I have received several inquiries and commentaries regarding the “offer you can’t refuse” (OYCR) mentioned in my recent articles on poker tournament strategy. The OYCR refers to the special rebuy offer made at the end of the rebuy period at certain poker tournaments. For example, let’s say that the initial buy-in to a local poker tournament, which guarantees a $1000 first prize, is five or ten dollars, for which you receive five hundred dollars in tournament chips. If you lose your initial stake during the first hour, you may rebuy an additional five hundred dollars of tournament chips for ten dollars. After the first hour or so comes a point in time when the rebuy period ends (called “the break” since there often is a five or ten minute break).

At this point you are given the OYCR, one very special last chance to rebuy (regardless of how many chips you might have) where twenty dollars gets you twelve hundred(!) in tournament chips or forty dollars gets you three thousand dollars(!!) in tournament chips! Compared to the earlier rebuy rates, this is clearly a super bargain! Can you say no to such an offer?

If you do not have a lot of chips at the break, and if you want to be in serious contention to win this tournament, you normally accept this OYCR rebuy offer. Since many other players will also be accepting this offer, this OYCR greatly dilutes most of what has happened earlier. For example, just before the break there would be a significant difference between two players, one with two hundred dollars and one with nine hundred dollars in tournament chips. But after the OYCR, the difference between the same two players, who now have thirty two hundred and thirty nine hundred dollars, is minimal. One way of looking at it is that the tournament practically starts anew at this point.

Note that for the great majority of players the tournament buy-in is not really the five or ten dollar initial buy-in. For most serious participants who want to go after the $1000 first prize, the tournament realistically costs $45, or $55, or more, depending on how many rebuys are burned up in reaching the break. But if a player reaches the break with a lot of chips, should he rebuy? This gives rise to an interesting question, just how many chips are enough to reject the OYCR rebuy?

It seems clear intuitively that if you already have something approaching five times the chips available from the OYCR rebuy, investing the additional $40 to get twenty percent or fewer additional chips is probably unwarrented.

I have heard various experienced tournament players give their “gut” opinion on this subject, and the consensus seems to be that if you have around twice the OYCR rebuy amount you should save the $40. There are some who think you should always rebuy to “preserve your advantage”.

It is obviously impossible to calculate an exact answer since there are a number of variables which can only be roughly estimated. The following is my abbreviated attempt at an analytic solution, making the indicated simplifications and assumptions. I will welcome other thoughts on the subject.

First, how much do you expect to win, when you win? It would clearly be wrong to base your estimates on either winning the $1000 first prize or not, since there are usually two or more lesser prizes. My opinion is that the best single number to use for expected winnings is the average of first through third prizes, ie. the sum of first, second and third prizes divided by three. This is actually a fairly realistic number, since there is often a settlement when the tournament gets down to three players. So in the typical tournament described above, with $1000, $500 and $300 as the first three prizes, if you make it to the final three with average chips, your expected win should be around $600.

Next, how often do you expect to be in the top three if you have made the OYCR rebuy? Using the above conditions, let’s assume that there now are five tables left in the event, and that about half the players make the OYCR rebuy, say about 25 players. Assume that of the other (no OYCR rebuy) players, only about five have good prospects of finishing in the top three. Of this group of around 30 players some will have better chances than others (including you).

But assuming that your playing skills are somewhat above average (the fact that you are reading this magazine tends to indicate this), then you should be in the top three around three out of thirty times, or about one out of ten. Thus the expected value of the tournament to you, an above average player, at this point should be around one tenth of $600 or around $60. With a few more chips or with a higher skill level your expected value would be somewhat higher.

Finally, how often will you be in the top three without the OYCR rebuy? Obviously your chances depend on how many chips you now hold. It may be possible to develop a relational (but very rough) formula for estimating win prospects from chips held (using current blinds, number of players left, average chips held, etc.). But a simpler approach is to estimate your chances if you had around eighty percent of the OYCR amount, which in the above example is $2400. With $2400 you would have about HALF the chances of finishing in the top three as you would if you made the OYCR rebuy (assuming additional chips have a slightly decreasing value).

Since your expected value with $5400 should be around $70 or $80, then your expected value with $2400 should be around $35 or $40. Thus, for the given example conditions, $2400 happens to be right around the break even point for accepting or refusing the OYCR rebuy.

Thus, the OYCR break even point may well be substantially lower than many players think, at least for a “somewhat above average” skill level (note 3 out of 30 assumption above). My best guess is that the additional “playability” of the extra chips from the OYCR rebuy in highly skilled hands would raise the break even point to slightly above the OYCR rebuy amount.