We play poker for a few reasons, two of the most important being that it’s a great form of entertainment, and that in an ideal world we might even win money in the process. What other hobbies and recreational sports and pastimes afford us that potential luxury?
So, on reading the title of this article some players might ask ‘Why should we bother with a formula about breaking even?’ which, of course, is a perfectly valid point. If our ultimate goal when sitting down to play is to make a profit, it might indeed seem a little unnecessary – and even rather unambitious – to go to the trouble of working out how this or that play might lead us to break even.
However, establishing this information is in fact very useful as it helps form a benchmark that becomes a reliable foundation on which to make decisions and formulate plans. Knowing that if a specific play has a certain success rate we’ll break even (i.e. the Expected Value is zero) means that, over time, we can expect to make a loss if the play works less, and a profit if it works more.
The simple formula we can use is…
Breakeven % = $Risk/($Risk + $Reward)
…where $Risk is the size the bet, and $Reward is the size of the target pot (N.B. before the bet). Here’s an example:
Pot size before bet is $30; Bet sizes are $10, $20, $30. Let’s look at the implications of these bet sizes in relation to the breakeven percentage by slotting in the values.
10/(10+30) = 10/40 = 25%
This means we’re risking $10 to win a $30 pot, and the breakeven percentage is 25% – so when we bet 1/3 of the pot we’ll break even if we succeed once from four attempts.
20/(20+30) = 20/50 = 40%
This translates to a breakeven percentage of 40% when we risk 2/3 of the pot.
30/(30+30) = 30/60 = 50%
Thus, a pot-sized bet equates to a 50% breakeven percentage.
These are interesting numbers and will come in very handy indeed given the frequency with which we’re presented with this scenario. Furthermore, 1/3, 2/3, and ‘pot’ are typical bet sizes when we’re trying to make a play for the pot, so automatically knowing in advance exactly what the breakeven percentage is for each of these plays helps us weigh up whether or not we should take a chance.
In practical terms, using breakeven percentages allows us – regardless of the cards we’re holding – to put opponents on a hand and execute a bluff, sizing the bet according to our expectation of their folding in relation to the breakeven percentage. When relevant factors strongly suggest that the opposition’s fold expectancy is higher than the breakeven percentage, we have an effective, profitable strategy in place.
This is what successful bluffing is all about – that it works sufficiently often to generate a profit. If we bet $5 into a $20 pot, the breakeven percentage is only 20% and this play is +EV if our opponent folds just 25% of the time. The higher our estimate of an opponent’s folding frequency, the more we should be looking to engineer a bluff and finding an appropriately sized bet. Only by constantly keeping up with breakeven percentages can we get into the habit of picking up pots even when we have cards that wouldn’t in themselves justify a bet.