Poker and the invisible ante

This article is an extension of my blog “Poker: Fowlds folds” (https://mikefowlds.medium.com/poker-fowlds-folds-53d9ec7ef64a) where I introduced David Sklansky’s ‘invisible ante’. I argued there for playing tighter preflop but, I regret to report, my home game hasn't taken this advice on board …

Sklansky characterises all poker as a “struggle for the antes”. He doesn’t think Texas no limit holdem (TNLH) is a successful game design sans antes. There’s just not enough incentive to enter the pot. Computer solvers bear this out by proposing raise first in (RFI) percentages of <20%. This is the requirement just to raise to 2.5 big blinds (BB), mind you. The requirement to raise to 3 BB (or 5, or 7 . .), is presumably a tighter range still. That’s a lot of sitting around waiting for a good hand . . .

Fortunately, recreational players save the game and the boredom by acting as if there is a gentleman’s agreement that the pot contains ‘invisible antes’, so that they voluntarily enter the pot (VPIP) more than is theoretically sound.

Requiring players to post an ante (e.g. 12.5% of a BB per player) would provide additional incentive to contest the pot. Again, computer solvers bear this out. In tournaments it is usual to have both blinds and antes. For example, in a 6-max cash game a computer would open under the gun to 2.5 BB with 17–18% of its hands. However, in a tournament with an additional 1BB in antes in the middle, the optimal opening percentage in corresponding position increases to 22–23%.

Note that the reason for having antes in tournaments is to force more money into the pot so that the tournament finishes in a reasonable timeframe, rather than because of the Sklansky argument.

As an aside, the 2nd most popular version of poker, pot limit Omaha (PLO) requires the more complicated structure of only allowing pot limit raises, because the game just isn’t very interesting if bets had no limits. The basic issue is that equities run closer together, so players would be incentivised to go all-in pre flop, or on the flop, to preserve their equity. It becomes a bingo game. In this situation the rules were adjusted.

So why is the betting structure not adjusted to make antes more common in cash games?

For one thing, antes are a bit finicky, especially in the past when every player had to post a small ante on every hand. Nowadays the player in big blind position will post a (much larger) ante on behalf of all the players. As a recent home tournament attests, it is still slightly more complicated to remember that the big blind’s outlay goes partially towards dead money and partially as a forced bet.

If there are no blinds or antes the theory assumes a death spiral to only AAs being opened. But this also assumes that the player pool adjusts to exploit each others play, a very big if! See, for example https://mikefowlds.medium.com/poker-mbs-signature-move-bc118d837190 where one player occasionally opens 100BB with 100% of his range i.e. sight unseen. In game theory language this is highly ‘exploitable’, yet still he does it :)

In poker stream events such as “Poker night at the lodge” the professional players are instructed to give some action in order to get a seat at the table. If they VPIPed 10% they wouldn’t be invited back, even though this would be the best strategy with tens of thousands of dollars on the line. If everyone is playing loosely the game ‘works’ without antes (by which I mean 30%-35% VPIP percentages, not the 80% my home poker group plays).

In addition to blinds & antes, the opening percentage also depends on the casino rake and propensity of opponents to 3-bet. With a casino rake (which is often only charged postflop) ranges need to tighten up a bit. On the other hand, if it’s assumed that the players in the blinds won’t 3-bet as much as they should per GTO, then ranges can widen. Finally, if there are antes and a straddle (viz. another player forced to make a 2BB blind bet), then the optimal opening frequency may go up from the 17% level we saw before to, say, 25%

Much more important than the variables mentioned above is position. If it folds around to the button, even the tight playing solver is incentivised to open up to half of all hands. Playing from the button we are less likely to be 3-bet and we don’t want the blinds to see a cheap / free flop.

The real World

But what to do when opponents are opening to 5BB with 80% of their range? Sitting in HJ position, the computer might assume that the LJ was opening with 17.6% of hands, so would raise with 8.9% of hands and fold the rest. It’s fair to assume we can call or raise a bit wider than this! But how loose can we be?

Standard advice (which I don’t necessary follow) is NEVER to limp in for one BB (though it’s more acceptable to call an earlier limp), and NEVER to cold call a raise (i.e. it’s 3 bet or fold) unless we’re positioned in the cut off, button or the blinds. This has the added benefit of automatically tightening our range. Limping and calling are excuses for playing medium strength hands, which as a general rule underperform their equity.

Even in the loosest games I do think we should pick hands that have a little something. In each case here the equity I give is against one random hand i.e. against an opponent with 100% range. Pocket pairs are either good in the own right (AA) or actually have worse equity than a random hand (22) but can flop trips. Pocket pairs make up 78 combinations, or 6% of all starting hands, and collectively have 69% equity.

Suited broadways (ATs+) make up another 40 combos (3.0%), with 63% equity. Next we might consider playing the remaining Ax suited (32 combos, or 2.4%) with 60% equity.

Unsuited broadway hands and Ax unsuited only have 2–3% less equity (against 1 opponent) than their suited cousins, but have much less playability. Neverthless, I’m not folding a hand with an Ace in it against the loosest opponents. Adding in suit connectors (eg 65 of diamonds) would bring us up to about 30% of all starting hands.

If we’re in late position then hands like Kx suited, suited gappers (86 of diamonds) and unsuited gappers all have a little something and translate to something like half of all opening hands.

The invisible ante

So Sklansky concluded that NLHE without antes doesn’t work as a game. And yet it does. Maybe consider folding those 93o hands pre-flop, otherwise good luck at at the tables!