Is PokerStars “The Deal” a zero-sum game?

In reality, the short answer to this question is no, “The Deal” is not a zero-sum game. Let’s take a closer look at it.

“The Deal” is a zero-sum game in a similar way you’d consider taking odds behind the pass line bet in Craps as “zero-sum”.  In order to get to that bet, you must take a losing proposition (i.e. the original pass line bet).

PokerStars Keith over at 2+2 says:

The Deal is a zero-sum game with all entry fees going back into the prize pool. In other words, the house does not rake this game. The prize pool is allocated as follows:

  • For every 7 StarsCoin used to play The Deal, we add $0.028 to the progressive jackpot – 77% goes into the current jackpot and 23% is set aside for future jackpots.
  • The rest is distributed to players in the form of regular prizes.
  • Each jackpot starts from $25,000.

This is accurate only if the 23% allocated for future jackpots is eventually paid out in full.

If we remove the $0.028 per 7 StarsCoin from the bet, assuming that the house pays it out fully in their progressive jackpots, the expected value of the remaining payouts is roughly $0.042 per 7 StarsCoin (in fact it shows it is slightly advantageous to bet 7 StarsCoin than 70 StarsCoin):

Hands Probability 7 SC Paytable 7 SC Modified EV ($0.042 w/o JP) 70 SC Paytable 70 SC Modified EV ($0.42 w/o JP)
Royal flush 4 1.5391E-06 805.5657 0.00123983 805.5657 0.00123983
Straight flush 36 1.3852E-05 250 0.00346292 806 0.01115845
Four of a kind 624 0.0002401 30 0.00720288 300 0.07202881
Full house 3,744 0.00144058 5 0.00720288 75 0.10804322
Flush 5,108 0.0019654 1 0.0019654 25 0.04913504
Straight 10,200 0.00392465 0.5 0.00196232 10 0.03924647
Three of a kind 54,912 0.02112845 0.25 0.00528211 3 0.06338535
Two pair 123,552 0.04753902 0.07 0.00332773 0.7 0.03327731
Pair 1,098,240 0.42256903 0.02 0.00845138 0.1 0.0422569
Ace High 502,860 0.19348509 0.01 0.00193485 0 0
Total 0.04203231 0.41977138

Again, this assumes that the jackpot wheel is evenly distributed, with a two-sevenths chance of winning $500, and a one-seventh chance of winning $1,000, $2,000, $3,000, $4,000 and $5,000 each.  There is no reason to doubt the validity of that distribution based on PokerStars’ claim the game has a zero house edge and the calculations above demonstrate that.

Referring back to my prior posts, Does PokerStars manually control when the Big Deal jackpot is won? and The expected value of playing The Deal at PokerStars, I still claim that “The Deal” is a bad deal for the player and a good deal for the house.

“The Deal” stands to benefit the house in the long run even though the rest of the payouts have zero house edge. This is assuming a fair probability of hitting the jackpot. The benefit to the house is exacerbated with a controlled or unevenly weighted jackpot probability.

  • Higher jackpots encourage players to play more raked hands of poker, their main source of revenue, in order to earn StarsCoin to put towards “The Deal”. This is like having to take the pass line bet in order to get to the 0% house edge odds bet in Craps.
  • A jackpot is replenished to only $25,000 using 23% of the $0.028 collected per $0.07 attempt at “The Deal”.
    • For PokerStars to not pay out of its own pocket to reseed the jackpot, it requires 25,000 ÷ $0.028 × 0.23 = 3,881,988 losing attempts at “The Deal” at 7 StarsCoin to ensure they do not dip into the red.
    • 3,881,988 attempts at 7 StarsCoin equates to a jackpot of more than $83,695. The jackpot right now stands at $475,000 at the time of this article. Safe to say PokerStars can replenish the next $25,000 jackpot reseeds for a while with the backup money they have accumulated.
    • If the actual odds of striking the jackpot are true at 5,197,920 to 1, then it follows that on average ((5,197,920 – 3,881,988) × $0.028 × 0.23) $8,474 of reseed money per jackpot paid out will never go back to the players unless at some point in time when “The Deal” is retired, the entire backup fund is put into the last progressive jackpot.

Will PokerStars redistribute their ever growing backup fund?  If they do, then it is a zero-sum game as they have promised.  If they don’t, then it is one very deceptive way of padding their profits. In either scenario, they will still achieve their likely desired effect of encouraging players to come back every day for a shot at the $1-$2 scraps of a 50% jackpot share, and for the players to play more raked hands in order to get more StarsCoin chasing a “Bad Deal”.

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There are no bad deals at (apart from the bad deals you might get playing a card game there).

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