[Disturbed]

Reading alot of books and articles online alot are suggesting playing groups 1-3 or 1-4 only in texas holdem and especially in cash games.

So I thought I would make this calculation to see what return would be. Unfotunately it was negative meaning I made a mistake (probably) or all those people are wrong.

Anyways here goes.

We will adopt this table for starting hand ranking and this is based on EV

TierHandsEV1AA, KK, QQ, JJ, AKs2.32 - 0.782AQs, TT, AK, AJs, KQs, 990.59 - 0.383ATs, AQ, KJs, 88, KTs, QJs0.32 - 0.204A9s, AJ, QTs, KQ, 77, JTs0.19 - 0.15


Lets play groups 1-4 in a $5/$10 cash table of 9 players. Assume I buy in at $5k.

We have a total of 23 hands in those groups to play out of a possible 169 possible hands. Hence we are playing at around 14% (23/169) of all hands only.

Now assume we see 1000 hands.

First each 9 hands will cost us $15 (1 big + 1 small blind) to see, hence we need $1667 (1000/9 *15) for blinds to see those 1000 hands. That will be our investment.

Now we will calculate the average EV for all 4 groups:

1: (2.32+0.78)/2 = 1.55 * 5 = 7.75
+
2: (0.59+0.38)/2 = 0.49 * 6 = 2.94
+
3: (0.32+0.20)/2 = 0.26 * 6 = 1.56
+
4: (0.19+0.15)/2 = 0.17 * 6 = 1.02

=13.27 => Average EV for first four groups is 13.27/23 = 0.58

Now we are gonna see 1000 hands, and we will play 14% of those ie 140 hands played.

EV per hand is 0.58 *BB ($10) = $5.8

so EV for all 140 hands is 5.8 * 140 = $808 This our return on the intial investments of the $1667.

Is this right? My ER wont cover the blinds to play groups 1-4?

Can anyone comment on this pls.

I think something is wrong with the EV monetary value on each hand.