is that I shouldn’t think only about my hand. When playing poker, we as players have several combos that make up our range. Meaning that we have some bluffs and draws, and our opponents should be aware that we have several possible combos.

Something to keep in mind is that my range was not as complex as it is now. I wasn’t thinking about playing certain suited Ax combos at Y frequencies or making sure to include suited connectors in my range or how to play certain combos when I checked back. Because I know that I didn’t think of my range the same way that I do today, I decided to set my range as AA-33,AKs-A7s,A5s,KQs-K9s,QJs-Q8s,JTs-J9s,T9s,98s,87s,76s,AKo-ATo,KQo,QJo,JTo. My opponent’s range is a guess at best, with the assumption that they were not calling with the top of their range. Their range is defined as 88-22,A9s-A2s,KTs-K2s,QJs-Q2s,JTs-J2s,T9s-T2s,98s-92s,87s-82s,76s-72s,65s-62s,54s-52s,43s-42s,32s,AJo-A2o,KQo-K4o,QJo-Q7o,JTo-J8o,T9o-T8o,98o-97o,87o-86o,76o-75o,65o-64o,54o.

According to the solve I shouldn’t be checking back the flop. There is a preference to making a range bet. The EV of betting is roughly about the same as checking. Some EV is lost when betting more than sixty percent of the pot. Since we don’t lose any EV betting small, I think this is why the solve shows betting should be done a higher percentage of the time. A lot of the bets appear to happen when there is a diamond. Bets also happen with sets, two pair, one pair with top kicker, one pair with a draw, and small pocket pairs. My opponent is not going to have many strong flush combos and the board blocks them from having certain combos since they in theory have a capped range. Why would I want to bet? There are still some combos that can improve. All their two pair can fill up, they have one pair combos that are drawing to straights, and they do have some flopped straights.

Would I have bet my small pocket pairs or bottom pairs with a draw back then?  Probably not but these days I am fully on board with betting my weaker hands and even raising them if my opponent decides to lead. Most players don’t realize how hard a flush is to make and assume that when there is a monotone board your opponent automagically has a flush. Often what you see is a lot of checking because everyone is afraid of the flush. Personally, I think you do need to be careful on monotone boards, but the action doesn’t need to slow down as much. By betting weaker hands this allows you to build the pot so that when you do have strong hands you can continue to extract value from your opponent.

Moving on we start to branch off into a different scenario. The game tree doesn’t exactly follow the same action that happened in the hand. The first thing I see is that if I check, my specific combo is no longer in my range. I can fix this, but it will change the end results of the original solve. When checking back the flop vs betting, my opponent doesn’t change their option very much. In both instances they are checking most of their range. The key difference is that when I check back, they do have more bets that are made on the turn. Why? I don’t have as many nutted hands when I check back on the flop. Because of this my opponent is free to bet more often with their flushes, two pair, and bluffs that block some of the key combos that I could have had if I had made a bet.

Checking back the flop loses a significant amount of EV when compared to betting the flop. Most of the diamond combos that I would have had on the flop are no longer there as well as any made hands that would dominate my opponent. Simply put, by checking I have allowed my opponent’s range to stay intact and continue which means that when we see the turn there are a lot of combos that could have improved. In both scenarios, checking back happens more often. But a small bet has a higher EV than checking. When I look at my specific hand, it is never checking. Even though checking happens at a higher frequency there are enough hands in my range that will want to bet for value along with a few semi-bluffs that I think I made the right decision to bet. The only problem I see is that I limited the amount of money that I could bet by not betting the flop.

On the river my opponent is basically checking one hundred percent of the time. When they do lead out, I am calling a lot, but my specific hand is always raising. Comparing the two scenarios that I have created here; one is betting more often and the other is checking back more often. Can you guess which one is which? If you guessed that the game tree where I bet the flop and turn is checking back the river more often, then you are right! Of course, my specific hand is never checking back but I have a lot of hands that would have been betting that made it to the river and could be losing. Why would my opponent check those winning hands? Well, if I bet then my opponent has an opportunity to get another bet in by raising. When they do raise, I am only calling with straights. The most interesting thing to note is that when I do get raised, I only have the nut flush when I have been betting the whole way.

Was I able to extract maximum value from my opponent? No, I think I left some money on the table. Working through the solves it seems to me that my opponent most likely had something like King-Ten or Queen-Jack. I can’t really think of any other combos that are in the range that I defined that logically make sense for this person to check-call the whole way down. I guess there are some naked Ten-x combos that could have called down, but that doesn’t make any sense to me. I don’t think they ever have any small flushes here and if they did, good for them. What I noticed the most is the growth in my game and the fact that I would play this hand more aggressively than I originally did.