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Old 10-11-2005, 03:39 PM
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Default Re: Hypothetical Question

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
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