BY BARRY GREENSTEIN / THREE-TIME WSOP CHAMP & TWO-TIME WPT CHAMP


Editor’s Note: This article is adapted from materials in the Red Pro Discussion Forum on PokerRoad.com.]

THE WAY POKER PLAYERS ARE, once we believe we are making the correct play, it is hard to convince ourselves that anything other than bad luck is to blame for the times it doesn’t work. And when it does work, we have been given positive reinforcement to keep playing incorrectly.
I was listening not long ago to Jimmy Fricke mentioning that Dan Kelly figured out that it is a positive expected value play (+EV) to shove with 22 big blinds with K-8 offsuit when you’re in the small blind and everyone acting before you has folded. I have played with both of these gentlemen and they are good players, but I take exception to their application of mathematics here.

When I read about mathematics being applied to poker, I find that the problem is often incorrectly solved—or the problem being explored is wrong to begin with. What follows was supposed to be a list of my top 10 reasons that I have objections to this particular shoving calculation, but I came up with some related reasons along the way, so instead, we have a top-13 list:

1. I haven’t seen Dan Kelly’s calculations, but I assume he used something like PokerStove, and gave the big blind random hands after taking a king and an eight out of the deck. In a nine-handed game, the big blind is stronger, on average, than it would be in a heads-up situation, because hands actually get stronger as people fold, since Hold ’Em is a game where high cards are correlated to better hand strength.

2. So that must mean that these calculations are right for when we are playing heads-up and we have the button, right? Wrong. There is less in the pot in the way of antes if you are only playing heads-up. Players with these incorrect shoving and calling ranges often forget that we don’t have eight or nine antes in the pot when we play heads-up poker.

3. These calculations and plays are dependent on the ante structure. If someone wanted to run a simulation, they should use a 1:5 ratio for ante-to-small-blind for online tournaments (that’s what PokerStars uses for later stages) or a 1:4 ratio for live tournaments (typical for big live tournaments).

4. So except for ante considerations, the calculation is right, isn’t it? No. As stated in Item 1, our opponent’s hand will be stronger than random. As I showed with a simulation (which you can find at http://barrygreenstein.com/aces.txt), you will get pocket aces around 1 out of 134 times, instead of 1 out of 221 times, if everyone folds to you in the big blind in a nine-handed game.
This is approximately the number you would get dealing with four aces in a deck of 40 or 41 cards without an ace instead of the normal 50, which people are using for their PokerStove calculations. So we can use this for a pretty reasonable approximation of the situation and figure out that our opponent will have an ace in the big blind 4/40.5 + (36/40.5)(3/39.5) instead of 4/50 + (46/50)(3/49) which is approximately .166 versus .136. So your opponent will wind up with at least one ace in his hand around 20 percent more often.

5. You may want to avoid pushing all your small edges if there are bigger ones available because your opponents are weaker players than you are. Don’t bet your whole tournament on this small edge.

6. These are all chip equity considerations that are fine for side games, but in a tournament, chips are worth more per unit when you are the shorter stack. Both mathematically and psychologically, the equation changes depending upon which blind has the other covered. You can shove any two cards against many opponents when they are the shorter stack and be +EV because people are averse to getting busted.

7. So how should you play this hand? Against normal passive opponents, ones against whom you may be able to shove any two cards profitably and who won’t shove against you with unexpected hands if you make your normal raise, I think it is more +EV to make your normal raise and fold to a shove.

8. However, right before the tournament bubble or a large pay jump, you may want to shove if you are the bigger stack but fold if you are the shorter stack.

9. Another benefit to folding is that you are about to get six or seven hands where you don’t have to put blinds in, and for the first few, you will have good position.

10. There are some opponents who will almost always raise if I limp there as the shorter stack. I will make more off them by limping and shoving after they raise.

11. The times you shove when effectively playing for 20 big blinds, you should do it for poker reasons. If you are against a tough, aggressive opponent who is on the shorter stack, and one who may shove on us with an ace and a small kicker if we make a normal raise, but will fold that hand against a shove out of fear of domination or facing a middle pair, then we can profitably shove because of the hands we will bluff out.

12. Similarly, here’s another poker situation where shoving may be correct: If your opponent isn’t aware that you are shoving this light, he will play incorrectly against you. But you probably shouldn’t shove against players who are aware of your tactics and won’t throw away a weak ace.

13. Many of us move all in with less than 10 big blinds, except when we have a big pair. Against strong opponents who are familiar with our game, we keep them off-balance by betting different hands similarly. Therefore we look for ways to balance these strong hands where we don’t shove with weaker ones. It will often look stronger in the flow that has been established if you make a normal raise with K-8 instead of shoving.

In summary, in many instances, people are fooling themselves thinking these calculations are important. The players who do well are those who make good judgments and use intelligent bet-sizing. The EV that players generate from making these mathematical calculations and figuring out these ranges is small and not necessarily positive. The poker considerations usually override whatever they may come up with.

Barry Greenstein is a member of Team PokerStars Pro and one of the founders of PokerRoad.com, where he frequently provides audio, video, and written blogs. He has won three WSOP bracelets, two WPT titles, and has career tournament earnings of more than $7-million.