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:
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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:
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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...
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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.
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