Risk vs Volatility

People usually use the phrase "risk versus reward", but if you’re a careful poker player, I suspect you don’t really think too hard about the reward.  Also, if you play small stakes like I do where your normal everyday income far outpaces your poker bankroll, then you don’t care so much about the reward as the analysis.

Bradley, a poker colleague of mine recently posted a snippet of a hand he had that begged the risk vs volatility (or variance) question about a cash game of no limit in a weekend where he dropped about $1,000:

A Q on the flop of 2 3 5 is still a favorite, even against K K

Bradley’s Ace-Queen is indeed a favorite on the flop against KK, but not that much of a favorite.  Furthermore, I think, "Am I a favorite?" is the wrong question to ask.  I don’t know the whole history of the hand or the player (key to the decision) so take this with a grain of salt, but consider this:

Before the flop, the AQs vs KK is 31.57% vs 68.43%.  You’re an underdog and frankly, you know it. After the flop with the board of 2d3d5s you improve, but only to a 51.414% vs 48.856% favorite.  Knowing you’re coming from behind before the flop, when you don’t hit your hand on the flop, is it worth it to continue shoving money into the pot?  Do you really wanna flip a coin for a bunch of money with a 1.4% edge?

For more analysis let’s go back to the preflop decision to call what was presumably a big raise from a player with AQs.  Most players develop the ability to sense a really big raise both from body language and betting pattern.  Assuming you get this, the hands you have to put a tight player on are: AA, KK, QQ, AKs, AKo, and AQs/o.  If you program this entire variation into poker stove, you discover that your average equity across those hands is about 35% to 65%.  An underdog no matter what the other player has.

Not until you widen the range of your opponents hands from AA down to 88 and AK-AJs/o and even KQs/o does the AQs start to become a favorite, and then it’s still very close to 50/50.  Do you really wanna flip a coin for a lot of money?

Someone said almost exactly that to me once at the now-busted illegal card club in NYC on W 72nd.  Another guy and I pushed all our chips for $50 a piece, and when someone challenged the wisdom of my call, I said, "I have an edge, but it’s almost a coin flip." 

A smarter player than I said to a neighbor, "You wanna flip a coin for $100?  No, I didn’t think so."

He had an excellent point.  There are many times to push your small edges in poker.   If you push all of them, your volatility goes sky high.  Assuming the player is an idiot, you can probably wait for a better spot to win his money.

In fact the two best contexts in which to put the rest of your money in the pot is:

1. If you’re in a tournament and you’re playing to "Go big or go home."  That’s a perfect time to push your small edges, or
2. If you don’t have a lot of money on the table and you know the other player will dump it back to you when you rebuy.  (Even this is kind of sketchy)

I find so much of poker to be about risk management, this situation is no exception.

(All the numbers, including the "range of hands analysis" is found using PokerStove, a great tool I highly recommend you pickup.)