Daily Series #1: Geeking out → Poker Math

I will continue with this series for people who like this kind of content, drop "+1" in the chat and I will tag you the next time I post content.

I assume you guys know some basics of Texas Hold'em Poker. Flop refers to "the dealing of the first three face-up cards to the board"

Now, let's look at the table and their positions:

1. Blinds: First to act every street after pre-flop.
2. Early positions: Under the Gun(UTG)
3. Middle positions
4. Late positions: Button and Cut Off

The order for a 10 person game would be: Small Blind(SB) → Big Blind(BB) → Under the Gun(UTG) → UTG+1 → UTG+2 → MP1 → MP2 → MP3 → Cutting off the Button (CO) → Button (BTN) and then order repeats ...

Some insights:

1. Blinds see the flop at a discount because they are compelled to play but are at a disadvantage because they are first to act.
2. This means that more money is made in late positions because they have more information to act on.
3. However in short stack situations, where effective stack size is small then early positions are better because you have the opportunity to go all in before someone else can as you can maintain Fold equity(Equity from Aggression).

So, Expected Value or E(V) is how do you determine whether you should call or fold basis the size of the pot and your contribution to it basis the number of outs(potential winning hands) you have.

E(V) = Win % * Win Amt - Lose % * Lose Amt

For example: Villain(V) [UTG+1] = $500 Hero(H) (MP1) = $500

SB/BB + Ante = 20/40 + 10 Here, Ante is the bet everyone has to make every hand. This is to make the pot worth playing for everyone.

Pre-Flop: $140 H = A 10 (suited Hearts) V = ? (Unknown)

1 Fold V raises $120 H calls $120, 5 Folds

Flop: $380 The flop is 8 Heart, 3 Heart, K Club V = $370 (All In) H = ? (Do you call or fold?)

Solution: A call is positive E(V) if: Win % > Call Amt/ Pot after Call

You have a strong hand if you can get a flush here. which means you need one of the next two cards Heart Heart Club | Heart* | Heart*

Which means: Win % = 1 - (Odds of 2 cards not being Hearts) = 1 - (40/49 * 39/48) = ~ 36%

So, 370/1120 = ~33% is Call Amt/Pot after Call

Since, 36% > 33% Hero should call.

E(V) = 36% * (380+x) - x * 66% E(V) cut off at 0,

x = $404

You stand to make $ if you decide to call that bet. You can raise any amount till $404 for a positive E(V) after which you should mathematically fold.

An easier way to calculate this is to use 2% if you can only see one card after flop and 4% if you can see both cards.

That way, Win % here would be = 4% * 9 = 36% 9 outs because, 9 cards that are Hearts are left in the deck.