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 GameSlush.com (apart from the bad deals you might get playing a card game there).

Does PokerStars manually control when the Big Deal jackpot is won?

(Update: the jackpot as of 12:30 GMT Friday,  January 27 is now over $470,000. Given that there now have been roughly 21.8 million losing entries, if the odds of the hitting the jackpot are truly 1 in 5,197,920, meaning that the jackpot wheel is fair, neither predetermined or unevenly weighted, we should have expected the jackpot to be hit 4 times by now. Stated in different terms, the probability of NOT hitting the jackpot after 21.8 million tries is roughly 1.5%. So in true PokerStars fashion, after just about one month since the introduction of “The Deal”, we are supposedly already hitting 66 to 1 long shots.)

Right after publishing the article on the expected value of The Deal, the jackpot has vaulted beyond the break-even point of $272,000 (at the time of writing this article, it stands at $307,000).

There is nothing in their rules stating the probability of spinning the jackpot, so far all we know it could be completely fixed.  But just to gauge the unlikelihood if the original assumption that every spot on the wheel has equal probability of getting hit, the odds of winning the jackpot per 7 StarsCoin is still 1 in 5,197,920.

For the current jackpot to be reached, given that 77% of $0.028 goes towards the progressive jackpot per 7 StarsCoin entry, there have been approximately at least 13,000,000 losing entries at the time of writing this article. This is well beyond the 5,197,920 expected average. (It should be noted there is no difference between entering with 70 StarsCoin versus playing 7 StarsCoin ten times in terms of probability of hitting the jackpot since adding the 36 straight flush possibilities in the 70 StarsCoin case increases the likelihood of a jackpot spin exactly ten times).

I suppose the jackpot could theoretically grow forever but the unlikelihood already of having a jackpot beyond the break-even point makes me wonder if the jackpot is manually controlled to encourage more people to spend their rakeback on a bad deal, since there is no indication anywhere on their Terms of Use or rules page denoting the exact probabilities of the wheel and the game itself.  Who knows, maybe the outcome of the cards in “The Deal” are controlled too.

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If you don’t like a rigged game, perhaps you’d enjoy playing instead at GameSlush.com.

The expected value of playing The Deal at PokerStars

“The Deal” is a recently released promotion from PokerStars that allows you to gamble their rakeback currency, “StarsCoin”, for a crack at a progressive jackpot — a concept no different than traditional slot machines.

For the purposes of evaluating an exact EV, 1 StarsCoin (SC) is assumed to be equal to $0.01 (since in the VIP store you can redeem 1,000 StarsCoin for $10).  Also, it is assumed the jackpot wheel has equal probability of hitting any space, and thus you have a 1 out of 8 chance of winning the jackpot on any jackpot spin.

For a $25,000 jackpot, which the winning share takes $12,500, the expectation hovers around -34%:

Hands Probability 7 SC Paytable 7 SC EV 70 SC Paytable 70 SC EV
Royal flush 4 0.00000154 3,563* 0.00548625 3,563* 0.00548625
Straight flush 36 0.00001385 250 0.0034625 3,563 0.049340625
Four of a kind 624 0.0002401 30 0.007203 300 0.07203
Full house 3,744 0.00144058 5 0.0072029 75 0.1080435
Flush 5,108 0.0019654 1 0.0019654 25 0.049135
Straight 10,200 0.00392465 0.5 0.001962325 10 0.0392465
Three of a kind 54,912 0.02112845 0.25 0.005282113 3 0.06338535
Two pair 123,552 0.04753902 0.07 0.003327731 0.7 0.033277314
Pair 1,098,240 0.42256903 0.02 0.008451381 0.1 0.042256903
Ace High 502,860 0.19349 0.01 0.001934851 0 0
0.04627845   0.462201442
        66.11%   66.03%

For a $150,000 jackpot, which the winning share takes $75,000, the expectation hovers around -17%:

Hands Probability 7 SC Paytable 7 SC EV 70 SC Paytable 70 SC EV
Royal flush 4 0.00000154 11,375* 0.0175175 11,375* 0.0175175
Straight flush 36 0.00001385 250 0.0034625 11,375 0.15754375
Four of a kind 624 0.0002401 30 0.007203 300 0.07203
Full house 3,744 0.00144058 5 0.0072029 75 0.1080435
Flush 5,108 0.0019654 1 0.0019654 25 0.049135
Straight 10,200 0.00392465 0.5 0.001962325 10 0.0392465
Three of a kind 54,912 0.02112845 0.25 0.005282113 3 0.06338535
Two pair 123,552 0.04753902 0.07 0.003327731 0.7 0.033277314
Pair 1,098,240 0.42256903 0.02 0.008451381 0.1 0.042256903
Ace High 502,860 0.19349 0.01 0.001934851 0 0
0.0583097   0.582435817
        83.30%   83.21%

* based on 1/8 probability of hitting the jackpot, 1/4 of winning $500, 1/8 of winning $1,000, $2,000, $3,000, $4,000 or $5,000.

