Don't Blow Your Tournament Bubble
One of our most important tournament strategies is how to play when we are "near" the bubble with a short stack. I discuss this topic in detail in Chapter 11.4 of my new book, Tournament Poker for the Rest of Us. The lesson is clear: folding our way to a min-cash is nearly always more profitable than risking our cash.
Suppose we begin Day 2 of a World Series of Poker event with a 15-big blind stack. We expect the bubble to burst in about an hour, costing us about 8 BBs if we fold every hand. We check the chip counts and see that we are 950th out of 1,000 players remaining, with 900 players cashing.
Should we play aggressively, trying to chip up? Or should we fold our way to a min-cash?
Many players (and pundits) might feel the need to gamble in order to make the money. Others feel they should gamble even with a much larger stack, believing this to be the best way to win the tournament. Fortunately, the correct answer can be determined by close study of WSOP finishing statistics.
For our purposes, let's go back and study results from the "Double Stack" event during the 2018 WSOP. I'm using reports of Day 2 starters and their starting stacks and of cashers as provided by the WSOP. Entering this data into a spreadsheet helps reveal some interesting trends.
This $1,000 no-limit hold'em event had exactly 5,700 entries take part over two starting days, with each entry starting with 10,000 chips. A total of 1,280 players made Day 2 and 856 players eventually cashed, meaning 424 players busted on Day 2 without cashing.
Based on previous WSOP history, the Day 2 starters could expect to cash after about 2.5 hours of play, so they would need about 20 BBs to (barely) fold their way to the money. "Figure 1" above depicts the Day 2 starting stack sizes for all of the Day 2 Busters, showing that 64 percent of them began the day with at least 20 BBs. About half of these Busters started Day 2 with at least 25 BBs, and 92 Busters (22 percent) started with at least 40 BBs!
In other words, at least half of the Busters simply blew their "guaranteed" cash. Perhaps they were trying to win the tournament, or perhaps they were simply unaware of their situation when beginning the second day.
Deeper Stacks Don't Help (Much)
Many players believe that they must build a large stack in order to finish high and are willing to take large risks to do so.
Figure 2 below shows the finishing place for all players who cashed, versus their Day 2 starting stacks. There is a clear trend line — more chips leads to a better average finish (duh!). But the scatter in the data is enormous. One remarkable fact about this graph is that I found the same trend for every WSOP tournament I analyzed, including the Main Event. This trend seems to be a fundamental aspect of tournament poker.
We all expect our Day 2 stack size to play an important role when determining our eventual finishing place, but this graph makes it clear that there is a huge random element as well. One Buster started the day with a whopping 145 BBs, while another player started with 237 BBs and barely min-cashed.
We can see in this event that the trend line finish for a player starting with 20 BBs was 490th place, which was worth $2,038. But a player starting with 100 BBs finished only a moderately better 333rd, worth just $2,819. On average, a 5x larger stack was worth only an extra $781 (38 percent). This is a consequence of the typically slow pay jump increases until we get closer to the final table.
The Value of Folding
These statistics make it clear that patience is key to making the money when we are close to the bubble. As an example, let's look at a situation I faced when playing the last hand of Level 10 at the 2018 WSOP Seniors event. At the time I had 10,400 chips in my stack and I knew that the bubble would burst about 20 hands into the next level.
The blinds were 400/800 with a 100 ante and the UTG+1 player (with 30,000 chips) opened to 2,400. It folded to me, four off the button, and I had pocket jacks. Many players would shove in this spot, but would that be the correct play?
Suppose I fold the jacks, plus my next 20 hands. My expected value for folding is at least a min-cash (Cash1 = $1,500).
Suppose I call instead. That would leave me with 8,000 chips and six players behind me yet to act. I am left in a tough postflop situation even if no one behind me raises; I can't put any more money in the pot without risking my cash. So I should not simply call the raise.
Suppose I shove. In that case my $EV would be: $EVShove = FE × (Cash2) + (1-FE) × (EWC) × (Cash3) where FE is my Fold Equity and EWC is my Equity When Called. The first term is my EV when everyone folds; Cash2 is the amount I make with my slightly larger stack. The second term is my EV when I get called and win the pot; Cash3 is the amount I win with my double stack.
Suppose my FE and EWC are both 50 percent. Then I will increase my stack to 15,200 chips half of the time, when everyone folds to my shove. Figure 2 suggests that these extra chips will not significantly impact my trend line finish, so Cash2 is similar to Cash1.
Half of the time I am called and half of those times I win, increasing my stack to about 22,600 chips. Again, doubling my stack from 10 BBs to 20 BBs does not significantly improve my trend line finish.
From this we can make an approximation and assume that Cash2 = Cash3 = $1,500. Then our $EV for shoving would be only $1,125. If we use Figure 2 to estimate the values of Cash2 and Cash3, our negative $EV for shoving would be only slightly higher. In either case, calling is much more profitable than shoving.
We can play around with the FE and EWC values and see that there are no practical situations where it is +$EV to shove.
If our FE is 100 percent (essentially never), our $EV is nearly unchanged since a few additional chips will not impact our eventual prize. When our EWC is 80 percent (such as with pocket aces), our $EVShove will be less than EVFold unless Cash3 is high enough to balance those times we lose. And Figure 2 shows that this will not be the case.
Useful for All Tournaments
This strategy is not just for the big WSOP summer tournament series. It is applicable for any tourney where we have an accurate knowledge of when the bubble will burst.
For example, we might play in our local $100 tourney every Sunday and have an excellent knowledge of when the bubble will burst. Playing well near that bubble can have a huge impact on our long term profit.
I realize this "cash first" philosophy is controversial. But the statistics are clear — taking excessive risks to build a huge stack does not return a commensurate reward. Doubling our stack does not come close to doubling our prize.
I am not suggesting that we always fold to a min-cash when we are near the bubble. When our stack is too small, or even borderline, we must take some risks to build it. When our stack is large, we should use it to build an even larger stack as long as we can do so without jeopardizing our cash.
Folding to a cash is our most profitable line only when we have the appropriate stack size.
Steve Selbrede is the author of six poker books: The Statistics of Poker, Beat the Donks, Donkey Poker Volume 1: Preflop, Donkey Poker Volume 2: Postflop, Donkey Poker Volume 3: Hand Reading, and Tournament Poker for the Rest of Us.