# An Analysis of the “Double Bubble” Payouts Planned for the 2015 PCA

As recently reported by Giovanni Angioni, PokerStars Head of Poker Communications Lee Jones posted a notice announcing that three preliminary events at the 2015 PokerStars Caribbean Adventure will use a new “Double Bubble” payout structure.

In the Double Bubble structure, half of the field gets back their full buy-in, paid at the table immediately after 50% of the players have been eliminated. The rest of the prize pool is then distributed to the top 8% of the players, using a standard graduated payout structure.

There are only three Double Bubble events on the current 2015 PCA schedule (two \$2,200 events and one for \$1,100, the latter being “Winner Take All” for the remaining 50% of the prize pool). But if they become more common, how would the structure affect long-term expected value compared to more standard payouts?

In order to address this question, I whipped up a couple of computer simulations to show what happens. Note: this version of the simulation does not take skill into account — in other words, all players in the simulation have an equal chance to cash.

Looking back over previous EPT series, preliminary events in the \$1,000 to \$2,000 buy-in range have tended to draw around 200 entries, so I used payout structures from those events as a starting point (without access to PokerStars’ formula for payout structures, this is simply an estimate).

At 200 entries, they pay around 27 places, and a graph of the payouts for a \$2,200 buy-in (with \$1,940 going to the prize pool) looks like this (click any of the images below to enlarge):

For a 200-entry game, 8% of the field would be 16 players. I didn’t find a 16-player payout, so I used an EPT structure paying 17 places. For a \$2,200 event with a prize pool of \$388,000 (200 x \$1,940), \$220,000 would be reserved for the base payouts (the 100 players getting their buy-ins back), with the other \$168,000 going to the players in the top 8% (on top of the \$2,200 each of those players also receives).

This, then, is an estimate of what the Double Bubble payout structure looks like in for 200 entries:

Over a number of similar tournaments, if the same players competed in 10 games each, here is what the graphs look like — the black line is median earnings for each position, while the green shows the range of earnings for players in a particular rank over 100 runs of the 10-game simulation:

As you can see, the non-profitable players in Double Bubble are quite a bit less non-profitable, on average. The median loss is about half what it is in a standard structure, about 40% instead of 80%. That money, of course, comes at the expense of the profitable players.

Here’s the same side-by-side comparison over a longer term — 100 games:

And if you really want to know how the really-long-term EV compares, all things being equal, we eventually reach equilibrium at about -12% ROI for both payout structures — not coincidentally at the amount of rake paid! It’s all a matter of how long it takes to get there. Looking at 10,000 games...

In his announcement, Lee Jones writes that “increasing the number of players who get something back is preferable to putting an extra bonus on top of the already staggering size of the prizes at the top.” The Double Bubble payout structure indeed does exactly that — sharply reducing the losses of most of the players, if not making anyone more profitable.

For a single tournament — as happens with almost any reconfiguration of payouts — the money comes off the top, roughly halving the top 3 or 4 payouts (if my estimates are correct). Depending on the actual formula used, it’s possible that players on the second table of a Double Bubble might get more than they would under the conventional structure.

If you’d like to try out a few variations for yourself, the EPT sim and Double Bubble sim were created on JSFiddle with JavaScript using the Amcharts graphing libraries.

Darrel Plant lives in Portland, Oregon. A computer programmer by profession and a game player at heart, he writes about math and poker at his blog, Mutant Poker.