It is unlikely* for the jackpot to exceed $150,000, so under no realistic jackpot conditions is “The Deal” favorable to the player. In fact, the jackpot needs to grow over $272,000 for the EV to be positive(*Update: the jackpot as of 12:30 GMT Friday,  January 27 is now over $470,000. Given that there now have been roughly 21.8 million losing entries, if the odds of the hitting the jackpot are truly 1 in 5,197,920, meaning that the jackpot wheel is fair, neither predetermined or unevenly weighted, we should have expected the jackpot to be hit 4 times by now. I said it was “rare” for the jackpot to exceed the break-even point, but it is likely that my assumption of the probabilities of the jackpot wheel are incorrect, despite the wheel graphic showing a supposed one-eighth likelihood per section. See Does PokerStars manually control when the jackpot is won?)

If you play once exactly every 12 hours for the minimum, then you may end up with a better return only because you may get a share of 50% of the jackpot that is evenly divided among all non-winners of “The Deal” in the past 12 hours when a jackpot is won. Anecdotally, this amounts to about $1 every three days or so (thus, $1 every 42 StarsCoin, which puts the expectation now in favour of the player, at the expense of all other players that play more than 7 StarsCoin per 12 hours).

It is evident that this strategy heavily relies on fewer unique players putting in a lot of their StarsCoin into the progressive jackpot. If everyone were to follow this strategy of maximum 7 StarsCoin per 12 hours, “The Deal” is a huge losing proposition for all players, and a very well-obfuscated one that greatly increases PokerStars’ profit.

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You may like playing at GameSlush.com instead, where you can lose fake money to the house and not real money.

Facebook Games: the 90’s called and MSN Messenger wants its users back

Facebook has decided to roll out games on its app.  We are reliving the technological cycle that came with MySpace and MSN Messenger in the late 90’s and early 00’s.

In the latest version of the app, open a conversation with a friend (or friends!), tap on the game controller icon just below where you type your message, and choose a game to start playing right away. After you finish a round, people in the conversation will see your score and will have the opportunity to challenge you back.

Game On: You Can Now Play Games on Messenger

If anyone remembers MSN Messenger back in the day, it had this exact same feature with its set of supposed “classic games”.  Since then, it has been obsoleted by Skype, which does not feature games in its app.

Is the idea to make its users spend more time in app, which supposedly will increase advertising or micro-transaction revenue? If history dictates anything, this fad will be short-lived. What makes Facebook less immune to a collapse like that of MySpace and MSN Messenger?

After all, I entered the online “classic game” arena with GameSlush.com after seeing the disappearance of Yahoo! Games and MSN Games. These behemoth companies, Yahoo! and Microsoft, have already cut their leisure gaming divisions because they simply don’t make enough return on investment for their upkeep and development costs.  On the other hand, it really does just take a staff of one (e.g. myself) to replace that niche market, resulting in a nimbler game venue that can pivot easier to what the users want.

If Facebook wants to pile on money hiring dozens of graphic artists, game developers, and software engineers for their new gaming division, that’s their choice. I’m not sure if they did their research on what happened in the past with Microsoft and Yahoo. Let’s see how investors react and whether they can recognize that history may be repeating itself.

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If supporting small business and classic games pique your interest, GameSlush.com might be for you. If you want to support Zuckerberg and his desire to build a tech monopoly, that’s up to you too.

List of MSN Gaming Zone Backgammon Cheaters

[Update: MSN has removed Backgammon from its games. Probably because of the rampant cheating. For a more fair place to play Backgammon that minimizes the chance of cheating (particularly because of the availability of instant replays) try https://www.gameslush.com/backgammon]

Figured I’d compile this list after seeing several cheaters that exploit the “repeated-undo stall/timeout” bug. Hopefully this list will help legitimate players safely quit the game before entering a match with these sociopaths. Don’t know why these cheaters spend so much time on such fruitless (and mindless) idiocy when they could instead devote their efforts to learning how to play properly. It becomes obviously fishy when these players rated 2000 and higher play so poorly … you can smell the undo-stall cheat coming from a mile.

