## Saturday, July 9, 2011

### Poker Quiz Question #17

Q#17: You're in a \$5/\$10 NL Hold'em 10-handed FR cash game. Everyone has about \$1000 stacks. The table is a mix of aggressive and passive players. Your image is tight-aggressive. You are UTG with Js-Th. What should you do?
1. Most limp but sometimes raise
2. Mostly limp but sometimes fold
3. Mostly lip but sometimes raise or fold
4. Limp
5. Fold
6. Raise
---

A#17: I think the answer to this one is pretty obvious to most players; i.e., conventional wisdom says to fold hands like this in EP. However, like last time, I want to work through the process via my RED-M method and see if I come up with the same (obvious) answer. Let's start with R is for Reads:

We're first to act in a 10-handed game. This means there are 9 players left to act after us preflop. The problem didn't state any particular tells, tendencies, or notes on the other players. It did state that the table was a mix of aggressive and passive players, which would just imply a normal table. In this situation, you can't put any of the other players on any particular hand range yet. In other words, the nine players each hold ATC at this point.

So, let's move to E is for Estimating. There are no pot or implied odds to estimate, but we can calculate how our JTo fairs against 9 other random hands. For this type of problem, pokerstove isn't really very useful; i.e., 'stove just tells you that your equity is something like 13% against 9 other random hands, but how do you evaluate this in an EV formula if you don't know anything else about the situation?

Instead, a better way (I believe) to estimate our relative hand strength is to look at the probability that someone at the table has a hand that dominates ours. For example, hands that dominate JTo include AA, KK, QQ, JJ, TT, AK, AKs, AQ, AQs, AJ, AJs, AT, ATs, KQ, KQs, KJ, KJs, KT, KTs, QJ, QJs, QT, and QTs. Ignoring combinatoric effects (as this is just a rough estimate), this means that there are 23 basic hands that dominate JTo. Therefore, any single player has approximately 23/169 chance of being dealt a hand that is superior to our JTo. Now, there are nine total players that we have to get by if we enter a pot from UTG. This means that each player has a (169-23)/169 = 86% chance of having a worse hand than us. The nine players together, therefore, have an (86%)^9 = 26% chance of having a worse hand than ours. In other words, there is a 100%-26% = 74% chance that someone has a dominating hand to our JTo. Said another way, our equity edge is pretty damn bad. Further, our positional edge is horrible; we're almost certainly going to be OOP for the remainder of the hand. We also don't have particularly good fold equity; yes our image is TAG, but we have nine players to get to fold. Our skill edge is a wash, too, as we're at an average table and are, presumably, average ourselves.

The next two steps are therefore trivially easy. With \$1000 stacks and no money in the middle for us, the D is for Decide step says that we're not committed. We have horrible hand strength edge, poor fold equity, and poor positional edge. These factors all lead us to deciding on the fold line. M is for Maximize is just the implementation of this fold line.

Ergo, the correct answer is: Fold. And guess what? RED-M gave us the same answer we guessed in the first place. Cool.

All-in for now...
-Bug