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Cash Equity at the Final Table by Rafe Furst

While playing the final table of the $1,500 Pot-Limit Hold 'em event, I found myself in a difficult spot when we were down to four-handed play. I was in the big blind and Rizen, a tough, respected online tournament pro, was in the small blind. It was folded to Rizen who announced that he would raise the pot. With blinds of 15K/30K, his raise made it 90K to me.

At the time, I had about 400K in chips; Rizen had 750k and the other two players had about 250K each.

I looked at my cards and found A 8, a pretty solid holding in short-handed play. I decided to raise the size of the pot. My total bet was 180. Rizen immediately re-raised, forcing me all-in.

The pot contained 580,000 (400,000 from Rizen, 180,000 from me) and I had 220,000 remaining. I was getting nearly 3 to 1 on my money, so this looked like an automatic call. I needed to win the pot only about 27 percent of the time to justify a call.

Against a big pocket pair (other than aces), my A-8 suited would win about 32 percent of the time. Against a bigger ace (A-K, A-Q, etc), my A-8 suited would win about 30 percent of the time. There was also a non-zero (though small) chance I was up against a small pocket pair and would win about 50 percent of the time.

So this was almost a zero-equity chip decision. That is, folding and calling would have pretty much same result over the long term. To find the correct action, I had to look beyond pot odds and consider (a) how this hand would affect my cash equity for the tournament (i.e., which action would maximize my expected cash payout) and (b) how this hand would affect my chances of winning the tournament.

There were two factors I looked at when considering my cash equity:

  1. Each chip in a short stack is more valuable in terms of cash-equity than each chip in a large stack. By calling in this situation I would have been risking chips of great value to pick up chips of lesser value.
  2. Folding removes any chance of busting. By folding, I would give my opponents a chance to bust on subsequent hands, which would move me up to a bigger payday.

After looking at these factors, it seemed that folding was the clear choice. But still, I had to think about how folding would effect my ability to win the bracelet - which was my primary concern. Would I be putting myself out of the running by giving up on so many chips? Not really.

When there are more than two players remaining, each additional chip you accumulate has a lesser impact on your ability to win the tournament. So when the chip-equity decision is a wash, you are better off folding than you are trying to accumulate more chips.

If you ever find yourself in a similar situation, you should also keep in mind that there's a big difference between moving all-in and calling all-in. When you move in, you can win the pot by forcing a fold. When you call, this obviously isn't possible.

I decided to fold and wait for a better spot, and I'm very glad that I did.

Rafe Furst

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