Here’s the list so far and I’ll update it as it grows:

nabnabnab8
Long_TeaBagger
rollierocket
OP91
Tricked_Safe1
yambag7
PerfectBalance5
SlowerLeech
BestInTheWest67
Deadly_Timing
Monteceito
StainableMetal
Master_of_Dice
quickie1913
SteadierPig6
OBX_7
TempFormula6
Emilian11

2015-01-07: WirierCloth

More as of 2014-07-31:
opticstwo
prancing_horse2
GogglesPaisano5

More as of 2014-06-13:
EnamoretedAunt
HitByABus
Length_Axis

More courtesy of the Microsoft community forums thread:
Ciscoman9
filini
smuglight
future_seer
sprite
Elephant__
LolaBadGirl
George1772
Guest (with 23,000+ games)
Guest (with 10,000+ games)
RiskQueen

Edit — thanks to Bob_Who for the following update:

Novy22
CrazyFastTD
TutorialCoder
Tigermartin7890
Sieeeeeeeb
MD_Danny
Tradable_Toast
ErrantMarlin
eastcoast_poker
Burdened_Steet
PADDLES__
Peak_Wizard0
Gammon4all
Eqlant
BobbyJ30
PSstarman1
Barmy_Quotient

Courtesy of this video (link):
CulichiGuapo

Prior to 2012-10-14:
Stereo_Chart
NathDan0615
Cursive_Tiger
BCCFMPTN
hunter_gunter

An efficient but effective artificial intelligence for Big 2

(tl;dr: You can play against an AI computer user I designed for an online Big 2 game here.  The bots are capable of calulcating the expectation for its score for every possible line of play very quickly, resulting in a rather worthy opponent for even the most seasoned Big 2 players).

The dynamics in Big 2 make programming AI for it an interesting problem.  The usual “game tree” approach when solving games like Chess or Reversi can still somewhat be applied.  However, like programming optimal AI for backgammon, there is an element of the unknown to be included.  We know the cards we hold in our hand, but how might they be distributed amongst the other concealed hands?

There are many other factors that human players have to their advantage.  They can spot and exploit players’ weaknesses and habits, bluff, and come to logical conclusions putting those two weapons together.

Emulating this behaviour and analyzing a fairly large “game tree” makes designing a fast, yet effective AI for Big 2 a challenge.  For AI that is controlled by the server (for obvious reasons it is server-side and not client-side), we have to be careful too to not take up many cycles per AI decision.  The assumption is that multiple computer players will be running at once, so for a multiplayer online gaming site, CPU cycles for AI should be minimal.

So instead of a game tree where we guess what cards will be played (and where they lie) and determine the optimal play by looking ahead, the approach taken is one giant heuristic: let’s calculate the expected value of a play simply from the cards we see and the cards we did not see up until the play.  Ultimately the goal of Big 2 is to get rid of all your cards, so we simplify the calculation by estimating how many cards will be shedded by playing a certain hand.

The process is simple: when it’s the computers turn, what are all the possible plays we have?  If a single was played, we can play another single, or pass.  If the computer is leading, then anything is possible, but passing.  Whichever the case, we have a small finite set of moves.  Now for each move, how will our hand look like after?  What will our possible plays be?  To answer this problem, we treat it as if the computer is leading a hand, and determine the set of all plays regardless if we are approached with a single, double, triple or poker hand.  Now, given the cards that are concealed in everyone else’s hand (and we know the exact set of cards, since the computer easily tracks what cards have already been played, we just don’t know how these cards are distributed — we could guess and assign probabilities, but for purposes of efficiency, we opt not to) let’s calculate how many cards we expect to shed by the end of the game.  If one of our plays in our “future” hand contains a poker hand, how likely is it going to beat all the other possible poker hands out there?  If it beats all the other possible poker hands (or a high percentage of them), how likely are we even going to be seeing a poker hand in play?  That factor is nil if the remaining players have 5 or less cards each.

Anyway, just by answering those questions above you have a relatively good gauge on expected value, and interestingly enough figuring out these probabilities is fast, by applying some good finite mathematics formulae.  One thing that human players do well is to have a game plan to run out their cards, waiting for a deuce to be played to promote one of their deuces, giving them an unbeatable exit plan.  To emulate this on the AI side, we simply do a small probability assignment ourselves: when we know a certain line of play has hands that can be unbeaten (or close to unbeaten), we can boost the probability to 1 (or close to 1) for a weaker hand that had no chance of being played unless the computer leads it itself.

So with the original probabilities calculated and the “fudging” of probabilities to emulate creating a “game plan” with a certain line of play, we have a rather decent AI for Big 2 that can give even the most seasoned players a challenge.  Although the computer still does funny stuff from time to time, it makes up for its shortcomings by doing pinpoint probability calculations quickly, and also has the inhuman ability to figure out exactly what cards are left, to accurately determine the strength of its hand.

So how does it play?  You be the judge!