Full Tilt has introduced yet another innovation to online poker: multientry tournaments. These tournaments give you the option to play anywhere from 1 to (typically) 4 entries in the same tournament. If you choose to play multiple entries, you may play multiple entries at the same time, or you may use your multiple entries for reentries during the late registration period. With multientries now available in many Full Tilt tournaments, should you ever take multiple simultaneous entries or be willing to pay for a reentry?

From the sole perspective of optimizing your ROI, you should never play multiple entries at the same time. Your ROI in tournaments is larerly dependent on your big money finishes. With 4 entries, your best possible finish is 1st, 10th, 19th, 28th. Because your 2nd, 3rd, and 4th entries have no shot of a first place finish (given that your first entry is a final table), your expected ROI on those additional entries is less. The smaller the field size is, the more this effect is….beacuse the probability of 4 extremely high finishes increases. In the most extreme example, taking 4 entries in a tournament with only 36 entries is financial suicide.

Real world playing examples are always fun to analyze. Since 36-player tournaments aren’t common, let’s take $10+$1 45-man SNGs at Full Tilt. The payout structure for these tournaments is as follows:

1st: $171

2nd: $112.50

3rd: $72

4th: $45

5th: $27

6th: $22.50

These tournaments don’t allow multiple entries or reentries, but let’s suppose that they do. And let’s further suppose that your ROI playing a single entry in these tournaments is 25% - meaning that you make $2.50 per tournament. If when you finish in the money, you finish in each place with an equal probability, your ITM% needs to be about 16.7% to make $2.50 per tournament. Now, assume that you finish in each ITM place with the same probability when you take multiple entries. To make the same $2.50 per tournament, you need to finish in the money 62% of the time. Do the three extra entries give you enough of an edge to place in the money 62% of the time when only one of your entries can be at the final table? Probably not. It should be noted that the multiple entries would likely give you a finishing distribution weighted towards higher ITM finishes (assuming no other players are taking multiple entries). However, unless the multiple entries drastically increase your probability of finishing in 1st, 2nd, and 3rd, taking multiple entries will make it hard to make the same $2.50 per tournament that you would with a single entry.

Meanwhile, making $2.50 per tournament entry is *much* more difficult. To make $2.50 per tournament entry, you’d have to place in the money over 100% of the time if your probability of finishing in each ITM position is equal. Suppose that when you place ITM, you finish top 3 *every *time. To make $2.50 per tournament entry, you’d have to place in the top 3 45.6% of the time. Clearly, taking a single entry in 4 separate tournaments is better than taking 4 entries in the same tournament.

As the number of players in a tournament increases, the less pronounced this effect becomes. When you’re playing in tournaments with fields so large that the probability of merging stacks becomes negligible, your ROI take only a very small hit (i.e. you’re playing in tournaments that are large enough where playing multiple entries in one tournament is pretty much the same as player four separate tournaments). And since your goal should be optimizing your hourly win rate instead of optimizing your ROI, there’s a situation where taking multiple entries in a single tournament could be worthwhile: when there are no other tournaments of a comparable buy-in starting soon and the tournament offering multiple entries has a large field size.

(This paragraph contains some probabilities and combinitorics. If you don’t follow it all, don’t worry about it…just skim through it and get to the results that follow). To get an idea of the minimum field size required to be willing to take 4 entries, let’s assume that you have an equal probability of finishing in each place. Let X be the number of entrants in the tournament. The probability that all four entries get to the final three tables and a merge occurs is (27/X)^4. The probability that all four entries don’t get to the final three tables but 3 entries get to the final two tables (and a merge occurs) is 4((x-27)/x)(18/X)^3. The probability that all four entries don’t get to the final three tables, 3 entries don’t get to the final 2 tables, but 2 entries get to the final table (and a merge occurs) is (4 nCr 2)((x-18)/x)^2(9/X)^2. The total probability of a merge is therefore:

P(Merge) = (27/X)^4 + 4((x-27)/x)(18/X)^3 + (4 nCr 2)((x-18)/x)^2(9/X)^2

Below are values of P(Merge) for various values of X:

X = 100; P(Merge) = 5.502%

X = 200; P(Merge) = 1.292%

X = 300; P(Merge) = 0.562%

X = 400; P(Merge) = 0.313%

X = 500; P(Merge) = 0.199%

X = 600; P(Merge) = 0.138%

X = 700; P(Merge) = 0.101%

X = 800; P(Merge) = 0.077%

X = 900; P(Merge) = 0.061%

X = 1000; P(Merge) = 0.049%

The highest probability of merging that you should be willing to accept is unknown; however, the minimum number of entrants required for multientries to be acceptable (in the absence of other tournaments with a similar buy-in) is probably somewhere around 500.

Now that you know when to take multiple entries and when not to take multiple entries, there’s one final consideration to be had. Suppose that you don’t take multiple entries off the bat. Should you take a reentry if you’re knocked out during the late registration period? Since there’s no difference between reentering a tournament and simply entering a tournament late, this question really boils down to whether you should take late registrations. I’ll be covering late registrations in an upcoming blog post.

May Your EV Always be Positive!

The Tsunami

Tags: Full Tilt, hourly, late reg, late registration, multientry, reentry, ROI