To start off this column let me propose a game.
In this game each player is given 100 chips to start and you must win 10 rounds to win any money.
Each player antes a single chip and after being dealt your two hole cards each player has the opportunity to bet and raise just like a standard game of Texas Holdem.
Now suppose in your first round matchup your opponent immediately bets his remaining 99 chips and tells you he has AK. You look down and you have 33 and are a slight favorite, what should you do?
The simple answer is to call, because you are a favorite (albeit just a 3% favorite) and have an advantage, and poker is all about pushing you edges right?
The not so simple answer is that if your opponent will make such wild plays you’ll find better, less riskier spots to get your money in against them and this is simply a risk you don’t have to take.
This is certainly a simplified scenario, but it’s also at the heart of every risk to reward calculation you’ll have to make at a poker table, and will be the jumping off point for this column, which asks the question, when should you turn down an edge?
In the example given above, you’ll stand to make about 7 chips per hand in the long-run. Over the course of 100 trials: 53 times you’ll move on to Round 2 and will still have to win nine more matches, and 47 times you’ll be eliminated from the game.
So the question becomes, is it better to push your small edge or is it better to wait and look for a possible better edge, which may not present itself by the way?
Everyone’s threshold for risk is different
A lot of this comes down to your willingness to take on risk. Some players are simply willing to push their margins a bit more, and these players will be rewarded in the long-run so long as they can survive the added variance they are creating.
For the more risk-averse player these small edges simply aren’t worth it, they’d rather make $52/hour than $55/hour if it means keeping their sanity and reducing their chances of going busto.
Personally I don’t think either approach is wrong, so long as you’re not passing up spots where you have an obvious edge. It’s one thing to say “it’s not worth it,” it’s an entirely different matter to make straw man excuses as to why you are passing up an edge.
What the math says
Looking at these types of situations through the eyes of a poker tournament player you also have to factor in how the early double up will impact your ROI.
Unlike the silly little game I outlined above, there are more variables and factors to consider in a tournament as stack sizes are not always equal and prize-money is awarded in progressively higher amounts; rarely is a poker tournament played with winner-take-all format.
With that out of the way let’s talk tournaments, a $300 buy-in tournament to be precise.
For simplicity sake let’s assume an early double up increases your ROI from 30%/$100 (30% of the buy-in for the tournament) to 50%/$150 (50% of the buy-in).
Under these parameters you’d be foolish to open yourself up to a lot of risk early on in the tournament, as you would need to be a considerable favorite to risk your tournament life since:
- If you pass up the 53/47 advantage you still have a 30% ROI and have $100 in equity.
- If you accept the 53/47 advantage, 53 times you have $150 in equity and 47 times you have $0 in equity: An average of just $80 in equity.
Now you can play with these numbers all you want, and everybody’s results will be somewhat different, but for this call to be “correct” you’d need to feel that an early double up nearly doubles your equity in the tournament, something even the most optimistic among us would have a hard time arguing for, although some do.
So what is an acceptable risk in the early stages of a poker tournament?
Again it all depends, but mathematically there is a threshold you can find.
Suppose you are a 60/40 favorite instead of a 53/47 favorite, and an early double does nearly double your equity, taking you from $100 to $180; would this be enough?
- If you pass up the edge you once again have $100 in equity.
- If you accept the 60/40 advantage than 60 times you will rise to $180 in equity and 40 times you will drop to $0: An average of $108 –increasing your ROI to 36%.
Even as a 60/40 favorite and a sizable jump in equity this is far from an automatic decision for a lot of players, especially if they lack confidence in the way they have computed their variables –which more conservative players will obviously lack.
But we also have to consider the human error involved. At this point most poker players would find this edge far too lucrative to pass up, but if our math is off even slightly than it will be the more cautious player who gets the last laugh.
Basically, risk averse players will always round down while players with a bit more gamble to them will always round up!
Think of it this way, if you’ve miscalculated your advantage perhaps you’re only 56/44, and your equity increase is only 175 instead of 180, this is suddenly a losing play, dropping you down to $98 in equity.
Conversely, if you’ve miscalculated and your advantage is actually higher say 65/35 you’re passing up a spot where you will go from $100 in equity to $117 in equity –which is a major, major mistake, even in the eyes of the nittiest nit.
Using this analysis
Don’t read too much into this analysis.
These types of calculations are hard to perform sitting behind your computer for a couple hours with different programs and simulation software open, so tackling them during the course of a hand is unlikely.
What you should get out of this column is that edges are not always good as you think, especially in tournament poker where the value of the chips is hard to quantify. Don’t leap into a call because you are a favorite, make sure you’ve thought through what ramifications winning and losing the hand will have on your equity and not just your chip stack.
Furthermore, don’t discount the possibility that your calculations may be off in either direction.
If you are an obvious risk-taker you may want to error on the side of caution to even things out, and if you are quite conservative you may want add a couple percentage points to make up for your lack of confidence.
