# Shoving mathematics

The way it works in poker, once we believe we are making the correct play, it is hard to convince ourselves that anything other than bad luck is the explanation for the times it doesn’t work. And when it does work, we have the positive reinforcement to keep playing incorrectly.

I was listening to Jimmy Fricke mention that Dan Kelly figured out that it is +EV to shove with 22 big blinds with K8 offsuit, when in the small blind and everyone 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.

As is often the case when I read mathematics applied to poker, the problem is often incorrectly solved and it’s the wrong problem anyway. I will post my top ten reasons that I have objections in this case. Hopefully Dan and Jimmy will have some comments and counterpoints in this thread.

Top Ten Problems with these kinds of shoving calculations (some are related, so I actually have 13 items)

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 K8 out of the deck. In a nine-handed game, the big blind is stronger, on average, than it would be in a head 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 these calculations are right for when we are playing head 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 head up.

3. These calculations and plays are dependent on the ante structure. If someone wanted to run a simulation they should use 1/5 ratio for ante to small blind for online tournaments (that’s what PokerStars uses for later stages) or 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 hands will be stronger than random. As I showed with a simulation, 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 blind in a nine-handed game.

http://barrygreenstein.com/aces.txt

http://barrygreenstein.com/out-aces.htm

This is approximately the number you would get dealing with 4 aces in a deck of between 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 more than 20% 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 which are fine for side games, but in a tournament, chips are worth more per unit when you are the shorter stack. They are two very different problems when we are the one with 20 BB versus when our opponent is and we have him well covered, not just mathematically but also psychologically. You can shove any two cards against many opponents when they are the shorter stack and be +EV when you have them well covered because people are averse to going busted.

7. So how should you play this hand? Against normal passive opponents, ones that you may be able to shove any two cards profitably with under 20BB 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 as the bigger stack but if you are the shorter stack it may be right to fold.

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 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 20BB, 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 Ax with a small kicker if we make a normal raise, but will fold this hand 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, 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 10BB, 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 K8 instead of shoving.

Summary: In many instances, people are fooling themselves thinking these calculations are important. The ones who do well are good players who make good judgments and have good betsizing. The EV they generate from figuring out these ranges is small and not necessarily positive. The poker considerations usually override whatever they may come up with.

Barry