MDF vs ICM: Rethinking Bluffing & Defense Strategies in MTTs

Unlike in Chip EV, ICM spots are not zero-sum between the players involved. A big confrontation is bad for both of them, because someone is going to lose something (the last 10bb of their stack) more valuable than what the other wins (another 10bb added to an already above-average stack).

If the loser loses more than the winner wins, what happens to the rest of that value?

It’s distributed to the other players in the tournament, especially the short stacks who are sweating the bubble. There is some raw intuition around this even amongst unstudied players. A player losing the last of their chips on the bubble of a major tournament is often met with cheers, because it means everyone else has just secured a min-cash.

This is why we see the counterintuitive equilibrium of BB calling less often on the bubble even though BTN bluffs more often. In the game of ICM chicken, a big collision is bad for both players, especially when the last of their chips are involved. The aggressor bluffs more often because they expect their opponent to fold more often. Bluffing often results in them winning a big pot without that disastrous confrontation.

The defender, however, folds more often even when they know the aggressor is bluffing more often. Once the bet is out there, the only way to avoid a collision is to fold. The collision would be so severe that they are incentivized to avoid it even though they would often win a large (but still not worth it) pot by calling.

With that in mind, let’s see what happens when we give the aggressor a choice of bet sizes:

In a Chip EV context, the player with the polarized range would prefer to bet as large as possible, even if that meant shoving for one million times the pot. As long as they didn’t run out of hands to bluff with—which they couldn’t in this scenario, because their bluffing frequency should never exceed 50% no matter how large they bet—a bigger bet just means more unexploitable bluffing. With a sufficiently large bet size, they essentially capture the entire pot.

When the polarized aggressor’s risk premium is high, they perform best by holding on to the last of their chips.

Winning an extra big blind with their value-bets isn’t nearly as good as losing the last of their chips on a bluff is bad, so they take a slightly more conservative approach in an ICM context, leaving themselves room to hopefully fold into the money even if their bluff fails. Or, if value-betting, they represent that they are hedging against a failed bluff by doing the same.

Note that they are still quite aggressive with the sizing, preferring to bet 80–90% of the remaining stack. Because the last of their chips are the most valuable, those are the only ones they really care about holding onto. The rest they’d rather invest in the bet, as a larger bet facilitates more bluffs and bigger wins when value-bets are called.

To be clear, this is a different phenomenon from other not-quite-all-in bets, which you may see at any stage of the tournament. While there is always some ICM effect in a tournament, the main reason to leave a few chips behind earlier in the tournament is to retain the ability, in the event that you lose the pot, to invest those chips on the next hand getting amazing odds thanks to the blinds and antes. That’s not the effect we’re seeing here, as this sim does not incorporate any future game considerations.

Here is BTN’s Chip EV strategy for this game when they are permitted a variety of bet sizes:

With QQ+, they shove. These hands are all unbeatable, though QQ will sometimes chop, as it is also in the defender’s range.

The 50% bet is for JJ. Though Jacks could profitably shove, the smaller bet size incentivizes BB to call with a wider range against which Jacks are a bigger favorite. Stronger hands never mix with this smaller bet size because the defender is not allowed to raise.

77–TT have too much equity to bluff but are not strong enough to value-bet (not for the bet sizes allowed in this sim, anyway).

Bluffs come from any combination of 44–66. These hands are all equally worthless and have no interaction with the defender’s range, so while the bluffing frequency is important, it doesn’t matter which combos are used for which bet size.

Inject ICM

Now, here’s the same game played on the bubble of a 1000-player tournament:

Even the nuts play better as a 90% pot-sized bet than a shove (100% pot), just as we saw in the ICM Clairvoyance game.

Unlike in the Chip EV sim, QQ prefers a smaller bet of 70% pot. The defender’s reduced incentive to catch bluffs means that Queens chops more often against the hands that call a shove. 70% pot still gets big value while incentivizing more calls from worse.

JJ also downsizes, betting 30% rather than 50% pot for the same reason.

Bluffs still slot equally well into any of the bet sizes. The overall bluffing frequency is higher because, just as we saw in the original clairvoyance game, this is necessary to make BB indifferent to bluff-catching on the bubble.

Bluff-catching gets increasingly undesirable as the bet size gets larger.

This is why the difference between BTN’s bluffing frequency on the bubble and in Chip EV grows disproportionately with bet size as well.

Conclusion

ICM changes incentives around bluffing and bluff-catching, which changes optimal bluffing and bluff-catching frequencies. Intuition derived from MDF and Chip EV simulations will be an unreliable guide, when risk premiums are high! Instead, adjust by considering the following heuristics: