Hypothetical Question

[Lawrence Ng]

$1458.20/hr.

Lawrence

[UMTerp]

FWIW, after reading some of your explanations and thinking about it some more, I realized my thinking was flawed before. I'm still not sure it's $1500 profitable, but it certainly is a profitbale game (over $500/hr I'd think).

In a no limit situation, this situation could certainly be -$EV if the stacks were deep enough, but I guess that's a different question altogether.

I also ignored the "typical game" disclaimer initially and assumed that your opponents would be playing optimally against you. That made a big difference as well, as Barron brought up some excellent points regarding that aspect of the question.

[elindauer]

[ QUOTE ]
$1458.20/hr.

Lawrence

[/ QUOTE ]

If everyone folds every hand, you only make $1620, and you'll run into aces nearly twice an hour. This estimate is too high.

-Eric

[tpir90036]

My claim was based on a number that I made up because I didn't think it would be as high as people were saying. At no point did I ever think my claim would be convincing... nor is there any math on earth that would make it so.

I was thinking along the lines of the pocket aces situation that Matt Matros talks about in his book where you could be dealt them every hand and be -EV if your opponent knew you had them. That was a no-limit scenario though and is not really applicable here.

good luck.
tpir

Assume:

1. The blind structure is a $15 SB and a $30 BB.
2. You raise with your KK preflop every hand.
3. If you are called you will employ a strategy of betting every street unless you are raised, wherupon you will check/call down.

Then

1. The only hands that are correct to call you when not in the blinds are AA and KK.
Reason: The hand is only getting 7:4 immediate pot odds to flop a winner or a draw worth continuing with.

2. The only hands that are correct to call you out of the Small Blind are AA and KK
Reason: The hand is only getting 7:3 immediate pot odds to flop a winner or a draw worth continuing with.

3. The only hands that are correct to call you out of the big blind are AA, KK, and AXs.
Reason:
The 3rd conclusion requires a little explanation. The big blind is getting 3.5:1 immediate pot odds. If he has an Ace in his hand, he cannot call your bet on the flop if the flop doesn't have an ace. This means that AXo doesn't have the proper odds (4:1) to call just to hit an ace (or possibly flop a straight or trips with its kicker) on the flop. AXs on the other hand, DOES have proper odds to call.

So, if they employ any strategy other than calling with AXs, AA, KK from the BB and AA,KK from any other position, you will GAIN over them employing just the above stretegy.

This means we can reach a lower bound on your earn by computing how much you'll make from your opponents employing the above strategy.

Stealing the blinds for a round will gain you:
1.5 SB * 8 + 1 SB + 0.5 SB = 13.5 SB.
ROUGHLY once every 2.5 rounds (9 players * 25 hands = 225 hands dealt) someone will be dealt AA, whence you will lose a maximum of 18 SB with your strategy.
I will neglect the case you run into 2 AA's and the case you run into both AA and KK.
You will also run into KK roughly once ever 2.5 rounds, whence you will usually split the blinds.

Roughly once every 3 rounds(46/1326 ~ 1/29), someone will be dealt AXs in the big blind, but I will assume that you will break even with in this case, since their call is marginal.

So my rough estimate to a conservative lower bound on your earn per hour is:

[13.5SB * 2 rounds +
1.35SB * 2 hands -
18SB (lose to AA) +
0.75SB (chop with KK) +
0SB (BB has AXs once every 3 rounds, fudging it to 2.5)
= roughly 12.5 SB won every 2.5 rounds.

In one hour there are 4 rounds =>

Win rate = (4/2.5) * 12.5 ~ 20 SB/hr =

10 BB/hr or $600/hr

If players play badly, you can make much more than this. But in a game where you're not quite making 1 BB / hr straight up, you would expect most people to properly respect your KK.

Also, no one would play with you if you got KK face up every hand. This is purely a hypothetical example of theoretical value. So arguments factoring boredom of your opponents, etc. into the analysis don't make much sense to me. If you are going to assume you can get a 10 handed game going where you get KK every hand, you might as well assume everyone keeps forgetting that you had KK the previous hand and that your exposure of the current hand happened accidentally.

-v

[elindauer]

I've replied twice, and you've deleted twice. Now I'm just going to say... wrong. You figure out why!

-Eric

[elindauer]

Here are some points for you to consider:

You should look at implied odds, not immediate odds, when deciding what hands are playable against the KK. Ax is definitely playable from either blind and probably outside the blinds as well, although somewhat marginal there.

You'll chop with KK much less often than you'll lose to AA.

You're doing a lot of rounding in your final EV calculation that is going to throw off your answer somewhat.

You're basically on the right track though I think, you just need to be more precise about how often the different events occur.

good luck.
Eric

[Sparks]

Here are my thoughts, which are along the lines of Eilindauer's.

According to the fundamental theorem of poker, your opponents will always be gaining against you, and you will always be losing; but, this is far outweighed by the power of your holding.

(1) With K's face up, you should raise every time preflop (very important).

(2) Always bet, never re-raise, and always call down (this could be modified, but this strategy keeps it simple)

Only AA has equity against you, and one of your 9 opponents will have it a little more than twice an hour, say 3 times. So 37 times an hour you win the blinds ($50) and 3 times an hour you lose 90 + 30 + 90 + 90 = $300. (when in position, you call, when first to act, you bet and call a raise, so the average is 90 on the turn and river)

You'll be making 1850 - 300 = $1550.

Once your opponents see that they can't bluff you, they will stop calling with anything but AA. Or, they will go broke.

Sparks

edit: should probably be 120 on the turn and river since your opponents will quickly learn to c/r you with AA.

[elindauer]

[ QUOTE ]
I was thinking along the lines of the pocket aces situation that Matt Matros talks about in his book where you could be dealt them every hand and be -EV if your opponent knew you had them. That was a no-limit scenario though and is not really applicable here.

[/ QUOTE ]

I'm not familiar with the example, but claim AA in no limit is always profitable. Move in preflop. Perhaps you meant pot-limit with deep stacks?

Either way... yeah... thinking along these extreme lines far overstates the impact that your opponent's knowledge of your cards is going to have. You'll make much less money than KK face down... but you'll still make a ton of money.

-Eric

[mike l.]

i must be getting good because my first answer was "an awful lot" and then i went straight to your answer and saw i was right. so now i dont even need to look at all the other answers ill just wait until sklansky posts his in about a month.