What changes with three or more players

What changes when three or more players see the flop: the job of defending is shared, bluffs work less and strong hands count for more.

Rail's flop library is heads-up. Multiway flops are read by the analysis' heuristic and the minimum-defence split, with facts and flags but no solver grade (a call or fold facing a bet gets an approximate one), so this lesson's practice is arithmetic and your own hands.

In this lesson

Explain why each extra opponent makes a strong hand out there more likely.
Share the job of defending with the other players still in the hand.
Bet tighter and smaller, and bluff less often.
Prefer hands that can make the nuts over dominated draws.
Avoid slowplays that let several opponents catch up.

Read first: Which hands bet and which check, Defending against a flop bet · Advice, not a lock: every lesson opens.

Concepts used: Multiway pots

Every extra player is another chance of a strong hand

Heads-up, a bluff works if one player folds. With two opponents both must fold; with three, all three. If each folds half the time on their own, both fold 0.5 × 0.5 = 25% of the time and all three only 12.5%.

The same arithmetic runs the other way for strong hands. The more players see the flop, the more likely someone holds two pair, a set or a strong draw, and the more a medium hand is up against.

Pot before the bet9 bb

Bet3 bb · 33.3% of the pot

Opponents the bet goes into2 opponents

How often each one folds50%

Everyone folds: 25%
Folds the bet needs (alpha): 25%
EV of a pure bluff: 0 bbBreak-even
Heads-up defence (MDF): 75%
Each defender needs to continue: 50%

A third-pot bet into two players who each fold half the time. Add a third opponent and watch the folds you can count on shrink.

Defence is shared

Minimum defence is about the whole table, not each player. Against a third-pot bet, 25% folds by everyone together is the most the defenders can allow. With two of them, each continuing with half its range already makes everyone-folds 0.5 × 0.5 = 25%: each defends 50%, where a lone defender would need 75%.

What it changes

Bluff less, and with hands that can still improve.
Value-bet a little tighter and a little smaller.
Prefer hands that make the nuts over draws to second-best hands.
Slowplay less: every free card is a free card for several players.

Rail's flop library is heads-up. Multiway flops are read by the analysis' heuristic and the MDF split, with facts and flags but no solver grade; this lesson's practice is the arithmetic and your own flagged hands.

Rules of thumb

Multiply the folds: a bluff needs every opponent to fold.
Share the defence: each player defends less than heads-up.
Bet tighter and smaller; slowplay less.
Prefer draws to the nuts over draws to second best.

When they break

Passive multiway tables that call too much reward thin value and punish bluffs even more.
With a short stack behind, commitment comes faster, multiway or not.

Example hands

Examples come from two places only: your own analysed hands in this lesson's spots, and a hand Rail deals and grades itself. Never a hand from outside Rail.

From your own hands

Practice

The lesson is mastered when every exercise below that Rail can grade is passed. Missed items come back later as review cards.

Exercise 1

Pass: 5 of 6 right

Six sums: how often everyone folds, and how much each player must defend.

Exercise 2

Optional

Your own hands flagged for bluffing into a crowd, slowplaying multiway or calling with a dominated draw.