Why You Can’t Beat Low-limit Games: Maximizing Bonus Profits, Part II

Part I recommended maximizing your total EV (expected value). You must often sacrifice one type of EV to gain more of another type. For example, your bet may have negative Pot-EV, but you may gain more Bonus-EV. Or the game is negative EV, but the bonuses make it worth playing.

Because they don’t calculate their total EV, some players give up too much of one type, hoping to win another type. They play aces passively, giving up Pot-EV, hoping for an Aces Cracked bonus. With a small pot and large bonus, it’s a good move. But, if several players have limped, passively, playing aces sacrifices too much Pot-EV.

Some players call raises with small pairs and suited connectors, hoping to win a high-hand bonus. Unless the bonus is very large, they’re essentially buying overpriced lottery tickets.

Matt Lessinger reported a spectacular example of ignoring Total-EV. He was playing $1-$2 limit hold’em on Paradise Poker because it was giving enormous bonuses for its 100 millionth hand: $500 to everyone at the table and $10,000 to the winning hand. Matt’s table was the lucky winner, so everyone got $500, but two players folded preflop!! Because the Bonus-EV for winning the hand was enormous, they should have called with any two cards.

Types of Bonus-EV

Freeroll Tournaments have Hourly-EV: It’s the amount gained per hour of play. Aces cracked and quads or better have Hand-EV: It’s the value of the bonus times the probability of winning it.

Calculating Hourly-EV

Let’s say that the freeroll prize pool is $15,000, you need 50 hours, and expect 50 players. Your basic Tournament-EV is $300 ($15,000/50), so it’s $6 (($300/50) per hour played. If you’re significantly stronger or weaker than average, adjust up or down.

WARNING: Most people overestimate their own skills and underestimate their opponents.
High Hand per Hour Bonuses (HHH) are partly Hourly-EV. Divide the amount of money paid per hour by the number of players. If 20 people are playing and $300 will be paid in three hours, your EV for three hours is $15, or $5 per hour.

Adjust that number for your style. Tight players get fewer HHH-Bonuses than loose ones. So decrease or increase your EV estimate if you’re tighter or looser than your opponents.
To get your Total-EV, add or subtract what you expect to win in the game itself. If the game is tough, you may lose more than you gain from the bonuses. If loose play will cost you more than you gain from winning more HHH bonuses, don’t loosen up too much.

Calculating Hand-EV

Calculations can be difficult because you usually can’t be sure that you’ll win a bonus even if you make your hand. In addition, trying for a bonus can make you give up too much Pot-EV. Start your calculations by answering three questions:

1. What does it cost?
2. How much is the bonus?
3. What’s the probability of getting the bonus?

Let’s work with HHH because these bonuses are popular and fairly easy to calculate. To make calculations even simpler, assume it’s the last hand of the hour, and only one table is playing. That situation greatly reduces the probability that you make a qualifying hand, but someone makes a higher one.

If you have two suited cards that you would normally fold (such as J 6), you have about a six percent chance of making a flush. If that flush will win probably a $100 bonus, your Bonus-EV is about $6. If you’re playing $3-$6, it costs $6 to cold-call a raise. Since your Bonus-EV is about equal to your cost, you’re getting a nearly-free shot at the pot and should probably call. But don’t call without thinking. Consider two negative factors. Someone could three- and four-bet, and you could make your flush and lose to a bigger hand.

If the High Hand bonus is only $25, your Hand-EV is only about $1.50, so just fold that trash.

If it was the first hand of the hour, or if more tables were competing, your HHH-EV would be much less. You could make your flush, but someone could make a higher hand. So you should lower your Bonus-EV estimate and play more tightly.

Balance Pot-EV and Hand-EV

Balancing can be difficult. I’ll describe a good play and a bad mistake. The HHH was $100, and the hour was almost over. We were playing $2-$6 spread limit, and I was the button with 10-2 suited. One player limped, then I limped. The flop gave me only a back-door flush draw, and everyone checked.

The turn gave me a flush draw. Someone bet $3. If I called, the pot would be less than the $20 needed to qualify for the HHH bonus. The odds against making the flush were about 4:1, so a $3 raise would clearly be –EV for the pot. I’d get only even money if he called and had little or no fold equity.

But a raise would have substantial Bonus-EV. If I made the flush, I’d probably win the $100 bonus. It cost me $3 to get about $20 of Bonus-EV. I raised, made the flush, and bet on the river. Nobody called. Without raising on the turn, I wouldn’t have won the $100 bonus.

Now I’ll tell you about a dumb mistake. The HHH bonus was $200, I had aces and eights on the turn, the HHH was a sixes full house, there were two opponents, and the $30 pot qualified for the bonus. I bet, and both players folded. If I checked, I had about a nine percent chance of filling up and winning $200, so my Bonus-EV was about $18. Of course, a free card could have beaten me, but there were no dangerous draws. Since I gained little Pot-EV by betting, but lost $18 of Bonus-EV, I should have checked.

Slow Down

It takes time to calculate various types of EV, review the bonus rules and situation, and make the best decision. You can’t do it all without slowing down, but many players —including me—often act too quickly. If I had taken a few seconds to think, I wouldn’t have bet the turn. If those two players who folded preflop on Paradise Poker had thought at all, they certainly would have called.

When we act quickly, our focus is too narrow. We don’t see the big picture. So take a moment and ask, “What will I gain or lose by betting, calling, and so forth?” Unless you’re sure you fully understand the situation and are making the right decision, take a little extra time. ♠

Dr. Al ([email protected]) coaches only on psychology issues, such as controlling impulses and emotions, coping with losing streaks, and developing yourself. He’s published five poker books, five other books, and is David Sklansky’s co-author for DUCY?