What does pot-limit mean?

This is an explanation of bet size limits in pot limit poker.

In pot limit, as in all poker, you may fold, or call the previous bet -- which may be a forced blind, if there is no previous voluntary bet -- or you may raise. A raise, as in all poker, must be at least as large as the previous bet or raise. In pot limit, however, your raise may be no larger than the size of the pot after your call. If you are the opening bettor on a round for which no blinds are made, your bet can be no more than the size of the pot.

Say that the pot contains p units before a previous bettor bets (or blinds) b units. You wish to raise the maximum. What is the total amount that you should bet?

The size of the pot when it is your turn to act is p+b. Your action includes a call, making the pot p+2b, and thus the amount of your raise will be p+2b and your total bet will be p+3b. Therefore:

If you wish to raise the previous bettor (or big blind) the maximum amount, your total bet will be three times the previous bet plus the size of the pot before the previous bet was made. If you are the first to act on the first round, the size of the pot before the previous bet is the total of the small blind(s), and the previous bet is the big blind.

Sometimes the minimum betting unit is larger than the size of one or more blinds. E.g., it may be that only $5 chips play for betting, but one or more blinds are smaller than $5. In this case, the maximum initial bring-in is rounded to the betting unit.

Some people state the general rule that the maximum initial bring-in is "four times the big blind." This is correct only if the total of the small blinds, after rounding if appropriate, is equal to the big blind, and this is not always the case. E.g., in a tournament when the blinds are $100 and $200, the maximum bring-in is $700, not $800. The correct rule is "three times the big blind plus the total of the small blinds, rounded as appropriate."

Examples:

• 1, 2, and 5 blinds. 3 times 5 = 15; 15 + 1 + 2 = 18. Assuming that the minimum betting unit is 5, the maximum initial bring-in would be 18 rounded up to become 20 -- a raise of 15.
• With 1, 2, and 5 blinds, someone brings it in for 10. The maximum bet of the next to act would be 3 times 10 = 30, plus the total blinds of 7, rounded up to 40 -- a raise of 30.
• The pot contains, say, 1 unit. Suppose each successive bettor wishes to raise the maximum; how fast will the bets increase?

  size of pot before                   3 x previous bet
  previous bet         previous bet   + size of pot before
                                        previous bet
                                         = next bet
       1                   -                 1
       1                   1                 4
       2                   4                14
       6                  14                48
      20                  48               164
      68                 164               560
     232                 560              1912

So, if the initial pot size were $100, the seventh maniacal raiser would be making a total bet of $191,200. The action can escalate quickly.