Probability theory in Texas Holldem

**Gramazeka** · 02-18-2018, 07:05 PM

AK offsuit vs 22.

Two players are standing near a table where players play Texas Hold'em. Everyone must first choose one of these hands. The calculation between the players occurs after they distribute 5 cards to the table. What player will win over a long distance. Which hand has more EV ?

**SpikeBJ** · 02-18-2018, 07:09 PM

AK-47 against 22LR. No contest.

**Meistro123** · 02-18-2018, 07:09 PM

22 is favoured.

**lij45o6** · 02-18-2018, 07:49 PM

AKo is great, as 22 is less than both AKs and AKo in terms of EV. 22 becomes -EV with 6 or fewer players.

Think of it this way: You have a higher probability of getting An Ace high straight, pair/set Aces with a King kicker, or Aces full or King full of Aces as far from nothing can beat those with respect to your winning hand (as in: AAAKK beats QQQJJ for instance.) With a pair of deuces, hope for a set/full or quads. 22 has fewer winning option than the AK.

Now, if we were playing Omaha 8's or better...that's a different question!

https://wizardofodds.com/games/texas-hold-em/

**Meistro123** · 02-18-2018, 07:52 PM

Hold'em Simulation ?
1,712,304 trials (Exhaustive)

Hand	Equity	Wins	Ties
AsKh	47.74%	811,899	11,179
2s2h	52.26%	889,226	11,179

**lij45o6** · 02-18-2018, 08:05 PM

Originally Posted by Meistro123

Hold'em Simulation ?
1,712,304 trials (Exhaustive)

Hand	Equity	Wins	Ties
AsKh	47.74%	811,899	11,179
2s2h	52.26%	889,226	11,179

Interesting! I wonder why Wiz got different results. And from some Google-fu, it seems that if AK and 22 are near each other in terms of Expectation for AK suited but not AK off. I wonder why that is?

**Gramazeka** · 02-18-2018, 08:09 PM

I have so far proved that comparing the counting systems ( Hi Lo vs Hi opt 2 ) on in computer simulations, the minimum is not correct-and before you got it, it took many years. Now take a look at this task. Where is your IQ ? ))

**lij45o6** · 02-18-2018, 08:10 PM

Originally Posted by Gramazeka

I have so far proved that comparing the counting systems ( Hi Lo vs Hi opt 2 ) on in computer simulations, the minimum is not correct-and before you got it, it took many years. Now take a look at this task. Where is your IQ ? ))

???

**Gramazeka** · 02-18-2018, 08:16 PM

that you do not understand from my text ? Sorry, my English is bad. I use google translate (( I did not mean you specifically, but most users on the forum...

**Meistro123** · 02-18-2018, 08:18 PM

, it seems that if AK and 22 are near each other in terms of Expectation for AK suited but not AK off. I wonder why that is?

I mean, it should be obvious, AKs hits a flush much more frequently than AKo.

**ShipTheCookies** · 02-18-2018, 08:23 PM

https://www.cardplayer.com/poker-too...r/texas-holdem

**lij45o6** · 02-18-2018, 08:23 PM

Originally Posted by Meistro123

I mean, it should be obvious, AKs hits a flush much more frequently than AKo.

*facepalm* You are right.

Yet, still surprised that AKo is beat by a pair of swans? Would this be due to the fact that we start off with a pair initially?

**lij45o6** · 02-18-2018, 08:26 PM

Originally Posted by Gramazeka

that you do not understand from my text ? Sorry, my English is bad. I use google translate (( I did not mean you specifically, but most users on the forum...

Thank you for saying. I was confused by your text.

Let me say that there are native speaker who posses worse English skills than you, sir.