*Official* Stars 700k Guaranteed Monthly Sunday

[Lee Jones]

[ QUOTE ]

This deal overcompensated pepe by $9,775. His EV at the time was $130,940 but under the deal his EV was $140,715 (he had 59.8% of the chips in play so his interest in the money left for the winner was $5,980).


[/ QUOTE ]

Hmmm. I'm not sure how you came with an EV of $130,940 for pepe. Just so everybody's clear on how we did it:

1. There was a total of $317,100 in prize money left.

2. Third place was $61,600, so each player was guaranteed that. That removes $184,800 (3 x $61,600) from any computations.

3. $317,100 - $184,800 = $132,300. So if you just wanted to chop up all the money, you'd take the chip percentages and multiply by $132,300, add each one to $61,600 and that's each player's share.

4. But we wanted to leave $10K on the table, so you subtract $10,000 from $132,300 = $122,300, and then take percentages of that. You are correct that pepe had 59.8% of the chips. .598 x $122,300 = $73,135 (ignoring pennies). Add the $73,135 to the guaranteed $61,600, you get $134,735.

5. Repeat for the other two players.

Needless to say, I have a spreadsheet that does these computations for me, and we've checked it multiple times (and had it in use for over a year). Is this the only "fair" way to compute a tournament deal? Of course not. Is it one fair way to compute a tournament deal? Yes.

If your way is better, please tell me how it is.

Best regards,
Lee Jones

PokerStars Poker Room Manager

[sloth469]

[ QUOTE ]
Sure enough - I verbally awarded dankdokodang an extra $1K the second time I quoted the numbers. Damn senior moment.

I've sent him an email apologizing and threw an extra 1K FPPs his way to say "sorry".

Best regards,
Lee Jones

PokerStars Poker Room Manager

[/ QUOTE ]

Lee,

I hope you missed a couple zeros after the 1 there if you gave him $1k less than you told him you would.

[M.B.E.]

[ QUOTE ]
Is this the only "fair" way to compute a tournament deal? Of course not. Is it one fair way to compute a tournament deal? Yes.

[/ QUOTE ]
I disagree.

The "chip count" method you described does not generate a reasonable estimate of each player's current tournament equity.

The scheduled payouts were $161K for first, $94.5K for second, and $61.6K for third. Thus each player was guaranteed $61.6K, with the winner receiving an additional $99.4K and the runner-up receiving an additional $32.9K.

The flaw in the method used by your spreadsheet is that it allocates to Pepe, who had 59.8% of the chips, 59.8% of the $99.4K and 59.8% of the $32.9K. That is tantamount to assuming that Pepe had a 59.8% probability of finishing first and a 59.8% probability of finishing second, which of course is absurd.

An easy way of seeing the flaw in your spreadsheet's method is to look at what results it would give if one player had a huge chip lead. Suppose the scheduled payouts are $161K, $94.5K, and $61.6K, and the chip positions are:

3,192,400 (Alice) (92%)
208,200 (Bob) (6%)
69,400 (Charlie) (2%)

Now, under your method, Alice's share would be:

.92 x $122,300 + $61,600 = $174,116.

But that's already more than the scheduled first-place money! And it doesn't even include the $10,000 left "on the table", which most likely would go to Alice.

The chip-count method is fine when the tournament is heads-up. But it is fundamentally flawed where there are three or more players remaining.

Any method for accurately estimating the equity of remaining players would have to take account of the specific payouts for first and second place. The method used by your spreadsheet does not: its parameter is, in effect, the sum of first and second place money (less twice third-place money). Try it: your spreadsheet will give exactly the same results when the scheduled payouts for the top three spots are

$161K, $94.5K, $61.6K

as it gives when the scheduled payouts are

$192K, $63.5K, $61.6K.

That demonstrates the flaw because if you have a big chip lead, then you clearly have much more equity under the second payout structure (with more money going to first place).

Is there a better formula for calculating equity when three players remain in a tournament? Yes: click here.

Applying that formula to this past Sunday's tournament, at the relevant time stack sizes were:

691,021 (dang)
703,930 (Anders)
2,075,049 (pepe)

so each player's respective equity was $92,808.02, $93,352.12, and $130,939.86. However, from those figures you need to subtract each player's interest in the $10,000 left on the table, namely $1,991.41, $2,028.62, and $5,979.97. Thus a deal which would have more accurately reflected each player's current equity is this:

$90,816.61 (dang)
$91,323.50 (Anders)
$124,959.89 (pepe)
$10,000.00 (left on table for winner)
------------
$317,100.00

[Lee Jones]

[ QUOTE ]

I disagree [that the PokerStars way of computing the chip count chop is fair].

The "chip count" method you described does not generate a reasonable estimate of each player's current tournament equity.


[/ QUOTE ]

Hi MBE -
I reviewed your proposed method for chip deals (and replied to your email to me at PokerStars).

I suspect your way is better mathematically. However, there are other considerations:

1. It's computationally much more complex. That makes it harder to check our work, have others verify it, and explain it to our staff and players.

2. The way that we currently do it is a de facto standard in the business. [1] Everybody knows and understands this method.

3. As I discussed in my email to you, PokerStars (corporately) is not particularly interested in advancing the state of deal-making technology. We do deals as a service to our players, but from our viewpoint, it's better when the event is played out. Improving the quality of poker literature in that particular domain is just not what would be called "core competency" of ours (to use a popular bizspeak expression).

So at least for now, we'll continue to use the current algorithm. Remember, of course, that the players at the table are more than welcome to propose their own deals, and anybody who feels the deal is slighting him is welcome to say "No thanks."

Best regards,
Lee Jones

PokerStars Poker Room Manager

[1] If you want to call this the "VHS" of deal-making algorithms, go for it.