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Why Make a Deal?

Reduce variance by making a deal

by Michael Wiesenberg |  Published: Dec 06, 2006

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Recently I wrote about making fair deals in tournaments when only a few players remain. Deals can favor those with the most chips and those with short stacks. Whether you opt to partake in an offered deal - or offer one yourself - is, of course, your own choice. If a deal is offered to you and you don't like it, you can always refuse to deal. In fact, some players are known for refusing ever to participate in any deals.

If you participate in a deal once, though, you probably ought to at least be willing to negotiate when any subsequent deal is offered. To agree to one deal and turn down the next implies that you think the person or persons offering the next deal are not worthy of your consideration. A spurned offerer might well think, "Michael took part in a deal just last week with Zod. Why won't he deal with me? He must think I don't play nearly as well as Zod." So, be consistent.

Of course, a reason to turn down a deal could always be, "I don't deal until it's down to the final two" (or three, or four, or whatever). It's difficult to ascertain what is a fair deal for more than two players. I presented two formulas, which are more or less near the extreme ends of the fairness spectrum. The Burns-Landrum estimator favors the small stacks, and probably comes close to overall expectation. For example, four players remain at a final table, with payouts of $12,500, $8,500, $5,500, and $3,500, producing a prize pool of $30,000. Their current chip totals are $90,000, $80,000, $42,000, and $22,000. Burns-Landrum would award $8,397, $8,113, $7,030, and $6,460. (You can find the math in "Let's Make a (Fair) Deal" in Vol. 19/No. 19, Sept. 27, 2006.) This means that if the identical situation came up thousands of times, with no deal being made, the four players would probably average close to those amounts. On the other hand, the "percentage of the remainder" estimator would give the players $9,660, $8,940, $6,380, and $5,020. That's quite a difference, and probably unfair to the two short stacks. (You can find the math in "Tournament Deals" in Vol. 19/No. 20, Oct. 11, 2006.) In a similar long run, again with no deal being made, the four players would probably not average close to those amounts.

Armed with the math, you can decide whether to take a deal and what to counter if one is offered.

Now, as long as the deal seems fair, why would you want to take it? Why wouldn't you prefer to take a chance on a big payoff? In many smaller tournaments, the blinds and antes are so high in relation to the players' stacks that the situation really comes close to what many call a crapshoot. Conventional wisdom has it that, in a no-limit hold'em game, when you have less than 20 times the big blind, you need to consider making a move soon, lest those blinds and antes just eat you up. And when you're down to 10 times the big blind or less, you probably want to pick the next decent starting hand and go all in. You can't wait for big pairs or large coordinated cards. Any ace, any pair, K-Q, Q-J, maybe any king or queen, and even lesser holdings if the table is tight, and it's time to move in. This takes much of the play out of the game. Knowing that short-stacked players are likely to go all in with less-than-premium cards, others will lower their calling requirements. This results in many coin-flip matchups. And even when the actual matchup isn't that close (such as one hand dominating another, like Q-J versus Q-10), it's still likely to be a coin flip as to which player holds the better hand. That is, a player willing to call an all-in bet with Q-J is probably also willing to call with Q-10, so it's pure chance as to who holds the better hand. I've seen many final tables at which the big stack might have 25 times the big blind, the next player 15, another 10, and the short stack eight. All that short stack needs to do is double up once against the big stack, and everyone is close in stack size and also near the point of needing to make a move soon. It's practically anyone's tournament at that point. Many players want to reduce variance by going for a deal in such a situation.

If you play a lot of tournaments, you'd probably be less likely to want to make a deal, because your playing time will come reasonably close to being "the long run." The longer the run, the smaller the part variance plays. But if you don't play that many tournaments, you might well be tempted by a deal offer - particularly when you have a short stack and the offer is close to the result produced by the Burns-Landrum estimator or when you have a big stack and the offer is close to the result produced by the "percentage of the remainder" estimator. spade

Michael Wiesenberg's The Ultimate Casino Guide, published by Sourcebooks, is available at fine bookstores and at Amazon.com and other online book purveyors. Send praise, protests, and propositions for presentations to [email protected].