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Expected Value — RISK LESS CHIPS
Fold EV = (% opponent folds) * (pot size when they fold)
Call EV = (% opponent calls) * ((% hero wins)(pot size + bet size) – (% hero loses)(bet size))
Total EV = Fold EV + Call EV
In the chart below, I’ve set-up two constants:
— (pot size = 100)
— (% opponent calls = 100%, they never fold)
The values represent the Total EV when changing two variables:
— % hero wins (10% – 40%)
— % bet size (10% – 100%)
Example:
If we bet $50 into $100 with only 10% equity against an opponent that calls 100% of the time, then we have 0 fold EV and some call EV.
According to the graph, the intersections with the x-axis represent break-even spots.
- With 10% equity, you can bet about 10% of the pot.
- With 20% equity, you can bet about 33% of the pot.
- With 30% equity, you can bet about 70% of the pot.
In general, betting smaller has more EV than making larger bets. This is because you are risking less money with the same equity to win.
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2 Replies
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So, in this example, we are assuming they will always call so that makes a lot of sense that as long as we have some equity we can bet, and that bet size is in proportion to our perceived equity. Love this. Gets interesting as the call % becomes dynamic as a function of the bet size.
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Our opponent never folds and always calls….
This is a worst-case scenario when we are bluffing or semi-bluffing.
Which is why I wanted to take a closer look at it!!!
The trends I’ve found are:
— as you increase your equity (%win), the call EV is only slightly affected by the amount being risked (bet %). At 40% win, the slope is small as you modify the bet % which means Call EV is changing very little. At 10% win, the slope is large and negative which means that risking more (large bet) is worse than risking less (small bet).
— when they never fold, betting less will increase your overall call EV when you’re semi-bluffing. This is because you’re risking less to hopefully hit your card and win X% of the time.
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