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interrobang
DramachinePosts: **25**Registered User

interrobang wrote: »...that my pair of 2s will beat A-K unsuited, with no other players in the game? This number might help me a little bit when trying to extract chips from bingo players.

Thanks!

RobR

22 will win 52.75% of the time. You have a coin flip scenario.

QQ sends you to 57%, still a coin flip.

## Comments

1Registered User New to the Forums12Registered UserI bet on black, not on red.

25Registered UserIsn't that 53% figure against an unknown hand, or is it against A-K unsuited?

But most of the time when I run into a bingo player, he doesn't go all in with every single hand. I can assume he's got something halfway decent, such as A-K unsuited. So I'm curious about what my chance of winning with 2-2 vs A-K is.

Let's see. The chance of filling a pair if your hand does not have a pair is 8 out of 50 for the first flop card, or one in 6.5. Muliplied by 5 for the five cards on the table, the chance of ending up with a pair is pretty close to 5 out of 6. On the other hand, for my 2s to win, either he has to miss his pair (1 out of 6 chance), or I have to get another 2 (2/50 * 5, or 1 in 5), or I have to fill a straight or flush from the table (odds too small to make a difference here). So I've got a 1/6 + 1/5 = about 1/3 chance of winning.

That analysis holds true for any hand where I have a pair and I guess my opponent does not have a pair but both his cards are higher than mine.

Am I correct?

RobR

150Suspended UserHi there Rob,

Odds of pocket 2s vs AK is 51.93% to 47.42%. Odds to tie are .65%. If the AK is suited, the hand is almost even. Pocket pair is favored, but essentially a coin flip.

17Registered UserIt would be a mistake to call with 22 against a bingo player you suspect is not shoving with any two. 22 is almost exactly 50/50 against a random hand. The more hands you can take out of his range, the worse 22 performs. If he's shoving good Aces, he is almost certainly shoving with good pairs too. Against a range of hands such as: A7 - AK, 66 - AA, the equity of your Deuces drops to 40%.

Even against someone you believe is shoving any two cards, you can pick better hands than 22. Obviously better pairs such as 66 and 77, but also any two broadway cards Jack or better, are going to be at least 60% against a random hand. If you're happy with 55%, any Ace and any King down to K7 will do. JT and T9, both suited, will also work.

Good luck at the tables.

5Registered User Not a Title, but a StarI am intrigued by your theories and would like to subscribe to your newsletter.

25Registered UserRobR

25Registered UserRobR

6Registered User Not a Title, but a StarThe thing is they're not always going to have AK, if you widen their range to something like; 66-22,ATs+,AsKh,AQo-ATo you'll have 41.275% equity vs their range.

I've only played like 50 hands of Zynga poker so I don't really know what they're thinking, maybe they shove tighter or looser IDK

You're pretty much never going to be ahead, try and play actual poker instead of just calling shoves pre.

25Registered User1. Mike and PokerOptmi5tic, what is the source of your numbers?

2. Where is the error in my analysis?

3. It should be possible to write a program that would compare a hand consisting of 22 and 5 random cards against AKo and 5 random cards repeatedly and keeping track of the wins vs number of hands (a Monte Carlo test). I am a software developer, and I'm sure I could write such a program. But like any good software developer, I'd rather use something someone else already wrote. Can anyone point me to a web site where I could download a program that does this?

Thanks again!

RobR

P.S. The following web site contains a download link for a library of sophisticated poker hand evaluators, in case anyone's curious: http://www.codingthewheel.com/archives/poker-hand-evaluator-roundup#senzee_eval7

25Registered UserYes, in practice that's true. I find that my bankroll increases as my frequency of trying to punish the bingo-players decreases.

RobR

76Facebook Connect UserSorry, not even close to being true.

AA versus AK os = 91.75% favorite for the Aces. I will win 92 out of 100 hands with this scenario, over the long run.

AA versus any other hand, heads up is always favored. That is why you want to isolate against one player while holding AA. **** near impossible in here but that is why Zynga seems to be tilted towards crappy hands. There are too many chasers who will chase anything.

17Registered UserPokerStove is a free app that does exactly what you have described, and more. It's where I got my 40% figure, taken against a range of hands A7-AK and 66 - AA.

You can download it here: http://www.pokerstove.com/

25Registered UserRobR, still curious about what's wrong with his analysis

80Registered User Black Sheep of ze Internet17Registered UserWhat's wrong with whose analysis? Actually, everyone who has posted actual figures (with exception to the 50/50 guy) has been correct. It's just that all of our numbers mean different things. The 52% figure is only if you're against specifically AK. But in practice you'll never know you're against specifically that hand or a similar hand, which is why we do what's called assigning

hand ranges. The 40% figure that Mike McD and I came up with, is how 22 plays against a range of hands that someone not playing any two cards is likely to shove.7Facebook Connect User Not a Title, but a Star25Registered UserNo, my analysis was specifically 2-2 vs AK offsuit. The same analysis applies to 2-2 vs any non-pair hand with cards higher than 2. So, according to me, 2-2 would win less than 40% of the time against 3-4 offsuit, against 5-6 offsuit, and so on. And everybody with exact numbers for 2-2 vs AKo has disagreed with me, including you, Mike, and expert commentators on poker tournaments. Someplace, I'm wrong, and I'd like to know where. I disregarded the chances for straights and flushes, figuring they'd be too rare to affect my approximation. Was that wrong?

RobR

25Registered UserRobR

159Registered UserI'll make this two approximations:

I'll calculate the probability of AKo to lose, so this will be the probability of 22 to win.

AKo loses, with our approximations,

Now the calculations:

Now the conclusions: the probability of AKo to lose is the probability to have at least one 2 in the board, or, in the case there aren't any 2, to not have any A nor any K on the board, and this is 20%+38% = 58%. So 22 wins against AKo approximately 58% of the times.

As I said before this calculation is still approximate because AKo has other ways to win (most relevant ones are straights and two pairs on the board). So 22 wins a little less frequently.

A more accurate calculation would say 22 wins about 52% of the times, with little dipendence on suits. In fact the result may vary from about 51.93% to about 52.75% depending on the suits. That's why Russki Nun said 52.75%, Poker0ptimi5tic said 51.93% and Mike McDermott said 53.04%

equity(in this case, equity is calculated as the odds to win plus half the odds to tie, and the odds to tie are about 0.65%).The advice I can give to you is to memorize the odds of the main situations preflop (you can't make these long calculations during the hand), and apply the approximate formulas you know after the flop (the approximations are very good after the flop is dealt).

5Registered User Not a Title, but a Star10char

8Registered User Loose Cannon25Registered UserTom,

See the detailed anaysis above. The chance of hitting a 2 when holding a pair of 2s is almost exactly 20%. And you have to figure the chance of your opponent not getting a pair out of his A-K.

RobR

25Registered UserRobR

159Registered UserYou're welcome. And yes, you'll end up with a set about 20% of the times you hold a pair, while the probability of getting the set right on the flop is "only" 12%.

12Registered UserLOL 10char outside of quote tags.

397Facebook Connect UserTo drift to the side a bit... That is 20% if you chase all the way to the river. When I see a flop I will be seeing 3 over cards negating my 22 as a viable hand. With any bet, other then 1 BB, depending on pot size, I am gone.

461Registered User Colossal Titan SlayerI need to check the boards here more often I guess.

8Registered User Loose CannonNot exactly true. If you have a pair and they don't, you don't need to hit any cards to win.